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The complex behaviour of dynamical systems can be discovered through the study of observed scalar time series via reconstruction of a suitable state space. Reconstruction can readily be achieved thanks to Takens embedding theorem and further insights about a system can be found by constructing complex networks based on the proximity to each other of these reconstructed states. An example of such a proximity network is the so-called phase space network which is a type of recurrence network. The structure and properties of these networks, including small induced subgraphs within them, describe the spatial distribution of reconstructed states in a way different from, but related to, correlation dimension. Beyond the makeup of the reconstructed states the time structure inherent in the time series is typically ignored in any subsequent analysis of proximity networks. Here, we construct proximity networks but retain information about the time structure of the reconstructed state space trajectory and hence assign time as an attribute of the nodes of the network. We show that metrics capturing the change in structure of induced subgraphs along the trajectory can qualitatively track behavioural changes of the system dynamics subject to a bifurcation parameter in a manner similar to time-averaging estimation methods of dynamical invariants. Moreover, we demonstrate that these new methods retain the capability of monitoring system change in the case of irregularly sampled data. [ABSTRACT FROM AUTHOR]

Rationale: Evaluation of alternative radionuclides for use in prostate-specific membrane antigen (PSMA)-targeted radioligand therapy (RLT) is currently focusing on 161 Tb, which may provide advantages by emitting additional Auger and conversion electrons. In this pilot study, we present preliminary dosimetry data for [ 161 Tb]Tb-PSMA-617 RLT in a direct comparison with [ 177 Lu]Lu-PSMA-617. Method: Six patients with metastatic castration-resistant prostate cancer (mCRPC) underwent treatment with [ 177 Lu]Lu-PSMA-617 and subsequently - after inadequate response - with [ 161 Tb]Tb-PSMA-617. Whole-body planar and SPECT imaging-based dosimetry of organs at risk (kidneys and salivary glands) and tumor lesions were calculated using IDAC for 177 Lu and OLINDA/EXM for 161 Tb. The therapeutic index (TI) of mean tumor-absorbed doses over relevant organs at risk was calculated. Results: Mean absorbed doses to organs at risk of PSMA-RLT were slightly higher for [ 161 Tb]Tb-PSMA-617 compared to [ 177 Lu]Lu-PSMA-617 (kidneys: 0.643 ± 0.247 vs. 0.545 ± 0.231 Gy/GBq, factor 1.18; parotid gland: 0.367 ± 0.198 vs. 0.329 ± 0.180 Gy/GBq, factor 1.10), but markedly higher regarding tumor lesions (6.10 ± 6.59 vs 2.59 ± 3.30 Gy/GBq, factor 2.40, p < 0.001). Consequently, the mean TI was higher for [ 161 Tb]Tb-PSMA-617 compared to [ 177 Lu]Lu-PSMA-617 for both, the kidneys (11.54 ± 9.74 vs. 5.28 ± 5.13, p = 0.002) and the parotid gland (16.77 ± 13.10 vs. 12.51 ± 18.09, p = 0.008). Conclusion: In this intra-individual head-to-head pilot study, [ 161 Tb]Tb-PSMA-617 delivered higher tumor-absorbed doses and resulted in superior TI compared to [ 177 Lu]Lu-PSMA-617. This preliminary data support 161 Tb as a promising radionuclide for PSMA-RLT in mCRPC., Competing Interests: Competing Interests: The authors have declared that no competing interest exists., (© The author(s).)

The gastrin-releasing peptide receptor (GRPr) is overexpressed in various cancer types including prostate and breast carcinomas, making it an attractive target for molecular imaging and therapy. In this work, we designed a novel GRPr antagonistic probe comprising metal chelator NODIA-Me. This 1,4,7-triazacyclononane-based chelator forms positively charged metal complexes due to its neutral methylimidazole arms. Because a positive charge at the N -terminus of GRPr conjugates is responsible for high receptor affinity as exemplified by the current gold standard DOTA-RM2, we investigated if a positively charged radiometal complex can be used as a pharmacokinetic modifier to also produce high-affinity GRPr conjugates. In this respect, the bioconjugate NODIA-Me-Ahx-JMV594 was prepared by a combination of solid-phase peptide synthesis and solution-based reactions in a 94% yield. Radiolabeling provided the 68 Ga-labeled conjugate in radiochemical yields of >95% and radiochemical purities of >98% with mean molar activities of A m ∼17 MBq nmol -1 . The competitive GRPr affinity of the metal-free and 69/71 Ga-labeled conjugate was determined to be IC 50 = 0.41 ± 0.06 and 1.45 ± 0.06 nM, respectively. The metal-free GRPr antagonist DOTA-RM2 and its corresponding 69/71 Ga complex had IC 50 values of 1.42 ± 0.07 and 0.98 ± 0.19 nM, respectively. Small-animal PET imaging of mice bearing GRPr(+) PC-3 tumors revealed high radioactivity accumulation in the tumors and in the pancreas as an organ with high levels of GRPr expression. These findings were corroborated by the corresponding ex vivo biodistribution data, in which the tumors and the pancreas exhibited the highest radioactivity accumulation. By coinjection of an excess of NODIA-Me-Ahx-JMV594, uptake in the tumors and GRPr(+) organs was significantly reduced, confirming specific receptor-mediated uptake. The estrogen receptor-positive tumor of a female breast cancer patient was clearly visualized by PET imaging using 68 Ga-labeled NODIA-Me-Ahx-JMV594. To summarize, the positive charge at the N -terminus of the conjugate induced by the Ga(NODIA-Me) complex resulted in high GRPr affinity comparable to that of the potent antagonist DOTA-RM2. The conjugate NODIA-Me-Ahx-JMV594 is a promising probe for imaging of GRPr tumors that warrants further evaluation in larger patient cohorts as well as in combination with other radiometals.

Delay embedding methods are a staple tool in the field of time series analysis and prediction. However, the selection of embedding parameters can have a big impact on the resulting analysis. This has led to the creation of a large number of methods to optimize the selection of parameters such as embedding lag. This paper aims to provide a comprehensive overview of the fundamentals of embedding theory for readers who are new to the subject. We outline a collection of existing methods for selecting embedding lag in both uniform and non-uniform delay embedding cases. Highlighting the poor dynamical explainability of existing methods of selecting non-uniform lags, we provide an alternative method of selecting embedding lags that includes a mixture of both dynamical and topological arguments. The proposed method, Significant Times on Persistent Strands (SToPS), uses persistent homology to construct a characteristic time spectrum that quantifies the relative dynamical significance of each time lag. We test our method on periodic, chaotic, and fast-slow time series and find that our method performs similar to existing automated non-uniform embedding methods. Additionally, n-step predictors trained on embeddings constructed with SToPS were found to outperform other embedding methods when predicting fast-slow time series.

Non-recurrent congestion disrupts normal traffic operations and lowers travel time (TT) reliability, which leads to many negative consequences such as difficulties in trip planning, missed appointments, loss in productivity, and driver frustration. Traffic incidents are one of the six causes of non-recurrent congestion. Early and accurate detection helps reduce incident duration, but it remains a challenge due to the limitation of current sensor technologies. In this paper, we employ a recurrence-based technique, the Quadrant Scan, to analyse time series traffic volume data for incident detection. The data is recorded by multiple sensors along a section of urban highway. The results show that the proposed method can detect incidents better by integrating data from the multiple sensors in each direction, compared to using them individually. It can also distinguish non-recurrent traffic congestion caused by incidents from recurrent congestion. The results show that the Quadrant Scan is a promising algorithm for real-time traffic incident detection with a short delay. It could also be extended to other non-recurrent congestion types.

Assessing model accuracy for complex and chaotic systems is a non-trivial task that often relies on the calculation of dynamical invariants, such as Lyapunov exponents and correlation dimensions. Well-performing models are able to replicate the long-term dynamics and ergodic properties of the desired system. We term this phenomenon "dynamics learning." However, existing estimates based on dynamical invariants, such as Lyapunov exponents and correlation dimensions, are not unique to each system, not necessarily robust to noise, and struggle with detecting pathological errors, such as errors in the manifold density distribution. This can make meaningful and accurate model assessment difficult. We explore the use of a topological data analysis technique, persistent homology, applied to uniformly sampled trajectories from constructed reservoir models of the Lorenz system to assess the learning quality of a model. A proposed persistent homology point summary, conformance, was able to identify models with successful dynamics learning and detect discrepancies in the manifold density distribution.

The aim of this study was to identify a high-affinity BODIPY peptidomimetic that targets the prostate-specific membrane antigen (PSMA) as a potential bimodal imaging probe for prostate cancer. For the structure-activity study, several BODIPY (difluoroboron dipyrromethene) derivatives with varying spacers between the BODIPY dye and the PSMA Glu-CO-Lys binding motif were prepared. Corresponding affinities were determined by competitive binding assays in PSMA-positive LNCaP cells. One compound was identified with comparable affinity (IC 50 =21.5±0.1 nM) to Glu-CO-Lys-Ahx-HBED-CC (PSMA-11) (IC 50 =18.4±0.2 nM). Radiolabeling was achieved by Lewis-acid-mediated 19 F/ 18 F exchange in moderate molar activities (∼0.7 MBq nmol -1 ) and high radiochemical purities (>99 %) with mean radiochemical yields of 20-30 %. Cell internalization of the 18 F-labeled high-affinity conjugate was demonstrated in LNCaP cells showing gradual increasing PSMA-mediated internalization over time. By fluorescence microscopy, localization of the high-affinity BODIPY-PSMA conjugate was found in the cell membrane at early time points and also in subcellular compartments at later time points. In summary, a high-affinity BODIPY-PSMA conjugate has been identified as a suitable candidate for the development of PSMA-specific dual-imaging agents., (© 2021 The Authors. ChemMedChem published by Wiley-VCH GmbH.)

Despite the promising results of prostate-specific membrane antigen (PSMA)-targeted radioligand therapy (RLT) in metastatic castration-resistant prostate cancer (mCRPC), some patients show worsening disease during PSMA-RLT. We investigated the value of combined [ 18 F]FDG and [ 68 Ga]Ga-PSMA-11 PET imaging in this setting. In n = 29 mCRPC patients with worsening disease after a median of four cycles of [ 177 Lu]Lu-PSMA-617 RLT, combined [ 18 F]FDG and [ 68 Ga]Ga-PSMA-11 PET imaging was performed to detect [ 18 F]FDG-avid lesions with low or no PSMA expression (mismatch lesions). To evaluate prognostic implication of mismatch, survival analyses regarding presence, location, and [ 18 F]FDG PET-derived parameters such as SUV max , metabolic tumor volume (MTV m ), and total lesion glycolysis (TLG m ) of mismatch findings were performed. Seventeen patients (59%) showed at least one mismatch metastasis. From the time point of combined PET imaging, the median overall survival (OS) of patients with mismatch findings was significantly (p = 0.008) shorter than those without (3.3 vs. 6.1 mo). Patients with a high MTV m revealed a significantly ( p = 0.034) shorter OS of 2.6 mo than patients with low MTV m (5.3 mo). Furthermore, patients with hepatic mismatch showed a significantly ( p = 0.049) shorter OS than those without (2.9 vs. 5.3 mo). Difference in OS regarding SUV max and TLG m was not significant. In mCRPC patients with worsening disease during PSMA-RLT, combined [ 18 F]FDG and [ 68 Ga]Ga-PSMA-11 PET imaging is essential to identify mismatch findings, as these are associated with poor outcomes requiring a change in therapy management.

Background: Radioligand therapy (RLT) targeting prostate-specific membrane antigen (PSMA) is an effective antitumor-treatment in metastatic castration-resistant prostate carcinoma (mCRPC). Concerns of potential nephrotoxicity are based on renal tubular PSMA expression and the resulting radiopharmaceutical retention during RLT, but data confirming clinically significant renal toxicity are still lacking. In this study, patients with significantly impaired baseline kidney function before initiation of therapy were investigated for treatment-associated nephrotoxicity and the potential relationship with administered activities of [ 177 Lu]Lu-PSMA-617. Methods: Twenty-two mCRPC patients with impaired renal function (glomerular filtration rate (GFR) ≤ 60 mL/min) who received more than two cycles of [ 177 Lu]Lu-PSMA-617 RLT (median 5 cycles and median 6-week time interval between consecutive cycles) were analyzed in this study. Patients were treated within a prospective patient registry (REALITY Study, NCT04833517). Cumulative administered activities ranged from 17.1 to 85.6 GBq with a median activity of 6.5 GBq per cycle. Renal function was closely monitored during and after PSMA-RLT. Results: Mean pre-treatment GFR was 45.0 ± 10.7 mL/min. After two (22/22 patients), four (20/22 patients), and six cycles (10/22 patients) of RLT, a significant increase of GFR was noted (each p < 0.05). End-of-treatment GFR (54.1 ± 16.7 mL/min) was significantly higher than baseline GFR ( p = 0.016). Only one patient experienced deterioration of renal function (change of CTCAE grade 2 to 3). The remaining patients showed no significant reduction of GFR, including follow-up assessments (6, 9, and 12 months), and even showed improved (10/22 patients) or unchanged (11/22 patients) CTCAE-based renal impairment grades during and after the end of PSMA-RLT. No significant correlation between the change in GFR and per-cycle ( p = 0.605) or cumulative ( p = 0.132) administered activities were found. Conclusions: As pre-treatment chronic kidney failure did not lead to detectable RLT-induced deterioration of renal function in our study, the nephrotoxic potential of [ 177 Lu]Lu-PSMA-617 RLT may be overestimated and not of clinical priority in the setting of palliative treatment in mCRPC. We suggest not to categorically exclude patients from enrolment to PSMA-RLT due to renal impairment.

The use of 225 Ac in prostate-specific membrane antigen (PSMA)-targeted radioligand therapy (RLT), either as monotherapy or in combination with 177 Lu, is a promising therapy approach in patients with metastatic castration-resistant prostate carcinoma (mCRPC). In this study, we report the efficacy and safety of [ 225 Ac]Ac-PSMA-617 augmented [ 177 Lu]Lu-PSMA-617 RLT in 177 Lu-naive mCRPC patients ( n = 15) with poor prognosis (presence of visceral metastases, high total tumor burden with diffuse bone metastases or a short PSA doubling time of <2 months). Biochemical (by PSA serum value) and molecular imaging response (by [ 68 Ga]Ga-PSMA-11 PET/CT) was assessed after two cycles of [ 177 Lu]Lu-PSMA-617 RLT, with at least one [ 225 Ac]Ac-PSMA-617 augmentation. In addition, PSA-based progression-free survival (PSA-PFS), overall survival (OS) and toxicity (according to CTCAE) were analyzed. We observed a biochemical- and molecular imaging-based partial remission in 53.3% (8/15) and 66.7% (10/15) of patients, respectively. The median PSA-PFS and OS was 9.1 and 14.8 months, respectively. No serious acute adverse events were recorded. Two out of fifteen patients experienced grade 3 anemia. No other grade 3/4 toxicities were observed. RLT-related xerostomia (grade 1/2) was recorded in 2/15 patients. Our data showed a high clinical efficacy with a favorable side effects profile of [ 225 Ac]Ac-PSMA-617 augmented [ 177 Lu]Lu-PSMA-617 RLT in this highly challenging patient cohort.

Background: Dosimetry is of high importance for optimization of patient-individual PSMA-targeted radioligand therapy (PSMA-RLT). The aim of our study was to evaluate and compare the feasibility of different approaches of image-based absorbed dose estimation in terms of accuracy and effort in clinical routine., Methods: Whole-body planar images and SPECT/CT images were acquired from 24 patients and 65 cycles at 24h, 48h, and ≥96h after administration of a mean activity of 6.4 GBq [ 177 Lu]Lu-PSMA-617 (range 3-10.9 GBq). Dosimetry was performed by use of the following approaches: 2D planar-based dosimetry, 3D SPECT/CT-based dosimetry, and hybrid dosimetry combining 2D and 3D data. Absorbed doses were calculated according to IDAC 2.1 for the kidneys, the liver, the salivary glands, and bone metastases., Results: Mean absorbed doses estimated by 3D dosimetry (the reference method) were 0.54 ± 0.28 Gy/GBq for the kidneys, 0.10 ± 0.05 Gy/GBq for the liver, 0.81 ± 0.34 Gy/GBq for the parotid gland, 0.72 ± 0.39 Gy/GBq for the submandibular gland, and 1.68 ± 1.32 Gy/GBq for bone metastases. Absorbed doses of normal organs estimated by hybrid dosimetry showed small, non-significant differences (median up to 4.0%) to the results of 3D dosimetry. Using 2D dosimetry, in contrast, significant differences (median up to 10.9%) were observed. Regarding bone metastases, small, but significant differences (median up to 7.0%) of absorbed dose were found for both, 2D dosimetry and hybrid dosimetry. Bland-Altman analysis revealed high agreement between hybrid dosimetry and 3D dosimetry for normal organs and bone metastases, but substantial differences between 2D dosimetry and 3D dosimetry., Conclusion: Hybrid dosimetry provides high accuracy in estimation of absorbed dose in comparison to 3D dosimetry for all important organs and is therefore feasible for use in individualized PSMA-RLT.

Rationale: Despite the promising results of prostate-specific membrane antigen (PSMA)-targeted 177 Lu radioligand therapy in metastatic castration-resistant prostate carcinoma (mCRPC), some patients do not respond and other patients with initially good response develop resistance to this treatment. In this study, we investigated molecular imaging and biochemical responses after a single cycle of [ 225 Ac]Ac-PSMA-617/[ 177 Lu]Lu-PSMA-617 tandem therapy in patients who had progressed on [ 177 Lu]Lu-PSMA-617 monotherapy. Methods: Seventeen patients with mCRPC were included in a retrospective, monocenter study. Molecular imaging-based response was assessed by modified PERCIST criteria using the whole-body total lesion PSMA (TLP) and molecular tumour volume (MTV) derived from [ 68 Ga]Ga-PSMA-11 PET/CT. Biochemical response was evaluated according to PCWG3 criteria using the prostate-specific antigen (PSA) serum value. Concordance and correlation statistics as well as survival analyses were performed. Results: Based on the molecular imaging-based response assessment, 5 (29.4%) patients showed partial remission and 7 (41.2%) had stable disease. The remaining 5 (29.4%) patients had further progression, four with an increase in TLP/MTV of >30% and one with stable TLP/MTV but appearance of new metastases. Based on the biochemical response assessment, 5 (29.4%), 8 (47.1%), and 4 (23.5%) patients showed partial remission, stable disease, and progressive disease, respectively. A comparison of the response assessment methods showed a concordance of 100% (17/17) between TLP and MTV and 70.6% (12/17) between TLP/MTV and PSA. Patients with partial remission, independently assessed by each method, had better overall survival (OS) than patients with either stable or progressive disease. The difference in OS was statistically significant for the molecular imaging response assessment (median OS not reached vs. 8.3 m, p = 0.044), but not for the biochemical response assessment (median OS 18.1 m vs. 9.4 m, p = 0.468). Conclusion: Based on both assessment methods, [ 225 Ac]Ac-PSMA-617/[ 177 Lu]Lu-PSMA-617 tandem therapy is an effective treatment for the highly challenging cohort of patients with mCRPC who have progressed on [ 177 Lu]Lu-PSMA-617 monotherapy. Molecular imaging response and biochemical PSA response were mostly concordant, though a considerable number of cases (29.4%) were discordant. Molecular imaging response reflecting the change in total viable tumour burden appears to be superior to PSA change in estimating survival outcome after tandem therapy., Competing Interests: Competing Interests: The authors have declared that no competing interest exists., (© The author(s).)

We propose a computationally simple and efficient network-based method for approximating topological entropy of low-dimensional chaotic systems. This approach relies on the notion of an ordinal partition. The proposed methodology is compared to the three existing techniques based on counting ordinal patterns-all of which derive from collecting statistics about the symbolic itinerary-namely (i) the gradient of the logarithm of the number of observed patterns as a function of the pattern length, (ii) direct application of the definition of topological permutation entropy, and (iii) the outgrowth ratio of patterns of increasing length. In contrast to these alternatives, our method involves the construction of a sequence of complex networks that constitute stochastic approximations of the underlying dynamics on an increasingly finer partition. An ordinal partition network can be computed using any scalar observable generated by multidimensional ergodic systems, provided the measurement function comprises a monotonic transformation if nonlinear. Numerical experiments on an ensemble of systems demonstrate that the logarithm of the spectral radius of the connectivity matrix produces significantly more accurate approximations than existing alternatives-despite practical constraints dictating the selection of low finite values for the pattern length.

Purpose: We recently developed a chelating platform based on the macrocycle 1,4,7-triazacyclononane with up to three five-membered azaheterocyclic arms for the preparation of 68 Ga- and 64 Cu-based radiopharmaceuticals. Based on this platform, the chelator scaffold NOTI-TVA with three additional carboxylic acid groups for bioconjugation was synthesized and characterized. The primary aims of this proof-of-concept study were (1) to evaluate if trimeric radiotracers on the basis of the NOTI-TVA 6 scaffold can be developed, (2) to determine if the additional substituents for bioconjugation at the non-coordinating NH atoms of the imidazole residues of the building block NOTI influence the metal binding properties, and (3) what influence multiple targeting vectors have on the biological performance of the radiotracer. The cyclic RGDfK peptide that specifically binds to the α v ß 3 integrin receptor was selected as the biological model system., Procedures: Two different synthetic routes for the preparation of NOTI-TVA 6 were explored. Three c(RGDfK) peptide residues were conjugated to the NOTI-TVA 6 building block by standard peptide chemistry providing the trimeric bioconjugate NOTI-TVA-c(RGDfK) 3 9. Labeling of 9 with [ 64 Cu]CuCl 2 was performed manually at pH 8.2 at ambient temperature. Binding affinities of Cu-8, the Cu 2+ complex of the previously described monomer NODIA-Me-c(RGDfK) 8, and the trimer Cu-9 to integrin α v ß 3 were determined in competitive cell binding experiments in the U-87MG cell line. The pharmacokinetics of both 64 Cu-labeled conjugates [ 64 Cu]Cu-8 and [ 64 Cu]Cu-9 were determined by small-animal PET imaging and ex vivo biodistribution studies in mice bearing U-87MG xenografts., Results: Depending on the synthetic route, NOTI-TVA 6 was obtained with an overall yield up to 58 %. The bioconjugate 9 was prepared in 41 % yield. Both conjugates [ 64 Cu]Cu-8 and [ 64 Cu]Cu-9 were radiolabeled quantitatively at ambient temperature in high molar activities of A m ~ 20 MBq nmol -1 in less than 5 min. Competitive inhibitory constants IC 50 of c(RDGfK) 7, Cu-8, and Cu-9 were determined to be 159.5 ± 1.3 nM, 256.1 ± 2.1 nM, and 99.5 ± 1.1 nM, respectively. In small-animal experiments, both radiotracers specifically delineated α v ß 3 integrin-positive U-87MG tumors with low uptake in non-target organs and rapid blood clearance. The trimer [ 64 Cu]Cu-9 showed a ~ 2.5-fold higher tumor uptake compared with the monomer [ 64 Cu]Cu-8., Conclusions: Functionalization of NOTI at the non-coordinating NH atoms of the imidazole residues for bioconjugation was straightforward and allowed the preparation of a homotrimeric RGD conjugate. After optimization of the synthesis, required building blocks to make NOTI-TVA 6 are now available on multi-gram scale. Modifications at the imidazole groups had no measurable impact on metal binding properties in vitro and in vivo suggesting that the NOTI scaffold is a promising candidate for the development of 64 Cu-labeled multimeric/multifunctional radiotracers.

We present a statistical finite element method for nonlinear, time-dependent phenomena, illustrated in the context of nonlinear internal waves (solitons). We take a Bayesian approach and leverage the finite element method to cast the statistical problem as a nonlinear Gaussian state-space model, updating the solution, in receipt of data, in a filtering framework. The method is applicable to problems across science and engineering for which finite element methods are appropriate. The Korteweg-de Vries equation for solitons is presented because it reflects the necessary complexity while being suitably familiar and succinct for pedagogical purposes. We present two algorithms to implement this method, based on the extended and ensemble Kalman filters, and demonstrate effectiveness with a simulation study and a case study with experimental data. The generality of our approach is demonstrated in SI Appendix , where we present examples from additional nonlinear, time-dependent partial differential equations (Burgers equation, Kuramoto-Sivashinsky equation)., Competing Interests: The authors declare no competing interest.

Purpose: Up to 30% of patients with prostate-specific membrane antigen (PSMA)-positive metastatic castration-resistant prostate cancer (mCRPC) never respond or develop resistance to 177 Lu-labeled PSMA-targeted radioligand monotherapy. Single-agent PSMA-targeted radioligand therapy (PRLT) with the alpha-emitter 225 Ac showed promise against mCRPC but may cause severe and/or persistent xerostomia, which may substantially impair patients' quality-of-life. We hypothesized that when 177 Lu-PSMA ligand alone is ineffective, tandem therapy with low-activity 225 Ac-PSMA ligand plus full activity of the beta emitter may enhance efficacy while minimizing xerostomia severity., Methods: We retrospectively analyzed pilot experience with 1 course of 225 Ac-PSMA-617/ 177 Lu-PSMA-617 tandem therapy in our first 20 patients with mCRPC receiving this intervention after insufficiently responding to 177 Lu-PSMA-617 monotherapy. This cohort had late-stage/end-stage disease with high baseline prostate-specific antigen (PSA) concentration (median 215 ng/mL), heavy pre-treatment (abiraterone and/or enzalutamide, and 177 Lu-PRLT [median cumulative activity, 26.3 GBq] in 20/20 patients, 100%; docetaxel and/or cabazitaxel in 13/20 patients, 65%), and frequent Eastern Cooperative Oncology Group performance status of 2 (8/20 patients, 40%)., Results: Median (minimum-maximum) administered activities were 225 Ac-PSMA-617, 5.3 (1.5-7.9) MBq, and 177 Lu-PSMA-617, 6.9 (5.0-11.6) GBq. Significant responders to tandem therapy received 177 Lu-PSMA-617 monotherapy as maintenance (median [minimum-maximum]: 1 [0-5] cycle). After a median (minimum-maximum) 22 (14-63) weeks' follow-up, 13/20 patients (65%) had as best biochemical response a PSA decline > 50%. Median (95% confidence interval) progression-free survival was 19 (12-26) weeks, and overall survival was 48 (4-92) weeks post-tandem therapy administration. Xerostomia was reported as grade 1 (very mild) in 8/20 patients (40%), grade 2 (mild) in 5/20 (25%), and grade 3/4 in 0/20., Conclusions: Our results suggest that a single course of tandem therapy with low-activity 225 Ac-PSMA-617/full-activity 177 Lu-PSMA-617 may safely enhance response to PRLT in men with late-stage/end-stage mCRPC while minimizing xerostomia severity. Formal study of this combination is warranted.

We study laminar chaos in an electronic experiment. A two-diode nonlinear circuit with delayed feedback shows chaotic dynamics similar to the Mackey-Glass or Ikeda delay systems. Clock modulation of a single delay line leads to a conservative variable delay, which with a second delay line is augmented to dissipative delays, leading to laminar chaotic regimes. We discuss the properties of this particular delay modulation and demonstrate experimental aspects of laminar chaos in terms of power spectra and return maps.

Mapping time series to complex networks to analyze observables has recently become popular, both at the theoretical and the practitioner's level. The intent is to use network metrics to characterize the dynamics of the underlying system. Applications cover a wide range of problems, from geoscientific measurements to biomedical data and financial time series. It has been observed that different dynamics can produce networks with distinct topological characteristics under a variety of time-series-to-network transforms that have been proposed in the literature. The direct connection, however, remains unclear. Here, we investigate a network transform based on computing statistics of ordinal permutations in short subsequences of the time series, the so-called ordinal partition network. We propose a Markovian framework that allows the interpretation of the network using ergodic-theoretic ideas and demonstrate, via numerical experiments on an ensemble of time series, that this viewpoint renders this technique especially well-suited to nonlinear chaotic signals. The aim is to test the mapping's faithfulness as a representation of the dynamics and the extent to which it retains information from the input data. First, we show that generating networks by counting patterns of increasing length is essentially a mechanism for approximating the analog of the Perron-Frobenius operator in a topologically equivalent higher-dimensional space to the original state space. Then, we illustrate a connection between the connectivity patterns of the networks generated by this mapping and indicators of dynamics such as the hierarchy of unstable periodic orbits embedded within a chaotic attractor. The input is a scalar observable and any projection of a multidimensional flow suffices for reconstruction of the essential dynamics. Additionally, we create a detailed guide for parameter tuning. We argue that there is no optimal value of the pattern length m, rather it admits a scaling region akin to traditional embedding practice. In contrast, the embedding lag and overlap between successive patterns can be chosen exactly in an optimal way. Our analysis illustrates the potential of this transform as a complementary toolkit to traditional time-series methods.

To understand the collective motion of many individuals, we often rely on agent-based models with rules that may be computationally complex and involved. For biologically inspired systems in particular, this raises questions about whether the imposed rules are necessarily an accurate reflection of what is being followed. The basic premise of updating one's state according to some underlying motivation is well suited to the realm of reservoir computing; however, entire swarms of individuals are yet to be tasked with learning movement in this framework. This work focuses on the specific case of many selfish individuals simultaneously optimizing their domains in a manner conducive to reducing their personal risk of predation. Using an echo state network and data generated from the agent-based model, we show that, with an appropriate representation of input and output states, this selfish movement can be learned. This suggests that a more sophisticated neural network, such as a brain, could also learn this behavior and provides an avenue to further the search for realistic movement rules in systems of autonomous individuals.

The selfish herd hypothesis provides an explanation for group aggregation via the selfish avoidance of predators. Conceptually, and as was first proposed, this movement should aim to minimise the danger domain of each individual. Whilst many reasonable proxies have been proposed, none have directly sought to reduce the danger domain. In this work we present a two dimensional stochastic model that actively optimises these domains. The individuals' dynamics are determined by sampling the space surrounding them and moving to achieve the largest possible domain reduction. Two variants of this idea are investigated with sampling occurring either locally or globally. We simulate our models and two of the previously proposed benchmark selfish herd models: k-nearest neighbours (kNN); and local crowded horizon (LCH). The resulting positions are analysed to determine the benefit to the individual and the group's ability to form a compact group. To do this, the group level metric of packing fraction and individual level metric of domain size are observed over time for a range of noise levels. With these measures we show a clear stratification of the four models when noise is not included. kNN never resulted in centrally compacted herd, while the local active selfish model and LCH did so with varying levels of success. The most centralised groups were achieved with our global active selfish herd model. The inclusion of noise improved aggregation in all models. This was particularly so with the local active selfish model with a change to ordering of performance so that it marginally outperformed LCH in aggregation. By more closely following Hamilton's original conception and aligning the individual's goal of a reduced danger domain with the movement it makes increased cohesion is observed, thus confirming his hypothesis, however, these findings are dependent on noise. Moreover, many features originally conjectured by Hamilton are also observed in our simulations., (Crown Copyright © 2019. Published by Elsevier Ltd. All rights reserved.)

Positioning and tracking a moving target from limited positional information is a frequently-encountered problem. For given noisy observations of the target's position, one wants to estimate the true trajectory and reconstruct the full phase space including velocity and acceleration. The shadowing filter offers a robust methodology to achieve such an estimation and reconstruction. Here, we highlight and validate important merits of this methodology for real-life applications. In particular, we explore the filter's performance when dealing with correlated or uncorrelated noise, irregular sampling in time and how it can be optimised even when the true dynamics of the system are not known.

Consistency is an extension to generalized synchronization which quantifies the degree of functional dependency of a driven nonlinear system to its input. We apply this concept to echo-state networks, which are an artificial-neural network version of reservoir computing. Through a replica test, we measure the consistency levels of the high-dimensional response, yielding a comprehensive portrait of the echo-state property.

The bifunctional chelator NODIA-Me holds promise for radiopharmaceutical development. NODIA-Me is based on the macrocycle TACN (1,4,7-triazacyclononane) and incorporates two additional methylimidazole arms for metal chelation and an acetic acid residue for bioconjugation. The original two step synthesis was less than optimal due to low yields and the requirement of semi-preparative RP-HPLC purifications. Here, the overall yield for the preparation of NODIA-Me was improved two- to five-fold via two synthetic routes using different protection/deprotection techniques. This way, it was possible (1) to prepare of NODIA-Me on multi-gram scale and (2) to avoid time-consuming HPLC purifications. Inspired by recent results with nat/68Ga3+, preliminary studies on the radiolabeling properties and complex formation of NODIA-Me with nat/111In3+ were performed. Quantitative radiochemical yields were achieved at ambient temperature providing molar activities of ∼30 MBq nmol-1, which could be increased to ∼240 MBq nmol-1 at 95 °C. At r.t., pH 5.5 was optimal for 111In-labeling, but quantitative yields were also achieved in the pH range from 5.5 to 8.2, when the reaction temperature was increased. Stability tests of 111In complexes in vitro revealed high kinetic stabilities in serum and ligand challenge experiments, which is a consequence of the formation of rigid 1 : 1 indium chelates as shown by NMR studies in solution. In summary, the new synthetic routes afford the BFC NODIA-Me in high yields and on large scale. Further, 111In complexation experiments broaden the scope of our chelating system for radiopharmaceutical applications.

Describing a time series parsimoniously is the first step to study the underlying dynamics. For a time-discrete system, a generating partition provides a compact description such that a time series and a symbolic sequence are one-to-one. But, for a time-continuous system, such a compact description does not have a solid basis. Here, we propose to describe a time-continuous time series using a local cross section and the times when the orbit crosses the local cross section. We show that if such a series of crossing times and some past observations are given, we can predict the system's dynamics with fine accuracy. This reconstructability neither depends strongly on the size nor the placement of the local cross section if we have a sufficiently long database. We demonstrate the proposed method using the Lorenz model as well as the actual measurement of wind speed.

In this study, we propose a new information theoretic measure to quantify the complexity of biological systems based on time-series data. We demonstrate the potential of our method using two distinct applications to human cardiac dynamics. Firstly, we show that the method clearly discriminates between segments of electrocardiogram records characterized by normal sinus rhythm, ventricular tachycardia and ventricular fibrillation. Secondly, we investigate the multiscale complexity of cardiac dynamics with respect to age in healthy individuals using interbeat interval time series and compare our findings with a previous study which established a link between age and fractal-like long-range correlations. The method we use is an extension of the symbolic mapping procedure originally proposed for permutation entropy. We build a Markov chain of the dynamics based on order patterns in the time series which we call an ordinal network, and from this model compute an intuitive entropic measure of transitional complexity. A discussion of the model parameter space in terms of traditional time delay embedding provides a theoretical basis for our multiscale approach. As an ancillary discussion, we address the practical issue of node aliasing and how this effects ordinal network models of continuous systems from discrete time sampled data, such as interbeat interval time series.This article is part of the themed issue 'Mathematical methods in medicine: neuroscience, cardiology and pathology'., (© 2017 The Author(s).)

Miniature GPS devices now allow for measurement of the movement of animals in real time and provide high- quality and high-resolution data. While these new data sets are a great improvement, one still encounters some measurement errors as well as device failures. Moreover, these devices only measure position and require further reconstruction techniques to extract the full dynamical state space with the velocity and acceleration. Direct differentiation of position is generally not adequate. We report on the successful implementation of a shadowing filter algorithm that (1) minimizes measurement errors and (2) reconstructs at the same time the full phase-space from a position recording of a flying pigeon. This filter is based on a very simple assumption that the pigeon's dynamics are Newtonian. We explore not only how to choose the filter's parameters but also demonstrate its improvements over other techniques and give minimum data requirements. In contrast to competing filters, the shadowing filter's approach has not been widely implemented for practical problems. This article addresses these practicalities and provides a prototype for such application.

Recently proposed ordinal networks not only afford novel methods of nonlinear time series analysis but also constitute stochastic approximations of the deterministic flow time series from which the network models are constructed. In this paper, we construct ordinal networks from discrete sampled continuous chaotic time series and then regenerate new time series by taking random walks on the ordinal network. We then investigate the extent to which the dynamics of the original time series are encoded in the ordinal networks and retained through the process of regenerating new time series by using several distinct quantitative approaches. First, we use recurrence quantification analysis on traditional recurrence plots and order recurrence plots to compare the temporal structure of the original time series with random walk surrogate time series. Second, we estimate the largest Lyapunov exponent from the original time series and investigate the extent to which this invariant measure can be estimated from the surrogate time series. Finally, estimates of correlation dimension are computed to compare the topological properties of the original and surrogate time series dynamics. Our findings show that ordinal networks constructed from univariate time series data constitute stochastic models which approximate important dynamical properties of the original systems.

We are motivated by real-world data that exhibit severe sampling irregularities such as geological or paleoclimate measurements. Counting forbidden patterns has been shown to be a powerful tool towards the detection of determinism in noisy time series. They constitute a set of ordinal symbolic patterns that cannot be realised in time series generated by deterministic systems. The reliability of the estimator of the relative count of forbidden patterns from irregularly sampled data has been explored in two recent studies. In this paper, we explore highly irregular sampling frequency schemes. Using numerically generated data, we examine the reliability of the estimator when the sampling period has been drawn from exponential, Pareto and Gamma distributions of varying skewness. Our investigations demonstrate that some statistical properties of the sampling distribution are useful heuristics for assessing the estimator's reliability. We find that sampling in the presence of large chronological gaps can still yield relatively accurate estimates as long as the time series contains sufficiently many densely sampled areas. Furthermore, we show that the reliability of the estimator of forbidden patterns is poor when there is a high number of sampling intervals, which are larger than a typical correlation time of the underlying system.

It has been established that the count of ordinal patterns, which do not occur in a time series, called forbidden patterns, is an effective measure for the detection of determinism in noisy data. A very recent study has shown that this measure is also partially robust against the effects of irregular sampling. In this paper, we extend said research with an emphasis on exploring the parameter space for the method's sole parameter-the length of the ordinal patterns-and find that the measure is more robust to under-sampling and irregular sampling than previously reported. Using numerically generated data from the Lorenz system and the hyper-chaotic Rössler system, we investigate the reliability of the relative proportion of ordinal patterns in periodic and chaotic time series for various degrees of under-sampling, random depletion of data, and timing jitter. Discussion and interpretation of results focus on determining the limitations of the measure with respect to optimal parameter selection, the quantity of data available, the sampling period, and the Lyapunov and de-correlation times of the system.

The East Asian-Indonesian-Australian summer monsoon (EAIASM) links the Earth's hemispheres and provides a heat source that drives global circulation. At seasonal and inter-seasonal timescales, the summer monsoon of one hemisphere is linked via outflows from the winter monsoon of the opposing hemisphere. Long-term phase relationships between the East Asian summer monsoon (EASM) and the Indonesian-Australian summer monsoon (IASM) are poorly understood, raising questions of long-term adjustments to future greenhouse-triggered climate change and whether these changes could 'lock in' possible IASM and EASM phase relationships in a region dependent on monsoonal rainfall. Here we show that a newly developed nonlinear time series analysis technique allows confident identification of strong versus weak monsoon phases at millennial to sub-centennial timescales. We find a see-saw relationship over the last 9,000 years-with strong and weak monsoons opposingly phased and triggered by solar variations. Our results provide insights into centennial- to millennial-scale relationships within the wider EAIASM regime.

Natural and man-made networks often possess locally treelike substructures. Taking such tree networks as our starting point, we show how the addition of links changes the synchronization properties of the network. We focus on two different methods of link addition. The first method adds single links that create cycles of a well-defined length. Following a topological approach, we introduce cycles of varying length and analyze how this feature, as well as the position in the network, alters the synchronous behavior. We show that in particular short cycles can lead to a maximum change of the Laplacian's eigenvalue spectrum, dictating the synchronization properties of such networks. The second method connects a certain proportion of the initially unconnected nodes. We simulate dynamical systems on these network topologies, with the nodes' local dynamics being either discrete or continuous. Here our main result is that a certain number of additional links, with the relative position in the network being crucial, can be beneficial to ensure stable synchronization.

Irregular sampling of data sets is one of the challenges often encountered in time-series analysis, since traditional methods cannot be applied and the frequently used interpolation approach can corrupt the data and bias the subsequence analysis. Here we present the TrAnsformation-Cost Time-Series (TACTS) method, which allows us to analyze irregularly sampled data sets without degenerating the quality of the data set. Instead of using interpolation we consider time-series segments and determine how close they are to each other by determining the cost needed to transform one segment into the following one. Using a limited set of operations-with associated costs-to transform the time series segments, we determine a new time series, that is our transformation-cost time series. This cost time series is regularly sampled and can be analyzed using standard methods. While our main interest is the analysis of paleoclimate data, we develop our method using numerical examples like the logistic map and the Rössler oscillator. The numerical data allows us to test the stability of our method against noise and for different irregular samplings. In addition we provide guidance on how to choose the associated costs based on the time series at hand. The usefulness of the TACTS method is demonstrated using speleothem data from the Secret Cave in Borneo that is a good proxy for paleoclimatic variability in the monsoon activity around the maritime continent.

We investigate a generalised version of the recently proposed ordinal partition time series to network transformation algorithm. First, we introduce a fixed time lag for the elements of each partition that is selected using techniques from traditional time delay embedding. The resulting partitions define regions in the embedding phase space that are mapped to nodes in the network space. Edges are allocated between nodes based on temporal succession thus creating a Markov chain representation of the time series. We then apply this new transformation algorithm to time series generated by the Rössler system and find that periodic dynamics translate to ring structures whereas chaotic time series translate to band or tube-like structures-thereby indicating that our algorithm generates networks whose structure is sensitive to system dynamics. Furthermore, we demonstrate that simple network measures including the mean out degree and variance of out degrees can track changes in the dynamical behaviour in a manner comparable to the largest Lyapunov exponent. We also apply the same analysis to experimental time series generated by a diode resonator circuit and show that the network size, mean shortest path length, and network diameter are highly sensitive to the interior crisis captured in this particular data set.

Preferential attachment, by which new nodes attach to existing nodes with probability proportional to the existing nodes' degree, has become the standard growth model for scale-free networks, where the asymptotic probability of a node having degree k is proportional to k^{-γ}. However, the motivation for this model is entirely ad hoc. We use exact likelihood arguments and show that the optimal way to build a scale-free network is to attach most new links to nodes of low degree. Curiously, this leads to a scale-free network with a single dominant hub: a starlike structure we call a superstar network. Asymptotically, the optimal strategy is to attach each new node to one of the nodes of degree k with probability proportional to 1/N+ζ(γ)(k+1)(γ) (in a N node network): a stronger bias toward high degree nodes than exhibited by standard preferential attachment. Our algorithm generates optimally scale-free networks (the superstar networks) as well as randomly sampling the space of all scale-free networks with a given degree exponent γ. We generate viable realization with finite N for 1≪γ<2 as well as γ>2. We observe an apparently discontinuous transition at γ≈2 between so-called superstar networks and more treelike realizations. Gradually increasing γ further leads to reemergence of a superstar hub. To quantify these structural features, we derive a new analytic expression for the expected degree exponent of a pure preferential attachment process and introduce alternative measures of network entropy. Our approach is generic and can also be applied to an arbitrary degree distribution.