Iterative Phase Optimization of Elementary Quantum Error Correcting Codes

Performing experiments on small-scale quantum computers is certainly a challenging endeavor. Many parameters need to be optimized to achieve high-fidelity operations. This can be done efficiently for operations acting on single qubits, as errors can be fully characterized. For multiqubit operations, though, this is no longer the case, as in the most general case, analyzing the effect of the operation on the system requires a full state tomography for which resources scale exponentially with the system size. Furthermore, in recent experiments, additional electronic levels beyond the two-level system encoding the qubit have been used to enhance the capabilities of quantum-information processors, which additionally increases the number of parameters that need to be controlled. For the optimization of the experimental system for a given task (e.g., a quantum algorithm), one has to find a satisfactory error model and also efficient observables to estimate the parameters of the model. In this manuscript, we demonstrate a method to optimize the encoding procedure for a small quantum error correction code in the presence of unknown but constant phase shifts. The method, which we implement here on a small-scale linear ion-trap quantum computer, is readily applicable to other AMO platforms for quantum-information processing.

Synthesis and characterization of cyclotriphosphazenes containing silicon as single solid-state precursors for the formation of silicon/phosphorus nanostructured materials

The synthesis and characterization of new organosilicon derivatives of N3P3Cl6, N3P3[NH(CH2)3Si(OEt)3]6 (1), N3P3[NH(CH2)3Si(OEt)3]3[NCH3(CH2)3CN]3 (2), and N3P3[NH(CH2)3Si(OEt)3]3[HOC6H4(CH2)CN]3 (3) are reported. Pyrolysis of 1, 2, and 3 in air and at several temperatures results in nanostructured materials whose composition and morphology depend on the temperature of pyrolysis and the substituents of the phosphazenes ring. The products stem from the reaction of SiO2 with P2O5, leading to either crystalline Si5(PO4)6O, SiP2O7 or an amorphous phase as the glass Si5(PO4)6O/3SiO2·2P2O5, depending on the temperature and nature of the trimer precursors. From 1 at 800 °C, core−shell microspheres of SiO2 coated with Si5(PO4)6O are obtained, while in other cases, mesoporous or dense structures are observed. Atomic force microscopy examination after deposition of the materials on monocrystalline silicon wafers evidences morphology strongly dependent on the precursors. Isolated islands of size ∼9 nm are observed from 1, whereas dense nanostructures with a mean height of 13 nm are formed from 3. Brunauer−Emmett−Teller measurements show mesoporous materials with low surface areas. The proposed growth mechanism involves the formation of cross-linking structures and of vacancies by carbonization of the organic matter, where the silicon compounds nucleate. Thus, for the first time, unique silicon nanostructured materials are obtained from cyclic phosphazenes containing silicon.

Phase Locked Loop and Modulo Games, The Dogma Loops; and “Finding Ibrida”

This dissertation consists of two independent musical compositions and an article detailing the process of the design and assembly of an electric guitar with particular emphasis on the carefully curated suite of embedded effects.

The first piece, 'Phase Locked Loop and Modulo Games' is scored for electric guitar and a single echo of equal volume less than a beat away. One could think of the piece as a 15 minute canon at the unison at the dotted eighth note (or at times the quarter or triplet-quarter), however the compositional motivation is more about weaving a composite texture between the guitar and its echo that is, while in theory extremely contrapuntal, in actuality is simply a single [superhuman] melodic line.

The second piece, 'The Dogma Loops' picks up a few compositional threads left by ‘Phase Locked Loop’ and weaves them into an entirely new tapestry. 'Phase Locked Loop' is motivated by the creation of a complex musical composite that is for the most part electronically transparent. 'The Dogma Loops' questions that same notion of composite electronic complexity by essentially asking a question: "what are the inputs to an interactive electronic system that create the most complex outputs via the simplest musical means possible?"

'The Dogma Loops' is scored for Electric Guitar (doubling on Ukulele), Violin and Violoncello. All of the principal instruments require an electronic pickup (except the Uke). The work is in three sections played attacca; [Automation Games], [Point of Origin] and [Cloning Vectors].

The third and final component of the document is the article 'Finding Ibrida.' This article details the process of the design and assembly of an electric guitar with integrated effects, while also providing the deeper context (conceptual and technical) which motivated the efforts and informed the challenges to hybridize the various technologies (tubes, transistors, digital effects and a microcontroller subsystem). The project was motivated by a desire for rigorous technical and hands-on engagement with analog signal processing as applied to the electric guitar. ‘Finding Ibrida’ explores sound, some myths and lore of guitar tech and the history of electric guitar distortion and its culture of sonic exploration.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Safety and efficacy of ledipasvir-sofosbuvir in black patients with hepatitis C virus infection: A retrospective analysis of phase 3 data.

UNLABELLED: Black patients chronically infected with genotype 1 hepatitis C virus (HCV) have historically had lower rates of response to interferon-based treatment than patients of other races. In the phase 3 ION program, the single-tablet regimen of the NS5A inhibitor ledipasvir and NS5B nucleotide polymerase inhibitor sofosbuvir was shown to be safe and highly effective in the general population. The aim of this study was to evaluate the safety and efficacy of ledipasvir/sofosbuvir in black patients using data from the three open-label ION clinical trials, which evaluated the safety and efficacy of 8, 12, and 24 weeks of ledipasvir/sofosbuvir with or without ribavirin for the treatment of treatment-naïve and treatment-experienced patients with genotype 1 HCV, including those with compensated cirrhosis. The primary endpoint was sustained virologic response at 12 weeks after the end of therapy (SVR12). For our analysis, rates of SVR12, treatment-emergent adverse events, and graded laboratory abnormalities were analyzed in black versus non-black patients. Of the 1949 patients evaluated, 308 (16%) were black. On average, black patients were older, had higher body mass index, were more likely to be IL28B non-CC, and had a lower serum alanine aminotransferase at baseline than non-black patients. Overall, 95% of black and 97% of non-black patients achieved SVR12. The rate of relapse was 3% in black patients as compared with 2% in non-black patients. The most common adverse events included fatigue, headache, nausea, and insomnia. The majority of adverse events occurred more frequently in the ribavirin-containing arms of the studies. No differences were observed in overall safety by race. CONCLUSION: A once-daily dosage of ledipasvir/sofosbuvir was similarly effective in black and non-black patients with genotype 1 HCV infection. The addition of ribavirin did not appear to increase SVR12 but was associated with higher rates of adverse events.

Ground and Electronic Excited States from Pairing Matrix Fluctuation and Particle-Particle Random Phase Approximation

The accurate description of ground and electronic excited states is an important and challenging topic in quantum chemistry. The pairing matrix fluctuation, as a counterpart of the density fluctuation, is applied to this topic. From the pairing matrix fluctuation, the exact electron correlation energy as well as two electron addition/removal energies can be extracted. Therefore, both ground state and excited states energies can be obtained and they are in principle exact with a complete knowledge of the pairing matrix fluctuation. In practice, considering the exact pairing matrix fluctuation is unknown, we adopt its simple approximation --- the particle-particle random phase approximation (pp-RPA) --- for ground and excited states calculations. The algorithms for accelerating the pp-RPA calculation, including spin separation, spin adaptation, as well as an iterative Davidson method, are developed. For ground states correlation descriptions, the results obtained from pp-RPA are usually comparable to and can be more accurate than those from traditional particle-hole random phase approximation (ph-RPA). For excited states, the pp-RPA is able to describe double, Rydberg, and charge transfer excitations, which are challenging for conventional time-dependent density functional theory (TDDFT). Although the pp-RPA intrinsically cannot describe those excitations excited from the orbitals below the highest occupied molecular orbital (HOMO), its performances on those single excitations that can be captured are comparable to TDDFT. The pp-RPA for excitation calculation is further applied to challenging diradical problems and is used to unveil the nature of the ground and electronic excited states of higher acenes. The pp-RPA and the corresponding Tamm-Dancoff approximation (pp-TDA) are also applied to conical intersections, an important concept in nonadiabatic dynamics. Their good description of the double-cone feature of conical intersections is in sharp contrast to the failure of TDDFT. All in all, the pairing matrix fluctuation opens up new channel of thinking for quantum chemistry, and the pp-RPA is a promising method in describing ground and electronic excited states.

Spatiotemporal Dynamics of CaMKI During Structural Plasticity of Single Dendritic Spines

Multifunctional calcium/calmodulin dependent protein kinases (CaMKs) are key regulators of spine structural plasticity and long-term potentiation (LTP) in neurons. CaMKs have promiscuous and overlapping substrate recognition motifs, and are distinguished in their regulatory role based on differences in the spatiotemporal dynamics of activity. While the function and activity of CaMKII in synaptic plasticity has been extensively studied, that of CaMKI, another major class of CaMK required for LTP, still remain elusive.

Here, we develop a Förster’s Resonance Energy Transfer (FRET) based sensor to measure the spatiotemporal activity dynamics of CaMK1. We monitored CaMKI activity using 2-photon fluorescence lifetime imaging, while inducing LTP in single dendritic spines of rat (Rattus Norvegicus, strain Sprague Dawley) hippocampal CA1 pyramidal neurons using 2-photon glutamate uncaging. Using RNA-interference and pharmacological means, we also characterize the role of CaMKI during spine structural plasticity.

We found that CaMKI was rapidly and transiently activated with a rise time of ~0.3 s and decay time of ~1 s in response to each uncaging pulse. Activity of CaMKI spread out of the spine. Phosphorylation of CaMKI by CaMKK was required for this spreading and for the initial phase of structural LTP. Combined with previous data showing that CaMKII is restricted to the stimulated spine and required for long-term maintenance of structural LTP, these results suggest that CaMK diversity allows the same incoming signal – calcium – to independently regulate distinct phases of LTP by activating different CaMKs with distinct spatiotemporal dynamics.

Using phase-space localized basis functions to obtain vibrational energies of molecules

For decades scientists have attempted to use ideas of classical mechanics to choose basis functions for calculating spectra. The hope is that a classically-motivated basis set will be small because it covers only the dynamically important part of phase space. One popular idea is to use phase space localized (PSL) basis functions. This thesis improves on previous efforts to use PSL functions and examines the usefulness of these improvements. Because the overlap matrix, in the matrix eigenvalue problem obtained by using PSL functions with the variational method, is not an identity, it is costly to use iterative methods to solve the matrix eigenvalue problem. We show that it is possible to circumvent the orthogonality (overlap) problem and use iterative eigensolvers. We also present an altered method of calculating the matrix elements that improves the performance of the PSL basis functions, and also a new method which more efficiently chooses which PSL functions to include. These improvements are applied to a variety of single well molecules. We conclude that for single minimum molecules, the PSL functions are inferior to other basis functions. However, the ideas developed here can be applied to other types of basis functions, and PSL functions may be useful for multi-well systems.

ARB: Phase II window of opportunity study of short-term preoperative treatment with enzalutamide in ER-positive and triple-negative breast cancer

The androgen receptor (AR) is expressed in 60-80% of breast cancers (BC) across all molecular phenotypes, with a higher incidence in oestrogen receptor positive (ER+) BC compared to ER negative tumours. In ER+ disease, AR-expression has been linked to endocrine resistance which might be reversed with combined treatment targeting ER and AR. In triple negative BCs (TNBC), preclinical and clinical investigations have described a subset of patients that express the AR and are sensitive to androgen blockade, providing a novel therapeutic target. Enzalutamide, a potent 2nd generation anti-androgen, has demonstrated substantial preclinical and clinical anti-tumour activity in AR+ breast cancer. Short-term preoperative window of opportunity studies are a validated strategy for novel treatments to provide proof-of-concept and define the most appropriate patient population by directly assessing treatment effects in tumour tissue before and after treatment. The ARB study aims to assess the anti-tumour effects of enzalutamide in early ER+ breast cancer and TNBC, to identify the optimal target population for further studies and to directly explore the biologic effects of enzalutamide on BC and stromal cells. Methods: ARB is an international, investigator sponsored WOO phase II study in women with newly diagnosed primary ER+ BC or AR+ TNBC of ≥ 1cm. The study has two cohorts. In the ER+ cohort, postmenopausal patients will be randomised 2:1 to receive either enzalutamide (160mg OD) plus exemestane (50mg OD) or exemestane (25mg OD). In the TNBC cohort, AR+ will receive single agent treatment with enzalutamide (160mg OD). Study treatment is planned for 15–29 days, followed by surgery or neo-adjuvant therapy. Tissue and blood samples are collected before treatment and on the last day of study treatment. The primary endpoint is inhibition of tumour-cell proliferation, as measured by change in Ki67 expression, determined centrally by 2 investigators. Secondary endpoints include induction of apoptosis (Caspase3), circulating hormone levels and safety. ARB aims to recruit ≈235 patients from ≈40 sites in the UK, Germany, Spain and USA. The study is open to recruitment.

HER2 in high-risk rectal cancer patients treated in EXPERT-C, a randomized phase II trial of neoadjuvant capecitabine and oxaliplatin (CAPOX) and chemoradiotherapy (CRT) with or without cetuximab.

BACKGROUND: HER2 is an established therapeutic target in breast and gastric cancers. The role of HER2 in rectal cancer is unclear, as conflicting data on the prevalence of HER2 expression in this disease have been reported. We evaluated the prevalence of HER2 and its impact on the outcome of high-risk rectal cancer patients treated with neoadjuvant CAPOX and CRT±cetuximab in the EXPERT-C trial. PATIENTS AND METHODS: Eligible patients with available tumour tissue for HER2 analysis were included. HER2 expression was determined by immunohistochemistry (IHC) in pre-treatment biopsies and/or surgical specimens (score 0-3+). Immunostaining was scored according to the consensus panel recommendations on HER2 scoring for gastric cancer. Tumours with equivocal IHC result (2+) were tested for HER2 amplification by D-ISH. Tumours with IHC 3+ or D-ISH ratio ≥2.0 were classified as HER2+. The impact of HER2 on primary and secondary end points of the study was analysed. RESULTS: Of 164 eligible study patients, 104 (63%) biopsy and 114 (69%) surgical specimens were available for analysis. Only 3 of 104 (2.9%) and 3 of 114 (2.6%) were HER2+, respectively. In 77 patients with paired specimens, concordance for HER2 status was found in 74 (96%). Overall, 141 patients were assessable for HER2 and 6 out of 141 (4.3%) had HER2 overexpression and/or amplification. The median follow-up was 58.6 months. HER2 was not associated with a difference in the outcome for any of the study end points, including in the subset of 90 KRAS/BRAF wild-type patients treated±cetuximab. CONCLUSIONS: Based on the low prevalence of expression as recorded in the EXPERT-C trial, HER2 does not appear to represent a useful therapeutic target in high-risk rectal cancer. However, the role of HER2 as a potential predictive biomarker of resistance to anti-EGFR-based treatments and a therapeutic target in anti-EGFR refractory metastatic colorectal cancer (CRC) warrants further investigation. TRIAL REGISTRATION: ISRCTN Register: 99828560.

Cabazitaxel for Hormone-Relapsed Metastatic Prostate Cancer Previously Treated With a Docetaxel-Containing Regimen: An Evidence Review Group Perspective of a NICE Single Technology Appraisal

As part of its single technology appraisal (STA) process, the National Institute for Health and Care Excellence (NICE) invited the company that manufactures cabazitaxel (Jevtana(®), Sanofi, UK) to submit evidence for the clinical and cost effectiveness of cabazitaxel for treatment of patients with metastatic hormone-relapsed prostate cancer (mHRPC) previously treated with a docetaxel-containing regimen. The School of Health and Related Research Technology Appraisal Group at the University of Sheffield was commissioned to act as the independent Evidence Review Group (ERG). The ERG produced a critical review of the evidence for the clinical and cost effectiveness of the technology based upon the company's submission to NICE. Clinical evidence for cabazitaxel was derived from a multinational randomised open-label phase III trial (TROPIC) of cabazitaxel plus prednisone or prednisolone compared with mitoxantrone plus prednisone or prednisolone, which was assumed to represent best supportive care. The NICE final scope identified a further three comparators: abiraterone in combination with prednisone or prednisolone; enzalutamide; and radium-223 dichloride for the subgroup of people with bone metastasis only (no visceral metastasis). The company did not consider radium-223 dichloride to be a relevant comparator. Neither abiraterone nor enzalutamide has been directly compared in a trial with cabazitaxel. Instead, clinical evidence was synthesised within a network meta-analysis (NMA). Results from TROPIC showed that cabazitaxel was associated with a statistically significant improvement in both overall survival and progression-free survival compared with mitoxantrone. Results from a random-effects NMA, as conducted by the company and updated by the ERG, indicated that there was no statistically significant difference between the three active treatments for both overall survival and progression-free survival. Utility data were not collected as part of the TROPIC trial, and were instead taken from the company's UK early access programme. Evidence on resource use came from the TROPIC trial, supplemented by both expert clinical opinion and a UK clinical audit. List prices were used for mitoxantrone, abiraterone and enzalutamide as directed by NICE, although commercial in-confidence patient-access schemes (PASs) are in place for abiraterone and enzalutamide. The confidential PAS was used for cabazitaxel. Sequential use of the advanced hormonal therapies (abiraterone and enzalutamide) does not usually occur in clinical practice in the UK. Hence, cabazitaxel could be used within two pathways of care: either when an advanced hormonal therapy was used pre-docetaxel, or when one was used post-docetaxel. The company believed that the former pathway was more likely to represent standard National Health Service (NHS) practice, and so their main comparison was between cabazitaxel and mitoxantrone, with effectiveness data from the TROPIC trial. Results of the company's updated cost-effectiveness analysis estimated a probabilistic incremental cost-effectiveness ratio (ICER) of £45,982 per quality-adjusted life-year (QALY) gained, which the committee considered to be the most plausible value for this comparison. Cabazitaxel was estimated to be both cheaper and more effective than abiraterone. Cabazitaxel was estimated to be cheaper but less effective than enzalutamide, resulting in an ICER of £212,038 per QALY gained for enzalutamide compared with cabazitaxel. The ERG noted that radium-223 is a valid comparator (for the indicated sub-group), and that it may be used in either of the two care pathways. Hence, its exclusion leads to uncertainty in the cost-effectiveness results. In addition, the company assumed that there would be no drug wastage when cabazitaxel was used, with cost-effectiveness results being sensitive to this assumption: modelling drug wastage increased the ICER comparing cabazitaxel with mitoxantrone to over £55,000 per QALY gained. The ERG updated the company's NMA and used a random effects model to perform a fully incremental analysis between cabazitaxel, abiraterone, enzalutamide and best supportive care using PASs for abiraterone and enzalutamide. Results showed that both cabazitaxel and abiraterone were extendedly dominated by the combination of best supportive care and enzalutamide. Preliminary guidance from the committee, which included wastage of cabazitaxel, did not recommend its use. In response, the company provided both a further discount to the confidential PAS for cabazitaxel and confirmation from NHS England that it is appropriate to supply and purchase cabazitaxel in pre-prepared intravenous-infusion bags, which would remove the cost of drug wastage. As a result, the committee recommended use of cabazitaxel as a treatment option in people with an Eastern Cooperative Oncology Group performance status of 0 or 1 whose disease had progressed during or after treatment with at least 225 mg/m(2) of docetaxel, as long as it was provided at the discount agreed in the PAS and purchased in either pre-prepared intravenous-infusion bags or in vials at a reduced price to reflect the average per-patient drug wastage.

Real-Time Visual SLAM Using Pre - Existing Floor Lines as Landmarks and a Single Camera

SANTANA, André M.; SANTIAGO, Gutemberg S.; MEDEIROS, Adelardo A. D. Real-Time Visual SLAM Using Pre-Existing Floor Lines as Landmarks and a Single Camera. In: CONGRESSO BRASILEIRO DE AUTOMÁTICA, 2008, Juiz de Fora, MG. Anais... Juiz de Fora: CBA, 2008.

Cholecystectomy by single incision laparoscopic surgery (SILS): early experience and technique standardization

Single Incision Laparoscopic Surgery (SILS) is a recent surgical technique, first described in the 1990s. Its aim is to optimize the esthetic result offered by laparoscopy by minimizing the number of abdominal incisions. Various preliminary studies have been carried out on the application of SILS, especially in cholecystectomy and appendectomy. This study evaluates the preliminary results of cholecystectomy by SILS (SILS™ Port) conducted between October 2009 and February 2011 on 21 patients (4 men and 17 women) with a mean age of 49.9 years and a mean Body Mass Index (BMI) of 22.8. All patients were treated by the same team, which had previously undergone six months’ simulator training. There were two main selection criteria, both evaluated intraoperatively: absence of adhesions and of significant inflammatory sequelae from previous cholecystitis; and suitable distance between gallbladder and SILS access port. Conversion to traditional laparoscopy was necessary in just two cases, while an accessory trocar was introduced in another two cases. Conversion to open surgery was not necessary in any case. One case of SILS cholecystectomy was complicated by postoperative bile leakage, which was treated conservatively, as the fistula had a low output. The mean duration of hospitalization was 3.6 days. This preliminary experience led us to conclude that SILS is safe and highly satisfactory in the postoperative phase, thanks to the reduced need for painkillers and the improved esthetic result.

3531: Neoadjuvant radiotherapy (RT) combined with capecitabine (Cape) and sorafenib (Sor) in patients (pts) with locally advanced, k-ras-mutated rectal cancer (LARC): A phase I/II trial SAKK 41/08

Background: K-ras mutation is found in up to 40% of LARC. Sor is a multitarget tyrosine kinase inhibitor including raf and VEGFR and has demonstrated radiosensitizing effects. Sor might improve outcome of standard preoperative radio-chemotherapy in patients with k-ras mutated LARC. Methods: Pts with k-ras mutated T3-4 and/or N+, M0 disease by MRI were included. Recommended doses from phase I part consisted of RT 1.8 Gy/day x25 with Cape 825mg/m2bid x 33 in combination with Sor 400mg/d. The primary endpoint for the phase II part was pathological complete response (pCR) prospectively defined as grade 3 (near complete regression) or 4 (complete regression) in the histological grading system according to Dworak (DC). A pCR rate of 8% or lower was considered uninteresting and of 22% or higher was promising. Secondary endpoints included sphincter preservation, R0 resection, downstaging and safety. Results: 54 pts were treated in 18 centers in Switzerland und Hungary, 40 pts were included into the single arm phase II part. Median dose intensity per day was 100.0% for RT, 98.6% for Cape and 100.0% for Sor respectively. pCR rate was 60.0% (95%CI: 43.3%, 75.1%) by central independent pathological review (15.0% DC grade 4; 45.0% DC grade 3). Sphincter preservation was achieved in 89.5%, R0 resection in 94.7% and downstaging in 81.6% of the pts. The most common grade 3 toxicities included diarrhea (15.0%), skin toxicity outside of the RT field (12.5%), pain (7.5%), skin toxicity in RT field, proctitis, fatigue and cardiac ischemia (each 5.0%). Laboratory AEs grade 3/4 were neutropenia (1 pt grade 4; 1 grade 3), creatinine elevation (1 pt grade 3). Conclusions: The combination of Sor to standard RCT with Cape in k-ras mutated LARC tumors is highly active with acceptable toxicity and deserves further investigation.

Tile-Based Two-Dimensional Phase Unwrapping for Digital Holography Using a Modular Framework

A variety of physical and biomedical imaging techniques, such as digital holography, interferometric synthetic aperture radar (InSAR), or magnetic resonance imaging (MRI) enable measurement of the phase of a physical quantity additionally to its amplitude. However, the phase can commonly only be measured modulo 2π, as a so called wrapped phase map. Phase unwrapping is the process of obtaining the underlying physical phase map from the wrapped phase. Tile-based phase unwrapping algorithms operate by first tessellating the phase map, then unwrapping individual tiles, and finally merging them to a continuous phase map. They can be implemented computationally efficiently and are robust to noise. However, they are prone to failure in the presence of phase residues or erroneous unwraps of single tiles. We tried to overcome these shortcomings by creating novel tile unwrapping and merging algorithms as well as creating a framework that allows to combine them in modular fashion. To increase the robustness of the tile unwrapping step, we implemented a model-based algorithm that makes efficient use of linear algebra to unwrap individual tiles. Furthermore, we adapted an established pixel-based unwrapping algorithm to create a quality guided tile merger. These original algorithms as well as previously existing ones were implemented in a modular phase unwrapping C++ framework. By examining different combinations of unwrapping and merging algorithms we compared our method to existing approaches. We could show that the appropriate choice of unwrapping and merging algorithms can significantly improve the unwrapped result in the presence of phase residues and noise. Beyond that, our modular framework allows for efficient design and test of new tile-based phase unwrapping algorithms. The software developed in this study is freely available.