Adaptive Checkpoint Research Articles

Galaxy morphology classification using neural ordinary differential equations

We introduce a continuous depth version of the Residual Network (ResNet) called Neural ordinary differential equations (NODE) for the purpose of galaxy morphology classification. We carry out a classification of galaxy images from the Galaxy Zoo 2 dataset, consisting of five distinct classes, and obtained an accuracy between 91%–95%, depending on the image class. We train NODE with different numerical techniques such as adjoint and Adaptive Checkpoint Adjoint (ACA) and compare them against ResNet. While ResNet has certain drawbacks, such as time consuming architecture selection (e.g. the number of layers) and the requirement of a large dataset needed for training, NODE can overcome these limitations. Through our results, we show that the accuracy of NODE is comparable to ResNet, and the number of parameters used is about one-third as compared to ResNet, thus leading to a smaller memory footprint, which would benefit next generation surveys.

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Dual checkpoint blockade of CD47 and PD-L1 using an affinity-tuned bispecific antibody maximizes antitumor immunity

BackgroundT cell checkpoint immunotherapies have shown promising results in the clinic, but most patients remain non-responsive. CD47-signal regulatory protein alpha (SIRPα) myeloid checkpoint blockade has shown early clinical activity in...

Repositioning Azelnidipine as a Dual Inhibitor Targeting CD47/SIRPα and TIGIT/PVR Pathways for Cancer Immuno-Therapy

Strategies boosting both innate and adaptive immunity have great application prospects in cancer immunotherapy. Antibodies dual blocking the innate checkpoint CD47 and adaptive checkpoint PD-L1 or TIGIT could achieve durable anti-tumor effects. However, a small molecule dual blockade of CD47/SIRPα and TIGIT/PVR pathways has not been investigated. Here, an elevated expression of CD47 and PVR was observed in tumor tissues and cell lines analyzed with the GEO datasets and by flow cytometry, respectively. Compounds approved by the FDA were screened with the software MOE by docking to the potential binding pockets of SIRPα and PVR identified with the corresponding structural analysis. The candidate compounds were screened by blocking and MST binding assays. Azelnidipine was found to dual block CD47/SIRPα and TIGIT/PVR pathways by co-targeting SIRPα and PVR. In vitro, azelnidipine could enhance the macrophage phagocytosis when co-cultured with tumor cells. In vivo, azelnidipine alone or combined with irradiation could significantly inhibit the growth of MC38 tumors. Azelnidipine also significantly inhibits the growth of CT26 tumors, by enhancing the infiltration and function of CD8+ T cell in tumor and systematic immune response in the tumor-draining lymph node and spleen in a CD8+ T cell dependent manner. Our research suggests that the anti-hypertensive drug azelnidipine could be repositioned for cancer immunotherapy.

Abstract PO018: Restoring the tumor-suppressed immune response during chemotherapy by targeting Mer:PTP1b interactions

Abstract The development of adaptive immune checkpoint inhibitors, which prevent tumor-mediated inactivation of lymphocytes, has drastically improved outcomes for advanced cancer patients. However, only 20-30% of patients benefit from these treatments and those that do often present moderate toxicity and/or later relapse. After discovering a novel innate immune checkpoint, we have identified a therapeutic strategy to restore the tumor-suppressed immune response during chemotherapy. Here, we show that multiple tumor types (including melanoma, lung, breast and pancreatic cancers) co-cultured with murine primary macrophages suppress the expression of the essential Toll-like Receptor (TLR) signal-transducing adapter protein MyD88 by 57-81% +/- 2-5% (mean +/- SEM). In the absence of MyD88, macrophages are unable to respond to TLR stimulating Damage Associated Molecular Patterns (DAMPs) released by dying tumor cells after chemotherapy, leading to as much as 97% +/- 6% reduction in pro-inflammatory gene expression in our co-culture models. Tumors exert this suppression by activating the macrophage Mer receptor, inducing recruitment of a phosphatase, known as PTP1b, and Stat1 to Mer. Increasing association between PTP1b and Stat1 leads to reduced Stat1 phosphorylation and translocation to the nucleus as well as a downstream reduction in MyD88 expression. Treatment with a pharmacological inhibitor of PTP1b (BVT948) blocks the association of Mer, PTP1b and Stat1, restoring MyD88 expression and responsiveness to chemotherapy-released DAMPs. In chemotherapy-resistant murine syngeneic melanoma models, including B16F10 and GEMM6 (Braf V600E, Pten-/-), we show that combination therapy with BVT948 and Cisplatin or Vemurafenib, respectively, leads to a 47% reduction in tumor growth rates. Treating chemo- and immuno-therapy resistant Lewis Lung Cancer (LLC) tumor-bearing mice with combination BVT948/Cisplatin therapy leads to a similar reduction in tumor growth that is magnified with the addition of adaptive immune checkpoint blockade. In summary, we have described a novel mechanism of cancer-mediated immune suppression that dramatically reduces the immune response during chemotherapy. PTP1b inhibition could represent a novel therapeutic strategy to improve the effectiveness of conventional chemotherapy in patients with advanced malignancies. Citation Format: Nestor Prieto-Dominguez, Eric S. Ubil. Restoring the tumor-suppressed immune response during chemotherapy by targeting Mer:PTP1b interactions [abstract]. In: Abstracts: AACR Virtual Special Conference: Tumor Immunology and Immunotherapy; 2020 Oct 19-20. Philadelphia (PA): AACR; Cancer Immunol Res 2021;9(2 Suppl):Abstract nr PO018.

Abstract 4849: YPN-005, an oral CDK7 inhibitor, shows a significant antitumor activity in Myc amplified solid tumors and MCL-1 overexpressed blood cancer

Abstract Background: Cyclin dependent kinase 7 (CDK7) has been recognized as one of potential therapeutic targets in Myc-driven cancers. Previously, we synthesized selective irreversible CDK7 inhibitor and we demonstrated a significant inhibition of the proliferation of TNBC and HCC cells by down-regulation of c-Myc and MCL-1. We further report YPN-005 of the preclinical data with biological characterization. Methods: Antiproliferative activity of YPN-005 was measured in solid tumor cell lines with Myc amplification and in hematologic cancer cells with MCL-1overexpression. To investigate the mechanism of action of YPN-005, the expression levels of phospho-RNA polymerase II, phospho-CDK2 and -CDK4, BClXL, cleaved-PARP, c-Myc and MCL-1 were analyzed by Western Blot analyses. CDK7 occupancy was determined by using a biotinylated small molecule probe following incubating of TNBC, HCC, AML cells and hPBMC with YPN-005. The therapeutic efficacy of YPN005 was evaluated in TNBC and HCC xenograft mouse model. Results: YPN-005 treatment induced apoptosis and cell cycle arrest. Selectivity of YPN-005 on CDK7 was confirmed in the 468 kinases panel assay. YPN-005 significantly inhibited the proliferation of TNBC, ER+ breast cancer, HCC, ovarian cancer, small cell lung cancer (SCLC), pancreas, prostate and various types of blood cancer cells and IC50's were determined in 1-20 nM range. Inhibition of cell proliferation was accompanied by down-regulation of RNA PolII phosphorylation, c-Myc and MCL-1 expression. Washout assay by Western Blot demonstrated that YPN-005 irreversibly blocked RNA PolII phosphorylation. In addition, YPN-005 downregulated the adaptive immune checkpoint PD-L1 by the depletion of c-Myc in TNBCs. CDK7 occupancy over 90% was observed in TNBC, HCC, and AML cells with 100nM of YPN-005. In vivo xenograft models of TNBC and HCC showed that daily oral administration of YPN-005 for 21 days (once, and 10~20mg/kg) efficiently inhibited the growth of tumor. All the mice survived and there was no significant changes in their hematologic profiles. Conclusion: Our findings suggest that YPN-005 is an orally available, potent, and selective CDK7 inhibitor which can be used for the treatment of Myc and MCL-1 overexpressing cancer patients. These data support the rationale for advancing YPN-005 towards IND-enabling studies. Citation Format: Jakyung Yoo, Jun Hee Lee, Mi Jung Lee, Kang Woo Lee, Ji Eun Min, Jinhwan Kim, Ki-Nam Min, Da-Hye Jeon, Dae Seong Lim, Kwang-Ok Lee. YPN-005, an oral CDK7 inhibitor, shows a significant antitumor activity in Myc amplified solid tumors and MCL-1 overexpressed blood cancer [abstract]. In: Proceedings of the Annual Meeting of the American Association for Cancer Research 2020; 2020 Apr 27-28 and Jun 22-24. Philadelphia (PA): AACR; Cancer Res 2020;80(16 Suppl):Abstract nr 4849.

Abstract 3238: SIRPa blockade reinvigorates myeloid cells in the tumor microenvironment and reverses T-cell exclusion

Abstract Cancer immunotherapies by immune checkpoint blockade (CKI) has shown great therapeutic efficacy by helping the immune system to recognize and attack cancer cells. However, a significant percentage of patients do not respond or develop resistance. T-cell exclusion from tumor core, mediated by myeloid cells and fibroblast colonizing the tumor micro-environment, has been described as an important factor of resistance to checkpoint inhibitors. Myeloid cells represent one of the most abundant immune cell types in many solid tumors and are often associated with a poor outcome. Interaction of SIRPalpha (SIRPá), expressed by myeloid cells, with the ubiquitous receptor CD47 is an important immune checkpoint of the innate response, involved in the regulation of macrophages and dendritic cells functions (e.g. phagocytosis, antigen presentation). Here we evaluated the impact of selective SIRPá blockade on the function of myeloid cells from tumor micro-environment. In vivo, in an orthotopic and syngeneic hepatocellular carcinoma (HCC) mouse model, anti-SIRPá antagonist monoclonal antibody in combination with an adaptive immune checkpoint inhibitor (anti-PD-L1) dramatically enhanced overall survival and lead to complete remission in up to 60% of immunocompetent mice (p<0.001; n=11/18). A robust memory immune response developed since a second tumor challenge after drug elimination was always rejected (p<0.01). Transcriptional analysis of tumor at early stage (10 days after treatment) using Nanostring technology revealed a significant enrichment of a multiple chemokine signature in animals that received anti-SIRPá and anti-PD-L1 combination. Histological analysis of HCC tumors revealed that anti-PDL1 mAb alone increased T-cell infiltrates, but T-cell remained excluded from tumor core. In contrast, tumor nodules were strongly reduced, and T-cell significantly enriched in tumor nest in combination with the SIRPá antagonist (p<0.01). In vitro, we next observed that CD47-induced signals inhibited secretion of chemokines by immature human macrophages. This inhibition could be reversed by a selective anti-SIRPá antagonist mAb. Ex-vivo, selective anti- SIRPá antagonist mAbs significantly increased the chemokine transcriptomic expression signature of human myeloid cells purified from ovarian cancer ascites or of HCC tumor explant fragment maintained in culture for 48 hours. Finally, we found in vivo in a humanized mice model of transmigration that SIRPá blockade significantly increased human T cell migration in microenvironment locally enriched by human macrophages. In conclusion, we showed that selective SIRPá antagonist mAbs synergized with T-cell CKI by modifying the tumor microenvironment, in particular the chemokine secretion by mouse or human myeloid cells which contributes to limit T cell exclusion and favors efficient and robust anti-tumor immune responses. Citation Format: Vanessa Gauttier, Sabrina Pengam, Justine Durand, Kévin Biteau, Mélanie Néel, Sophie Conchon, Dominique Costantini, Bernard Vanhove, Nicolas Poirier. SIRPa blockade reinvigorates myeloid cells in the tumor microenvironment and reverses T-cell exclusion [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2019; 2019 Mar 29-Apr 3; Atlanta, GA. Philadelphia (PA): AACR; Cancer Res 2019;79(13 Suppl):Abstract nr 3238.

A digital pathology demonstration of an "immune hot" ICOS+/CD45RO+ immunephenotype and the impact on survival in patients with esophageal adenocarcinoma.

4062 Background: Therapies targeting immune checkpoints are changing our understanding of the biology and treatment of cancer. Analysing the immune landscape in esophageal adenocarcinoma (EA) may help future prognostication and therapeutic decision-making. Methods: We assembled 310 EA cases in a tissue microarray format with associated clinicopathological information, including a discovery cohort of 156 EA from Northern Ireland and a 154 EA validation cohort from Aberdeen. We carried out validated immunohistochemistry (IHC), stained for range of adaptive immune (CD3, CD4, CD8 and CD45RO) and immune checkpoint biomarkers (ICOS and IDO-1). Slides were digitised and assessed using QuPath image analysis software program to quantify their expression and correlate them with outcome. Results: In the discovery cohort we identified a group of patients highly expressing several immune biomarkers, conferring a significant positive survival advantage (p = 0.022). CD3, CD4, CD8, CD45RO, and ICOS were individually prognostic for better overall survival (Log rank p = 0.0003; p = 0.0292; p = 0.0015; p = 0.0008; p = 0.0051 and p = 0.0264 respectively). Multivariate and correlation analysis identified a subgroup of CD45RO+/ICOS+ patients with significantly improved overall survival (p = 0.0002). The co-expression of CD45RO+/ICOS+ immunophenotype was investigated in the validation cohort and a confirmed survival advantage was seen (p = 0.042). Additionally, the Opal Multiplex IHC technology revealed the much higher frequency of single-cell, dual labelling of CD45RO+/ICOS+ in immune hot cases. Conclusions: These data demonstrate the advantage of immune markers other than the traditional CD3/CD4/CD8 in EA prognostication. The fact that one of these biomarkers is an immune checkpoint inhibitor may have therapeutic implications.

Abstract B069: Characterization of inflammatory cell patterns and densities using multiplex immunohistochemistry immuno-oncology assays

Abstract Definiens and Mosaic Laboratories developed an immuno-oncology (IO) panel consisting of multiplex chromogenic IHC assays and image and data analysis solutions to determine a standardized profile of the tumor microenvironment in non-small cell lung cancer (NSCLC). Expression of PD-L1 on tumor and immune cells, the density of infiltrating immune cell populations, and their spatial pattern have been shown to be predictive for response to immunotherapy. These factors are currently being evaluated to determine whether they can guide treatment across different categories of immunotherapies (e.g., checkpoint inhibition, vaccination, CAR-T cell therapy, or combinations thereof). Multiplex chromogenic IHC assays were developed for PDL1/CD68/CD3 and FoxP3/PD-1/CD8 and single-stain IHC was used to detect cells that were positive for granzyme B. Image analysis were optimized to detect biomarker positive cells (e.g., PD-L1+, CD3-, CD68-), double positive cells (e.g., PD-L1+, CD3-, CD68+), negative cells, or percent of area positive for Granzyme B. Densities for each cell population were quantified and pathologist annotations were used to distinguish between tumor core and invasive margin regions. Machine learning with random forests and decision trees was used to automatically distinguish tumor and stroma compartments to evaluate differences in densities of infiltrating immune cells. Densities of the different cell populations and their spatial relationships were analyzed to assign cases to one of the following immune status categories: acquired immune resistance, immune tolerance, adaptive checkpoint inhibitor resistance (all three are subtypes of high immune cell density), impaired infiltration, immune ignorance, intrinsic checkpoint inhibitor resistance (subtypes of low immune cell density). NSCLC tissues were analyzed and examples of biomarker profiles for each category are shown. The distribution of immune categories between squamous and non-squamous NSCLC subtypes and a comparison of immune cell densities and spatial relationships are shown. We conclude that the IO panel can be used to establish standardized immune profiles in NCCLC. In the future, it can be used to search for novel prognostic and predictive signatures and to establish the prevalence of patients with defined biomarker profiles in different subsets of patients (e.g, different stages, morphologic subtypes, or mutational status). Citation Format: Lisa M. Dauffenbach, Christopher A. Kerfoot, Gela Sia, Anthony Masci, Johannes Zimmermann, Jan Lesniak, Alexei Budco, Svenja Lippok, Katrin Schneider, René Korn, Tobias Wiestler, Dasa Medrikova, Florian Leiß. Characterization of inflammatory cell patterns and densities using multiplex immunohistochemistry immuno-oncology assays [abstract]. In: Proceedings of the AACR-NCI-EORTC International Conference: Molecular Targets and Cancer Therapeutics; 2017 Oct 26-30; Philadelphia, PA. Philadelphia (PA): AACR; Mol Cancer Ther 2018;17(1 Suppl):Abstract nr B069.

Fault Tolerance using Adaptive Checkpoint in Cloud–An Approach

Fault Tolerance using Adaptive Checkpoint in Cloud–An Approach

Abstract LB-188: Selective targeting of SIRP alpha induces potent memory antitumor immune responses without presenting hematological toxicity

Abstract Targeting immune checkpoints of the adaptive immunity has shown great therapeutic efficacy to fight cancers, but in a limited proportion of patients. Myeloid cells represent the most abundant immune cell type in many solid tumors, and are often associated with a poor outcome. Interaction of SIRPalpha (SIRPα), expressed by myeloid cells, with the ubiquitous receptor CD47 is an important immune checkpoint of the innate response, involved in the regulation of macrophages, dendritic cells and neutrophils function (e.g. phagocytosis). Thus, combining immunotherapies targeting both adaptive and innate immune cells represents a promising therapeutic strategy against cancer. Since agents targeting CD47 (anti-CD47 or SIRPa-Fc) recently experienced hematological toxicity (anemia or thrombocytopenia), we evaluated the preclinical safety and efficacy of an antagonistic anti-SIRPa monoclonal antibody (mAb). Here, we found that administration of anti-SIRPa mAb at high dose (10 mg/kg) in healthy or tumor-bearing mice did not modify red blood cells and platelets numbers, hematocrit and hemoglobin levels, while in parallel anti-CD47 mAbs rapidly induced anemia within three days, owing to the high expression of CD47 on red blood cells. Next, we evaluated the therapeutic potential of antagonist anti-SIRPa mAbs in combination with adaptive immune checkpoint inhibitors (anti-PD-L1 mAb) or an adaptive immune checkpoint agonist (anti-4-1BB mAb) using an orthotopic hepatocellular carcinoma (HCC) preclinical model in immunocompetent mice. Monotherapy with antagonist anti-SIRPa mAbs prolonged survival in 25% of mice but did not induce remission (p<0.01). While PD-1 blockade alone was also poorly effective in this model (MST: 22 days, n=8), combination with SIRPα blockade induced durable remission in 60% of mice (p<0.05). Association of SIRPα blockade with 4-1BB agonist was highly efficient with 80% of long-term remission (p<0.01) while monotherapy with 4-1BB mAb led to tumor elimination in only 26% of mice (ns). Mice presenting a remission after selective SIRPα blockade in combination with PD-L1 or 4-1BB agents acquired a robust memory immune responses mediated, at least, by T lymphocytes since a second tumor challenge (performed up to one month after treatment withdrawal) was always rejected (p<0.01). In addition, adoptive transfer of T lymphocytes from cured mice in naïve untreated mice protected them from orthotopic HCC development. In conclusion, we showed that targeting selectively SIRPa is devoid of hematological toxicity and that combination of immunotherapies targeting both adaptive and innate immune cells is promising to generate robust antitumor memory immunity. Citation Format: Vanessa Gauttier, Sabrina Pengam, Sophie Conchon, Bernard Vanhove, Nicolas Poirier. Selective targeting of SIRP alpha induces potent memory antitumor immune responses without presenting hematological toxicity [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2017; 2017 Apr 1-5; Washington, DC. Philadelphia (PA): AACR; Cancer Res 2017;77(13 Suppl):Abstract nr LB-188. doi:10.1158/1538-7445.AM2017-LB-188

Optimizing checkpoint data placement with guaranteed burst buffer endurance in large-scale hierarchical storage systems

Non-volatile devices, such as SSDs, will be an integral part of the deepening storage hierarchy on large-scale HPC systems. These devices can be on the compute nodes as part of a distributed burst buffer service or they can be external. Wherever they are located in the hierarchy, one critical design issue is the SSD endurance under the write-heavy workloads, such as the checkpoint I/O for scientific applications. For these environments, it is widely assumed that checkpoint operations can occur once every 60 min and for each checkpoint step as much as half of the system memory can be written out. Unfortunately, for large-scale HPC applications, the burst buffer SSDs can be worn out much more quickly given the extensive amount of data written at every checkpoint step. One possible solution is to control the amount of data written by reducing the checkpoint frequency. However, a direct effect caused by reduced checkpoint frequency is the increased vulnerability window of system failures and therefore potentially wasted computation time, especially for large-scale compute jobs.In this paper, we propose a new checkpoint placement optimization model which collaboratively utilizes both the burst buffer and the parallel file system to store the checkpoints, with design goals of maximizing computation efficiency while guaranteeing the SSD endurance requirements. Moreover, we present an adaptive algorithm which can dynamically adjust the checkpoint placement based on the system’s dynamic runtime characteristics and continuously optimize the burst buffer utilization. The evaluation results show that by using our adaptive checkpoint placement algorithm we can guarantee the burst buffer endurance with at most 5% performance degradation per application and less than 3% for the entire system.

Adaptive Checkpoint Interval Algorithm Considering Task Deadline and Lifetime Reliability for Real-Time System

Abstract Checkpointing mechanism is used to tolerate the impact of transient faults by rollback operation. Recently, it has also been used as a mechanism to enhance system's lifetime by identifying and tolerating permanent fault 5,19,10,12. However, equidistant checkpoint interval may cause task deadline violation in the system. Here, we propose an adaptive checkpoint interval placement algorithm (ADeLiRACI) that meets all tasks deadline. The checkpoint intervals are adjusted to minimize the impact of stresses and permanent faults on the running hosts. This novel mechanism allows greater applicability in real time systems with hard deadline such as weather prediction, financial transactions etc. We compare the estimated completion time for increasing fault-rate in the system against five existing algorithms. For all applications, ADeLiRACI is able to meet the hard deadline along with enhancing lifetime reliability of the system.

An approach to fault tolerance in the cloud using the checkpointing technique

Reliability refers to the probability that a system will offer failure-free service for a specified period of time within the bounds of a specified environment. For the cloud, reliability is broadly a function of the reliability of four individual components: 1 the hardware and software facilities offered by providers; 2 the provider's personnel; 3 connectivity to the subscribed services; 4 the subscriber's personnel. It is too expensive to provide redundant alternative components for all the cloud components. To reduce the cost and to develop highly reliable cloud within the limited budget, we proposed in this paper a fault tolerant architecture to cloud computing that uses a dynamic and adaptive checkpoint mechanism to provide a reliable cloud computing system.

Fault Tolerant Architecture to Cloud Computing Using Adaptive Checkpoint

Cloud computing refers to both the applications delivered as services over the Internet and the hardware and systems software in the datacenters that provide those services. Failures of any type are common in current datacenters, partly due to the number of nodes. Fault tolerance has become a major task for computer engineers and software developers because the occurrence of faults increases the cost of using resources and to meet the user expectations, the most fundamental user expectation is, of course, that his or her application correctly finishes independent of faults in the node. This paper proposes a fault tolerant architecture to Cloud Computing that uses an adaptive Checkpoint mechanism to assure that a task running can correctly finish in spite of faults in the nodes in which it is running. The proposed fault tolerant architecture is simultaneously transparent and scalable.

Checkpoint allocation and release

Out-of-order speculative processors need a bookkeeping method to recover from incorrect speculation. In recent years, several microarchitectures that employ checkpoints have been proposed, either extending the reorder buffer or entirely replacing it. This work presents an in-dept-study of checkpointing in checkpoint-based microarchitectures, from the desired content of a checkpoint, via implementation trade-offs, and to checkpoint allocation and release policies. A major contribution of the article is a novel adaptive checkpoint allocation policy that outperforms known policies. The adaptive policy controls checkpoint allocation according to dynamic events, such as second-level cache misses and rollback history. It achieves 6.8% and 2.2% speedup for the integer and floating point benchmarks, respectively, and does not require a branch confidence estimator. The results show that the proposed adaptive policy achieves most of the potential of an oracle policy whose performance improvement is 9.8% and 3.9% for the integer and floating point benchmarks, respectively. We exploit known techniques for saving leakage power by adapting and applying them to checkpoint-based microarchitectures. The proposed applications combine to reduce the leakage power of the register file to about one half of its original value.

A-revolve: an adaptive memory-reduced procedure for calculating adjoints; with an application to computing adjoints of the instationary Navier–Stokes system

This article presents a low-storage and low-run-time approach for calculating numerical approximations of adjoint equations for the instationary Navier–Stokes equations with adaptive evaluation of the discretization step. It utilizes adaptive checkpointing. The amounts of memory reduction due to checkpointing and of the increase in run-time caused by repeated forward integration of the Navier–Stokes equations are reported. It is one result that memory reduction of two orders of magnitude only causes a slow down factor of 2–3 in run-time. It is a further result that the adaptive checkpointing for the instationary Navier–Stokes equations causes only a slight increase of the run-time compared to the static optimal checkpointing. The amounts of run-time increase caused by the adaptive checkpoint allocations compared with the static optimal checkpointing are reported as well.