Realizing repeated quantum error correction in a distance-three surface code.

Quantum computers hold the promise of solving computational problems that are intractable using conventional methods1. For fault-tolerant operation, quantum computers must correct errors occurring owing to unavoidable decoherence and limited control accuracy2. Here we demonstrate quantum error correction using the surface code, which is known for its exceptionally high tolerance to errors3-6. Using 17 physical qubits in a superconducting circuit, we encode quantum information in a distance-three logical qubit, building on recent distance-two error-detection experiments7-9. In an error-correction cycle taking only 1.1 µs, we demonstrate the preservation of four cardinal states of the logical qubit. Repeatedly executing the cycle, we measure and decode both bit-flip and phase-flip error syndromes using a minimum-weight perfect-matching algorithm in an error-model-free approach and apply corrections in post-processing. We find a low logical error probability of 3% per cycle when rejecting experimental runs in which leakage is detected. The measured characteristics of our device agree well with a numerical model. Our demonstration of repeated, fast and high-performance quantum error-correction cycles, together with recent advances in ion traps10, support our understanding that fault-tolerant quantum computation will be practically realizable.

Observation of quantized conductance in neutral matter.

In transport experiments, the quantum nature of matter becomes directly evident when changes in conductance occur only in discrete steps, with a size determined solely by Planck's constant h. Observations of quantized steps in electrical conductance have provided important insights into the physics of mesoscopic systems and have allowed the development of quantum electronic devices. Even though quantized conductance should not rely on the presence of electric charges, it has never been observed for neutral, massive particles. In its most fundamental form, it requires a quantum-degenerate Fermi gas, a ballistic and adiabatic transport channel, and a constriction with dimensions comparable to the Fermi wavelength. Here we report the observation of quantized conductance in the transport of neutral atoms driven by a chemical potential bias. The atoms are in an ultraballistic regime, where their mean free path exceeds not only the size of the transport channel, but also the size of the entire system, including the atom reservoirs. We use high-resolution lithography to shape light potentials that realize either a quantum point contact or a quantum wire for atoms. These constrictions are imprinted on a quasi-two-dimensional ballistic channel connecting the reservoirs. By varying either a gate potential or the transverse confinement of the constrictions, we observe distinct plateaux in the atom conductance. The conductance in the first plateau is found to be equal to the universal conductance quantum, 1/h. We use Landauer's formula to model our results and find good agreement for low gate potentials, with all parameters determined a priori. Our experiment lets us investigate quantum conductors with wide control not only over the channel geometry, but also over the reservoir properties, such as interaction strength, size and thermalization rate.

Lung Contusion in Polytrauma: An Analysis of the TraumaRegister DGU.

BACKGROUND: Thorax trauma frequently occurs in which injuries to the bony chest, lung contusions (LCs), and others are diagnosed. The significance of this violation is described very differently and is mostly based on monocentric data. METHODS: A retrospective analysis of the TraumaRegister DGU® (TR-DGU) dataset (Project 2014-062) was performed between 2009 and 2014 (injury severity score [ISS] ≥ 16, primary admission to a trauma center, no isolated traumatic brain injury). Patients with LC (Abbreviated Injury Scale [AIS] 3 + 4) were compared with the control group, and an analysis of different age groups was performed. RESULTS: A total of 49,567 patients were included, thereunder 14,521 (29.3%) without relevant thoracic trauma (TT); 95.9% blunt traumas. 18,892 patients (38.1%) had LC and 14,008 (28.3%) had severe LC with AIS 3 + 4; thereunder 72.7% males. For severe LC, the average age was the lowest (44.7 ± 19.7 years) and ISS the highest (30.4 ± 12.1 points).Intubation, intensive care, (multi-) organ failure, sepsis, and extrathoracic injuries were most common in severe LC. Shock, chest tubes, further thoracic injuries, and patient death occurred most frequently in TT without LC.Younger patients showed a higher incidence of LC than the older ones; however, high patient age was a highly significant risk factor for the development of complications and poor outcome. CONCLUSION: Since LC was present in almost 40% of the severely injured and was related to higher morbidity, LC should be detected and managed at the earliest possible time. Proper follow-ups employing chest X-rays and computed tomography (CT) scans are recommended.

Mapping out spin and particle conductances in a quantum point contact.

We study particle and spin transport in a single-mode quantum point contact, using a charge neutral, quantum degenerate Fermi gas with tunable, attractive interactions. This yields the spin and particle conductance of the point contact as a function of chemical potential or confinement. The measurements cover a regime from weak attraction, where quantized conductance is observed, to the resonantly interacting superfluid. Spin conductance exhibits a broad maximum when varying the chemical potential at moderate interactions, which signals the emergence of Cooper pairing. In contrast, the particle conductance is unexpectedly enhanced even before the gas is expected to turn into a superfluid, continuously rising from the plateau at [Formula: see text] for weak interactions to plateau-like features at nonuniversal values as high as [Formula: see text] for intermediate interactions. For strong interactions, the particle conductance plateaus disappear and the spin conductance gets suppressed, confirming the spin-insulating character of a superfluid. Our observations document the breakdown of universal conductance quantization as many-body correlations appear. The observed anomalous quantization challenges a Fermi liquid description of the normal phase, shedding new light on the nature of the strongly attractive Fermi gas.

Observing the drop of resistance in the flow of a superfluid Fermi gas.

The ability of particles to flow with very low resistance is characteristic of superfluid and superconducting states, leading to their discovery in the past century. Although measuring the particle flow in liquid helium or superconducting materials is essential to identify superfluidity or superconductivity, no analogous measurement has been performed for superfluids based on ultracold Fermi gases. Here we report direct measurements of the conduction properties of strongly interacting fermions, observing the well-known drop in resistance that is associated with the onset of superfluidity. By varying the depth of the trapping potential in a narrow channel connecting two atomic reservoirs, we observed variations of the atomic current over several orders of magnitude. We related the intrinsic conduction properties to the thermodynamic functions in a model-independent way, by making use of high-resolution in situ imaging in combination with current measurements. Our results show that, as in solid-state systems, current and resistance measurements in quantum gases provide a sensitive probe with which to explore many-body physics. Our method is closely analogous to the operation of a solid-state field-effect transistor and could be applied as a probe for optical lattices and disordered systems, paving the way for modelling complex superconducting devices.

Age Distribution and Concomitant Injuries in Pulmonary Contusion: An Analysis Based on Routine Data.

BACKGROUND: As the population ages, low-energy thoracic injuries are becoming increasingly relevant in individual injuries, particularly pulmonary contusions (PCs) and their common concomitant injuries. The objective of this study was to determine the prevalence and age distribution of thoracic trauma, especially PC, to make conclusions about common secondary diagnoses and developments in management. METHODS: A retrospective analysis of 209,820 cases, based on German routine data from the years 2009 to 2015, with a main diagnosis (MD) or secondary diagnosis (SD) of thoracic trauma (S27 according to ICD-10) was performed. The entire patient collective with a MD of S27 was examined as well as those with PCs (S27.31). RESULTS: In all 61,016 patients with a MD of S27, 7,558 (12.4%) had a MD of PC and among the 148,804 patients with a SD of S27, 58,247 patients (39.1%) had a SD of PC. PC occurs mostly in the age groups of 20 to 25, 45 to 50, and 70 to 75 years. The proportion of older people tends to be increasing. The most concomitant thoracic injuries were serial rib fractures (27.1%), pneumothorax (11.9%), and sternum fractures (6.2%). Computed tomography scan is the most common diagnostic tool in PC (MD >80%, SD >60%). Therapeutically, intensive care (>50%) and chest drainage are most important (MD: 12.5%, SD: 60.1%), while operative measures are rare (≤ 4%). CONCLUSION: PC shows a marked increase in the incidence, especially in older patients and as a companion diagnosis in thoracic injuries. It should be diagnosed early as well as its concomitant injuries to avoid complications.

Analysis on the Age Distribution of Sternum Fractures.

BACKGROUND: Sternum fractures (SFs) are described as a rare entity of bony fractures. Various accident mechanisms may cause SF such as the direct impact of traffic accidents and also by indirect mechanisms within the framework of falls. Osteoporotic fractures also play an increasing role in SF, but no reliable data on the age distribution of SF in a representative collective have been published so far. MATERIAL AND METHODS: The age distribution of all inpatients treated with SF (S22.2) in Germany from 2005 to 2012 using diagnosis-related group-based routine data was evaluated. Various accident statistics are included in the interpretation of age peaks. RESULTS: A total of 47,893 patients (24,960 as main diagnosis and 22,933 as secondary diagnosis) were included in the study. SF is a rarity in childhood, with a share of 1.83% before the age of 16 years, followed by a sudden increase in the frequency up to the age of 20 years. A decrease in the frequency is observed up to the age of 35 years before it increases again to the age of 75 years. Three age peaks can be observed at 18, 55, and 75 years. Those who are older than 65 years account for 43.3% of total SF. DISCUSSION AND CONCLUSION: The first age summit after the age of 16 years shows an identical course to the frequency of traffic accidents of this age group, as well as the decline to the fourth decade and the subsequent resurgence up to the fifth decade. After 65 years, the incidence of accidents increases, in particular, the risk of falling in elderly people. In the context of a weaker bone structure, low falls are a common course for fragility fractures. The present analysis of routines shows for the first time the age distribution of the SF taking into account all hospital cases of the observation period.

Scanning Gate Microscope for Cold Atomic Gases.

We present a scanning probe microscopy technique for spatially resolving transport in cold atomic gases, in close analogy with scanning gate microscopy in semiconductor physics. The conductance of a quantum point contact connected to two atomic reservoirs is measured in the presence of a tightly focused laser beam acting as a local perturbation that can be precisely positioned in space. By scanning its position and recording the subsequent variations of conductance, we retrieve a high-resolution map of transport through a quantum point contact. We demonstrate a spatial resolution comparable to the extent of the transverse wave function of the atoms inside the channel and a position sensitivity below 10 nm. Our measurements agree well with an analytical model and ab initio numerical simulations, allowing us to identify a regime in transport where tunneling dominates over thermal effects. Our technique opens new perspectives for the high-resolution observation and manipulation of cold atomic gases.

Concomitant Sternal Fracture in Flail Chest: An Analysis of 21,741 Polytrauma Patients from the TraumaRegister DGU®.

Background Isolated sternal fractures (SFs) rarely show complications, but their influence in a thorax trauma of the seriously injured still remains unclear. Methods A retrospective analysis of the TraumaRegister DGU® was performed involving the years 2009 to 2013 (Injury Severity Score [ISS] ≥ 16, primary admission to a trauma center). Cohort formation: Unilateral and bilateral flail chest (FC) injuries with and without a concomitant SF, respectively. Results In total, 21,741 patients (25% female) met the inclusion criteria, with 3,492 (16.1%) showing SF. Unilateral FC patients were on average 53.6 ± 18.4 years old, and bilateral FC patients were on average 55.2 ± 17.7 years old. The ISS in unilateral FC and bilateral FC amounted to 31.2 ± 13.0 and 43.4 ± 13.1 points, respectively. FC with an SF occurred more frequently as an injury to car occupants and less frequently as an injury to motorcyclists or in injuries due to falls. Conclusion Patients with an SF additional to an FC had longer hospital and intensive care unit stays and were longer artificially respirated than those patients without an SF. SF indicates possible cardiac and thoracic spine injuries.

Acute Effects of Lateral Thigh Foam Rolling on Arterial Tissue Perfusion Determined by Spectral Doppler and Power Doppler Ultrasound.

Hotfiel, T, Swoboda, B, Krinner, S, Grim, C, Engelhardt, M, Uder, M, and Heiss, R. Acute effects of lateral thigh foam rolling on arterial tissue perfusion determined by spectral Doppler and power Doppler ultrasound. J Strength Cond Res 31(4): 893-900, 2017-Foam rolling has been developed as a popular intervention in training and rehabilitation. However, evidence on its effects on the cellular and physiological level is lacking. The aim of this study was to assess the effect of foam rolling on arterial blood flow of the lateral thigh. Twenty-one healthy participants (age, 25 ± 2 years; height, 177 ± 9 cm; body weight, 74 ± 9 kg) were recruited from the medical and sports faculty. Arterial tissue perfusion was determined by spectral Doppler and power Doppler ultrasound, represented as peak flow (Vmax), time average velocity maximum (TAMx), time average velocity mean (TAMn), and resistive index (RI), and with semiquantitative grading that was assessed by 4 blindfolded investigators. Measurement values were assessed under resting conditions and twice after foam rolling exercises of the lateral thigh (0 and 30 minutes after intervention). The trochanteric region, mid portion, and distal tibial insertion of the lateral thigh were representative for data analysis. Arterial blood flow of the lateral thigh increased significantly after foam rolling exercises compared with baseline (p ≤ 0.05). We detected a relative increase in Vmax of 73.6% (0 minutes) and 52.7% (30 minutes) (p < 0.001), in TAMx of 53.2% (p < 0.001) and 38.3% (p = 0.002), and in TAMn of 84.4% (p < 0.001) and 68.2% (p < 0.001). Semiquantitative power Doppler scores at all portions revealed increased average grading of 1.96 after intervention and 2.04 after 30 minutes compared with 0.75 at baseline. Our results may contribute to the understanding of local physiological reactions to self-myofascial release.

Antibacterial Effect of a 4x Cu-TiO2 Coating Simulating Acute Periprosthetic Infection-An Animal Model.

The purpose of our study was to investigate the antibacterial effect of a spacer (Ti6Al4V) coated with 4x Cu-TiO2 in an animal model simulating an acute periprosthetic infection by Staphylococcus aureus. Ti6Al4 bolts contaminated with Staphylococcus aureus were implanted into the femoral condyle of rabbits (n = 36) divided into 3 groups. After one week in group 1 (control) the bolts were removed without any replacement. In group2 Ti6Al4V bolts with a 4x Cu-TiO2 coating and in group 3 beads of a gentamicin-PMMA chain were imbedded into the borehole. Microbiological investigation was performed at the primary surgery, at the revision surgery and after scarification of the rabbits 3 weeks after the first surgery. Blood tests were conducted weekly. The initial overall infection rate was 88.9%. In group 2 and 3 a significant decrease of the infection rate was shown in contrast to the control group. The C-reactive protein (CRP) levels declined one week after the first surgery except in the control group where the CRP level even increased. This is the first in vivo study that demonstrated the antibacterial effects of a fourfold Cu-TiO2 coating. For the future, the coating investigated could be a promising option in the treatment of implant-associated infections.

The Operative Management of Flail Chest Injuries with Concomitant Sternal Fracture.

Background: Flail Chest Injuries (FCI) are one of the most severe thoracic injuries. Moreover, an additional sternal fracture (SF) even worsens the outcome, such as the duration of mechanical ventilation, therefore an surgical fixation of the fractures could be considered in certain cases to improve the weaning from the ventilator. This paper aims to emphasize on the management of different types of SF in FCI. Methods: All surgically treated cases (2012-2016) that showed the combination of FCI and SF have been evaluated for their clinical details, the morphology of the fractures and the technical aspects of the surgical procedure in a retrospective investigation. Results: All of the SF (n=15) had been fixed by locked plate osteosynthesis through a median approach in a supine position. Three main regions of the sternum showed the need for different fixation strategies: the upper manubrium, central and lower corpus sterni. Concomitant rib fractures were addressed either through the same approach or through additional limited incisions. Conclusions: Combinations of SF and FCI are high risc injuries with high demand on surgical skills. They can be properly fixed with a locking plate osteosynthesis through a combination of limited incisions employing different types of plates depending on the type of SF.

Surgical Stabilization of Costoclavicular Injuries - A Combination of Flail Chest Injuries and a Clavicula Fracture.

Background: Flail chest injuries (FCI) are associated with a high morbidity and mortality rate. As a concomitant clavicle fracture in FCI even worsens the outcome, the question is how can those costoclavicular injuries (CCI) be managed surgically. Methods: 11 patients with CCI were surgically treated by a locked plate osteosynthesis of the Clavicle and the underlying ribs through limited surgical approaches under general anesthesia. Patients were followed up after 2, 6, 12, 26 and 52 weeks. Results: All patients showed severe chest wall deformity due to severely displaced fractures of the ribs and the clavicle. They were suffering from pain and restriction of respiratory movements. The chest wall could be restored to normal shape in all cases with uneventful bone healing and a high patient convenience. Fractures of the clavicle and the second rib were managed through an innovative clavipectoral approach, the others through standard approaches to the anterolateral and the posterolateral chest wall. Two patients complained about numbness around the lateral approach and lasting periscapular pain. Conclusions: Surgical stabilization might be the appropriate therapy in CCI with dislocated fractures since they would cause severe deformity and loss of function of the chest wall and the shoulder.

The oblique fracture of the manubrium sterni caused by a seatbelt--a rare injury? Treatment options based on the experiences gained in a level I trauma centre.

INTRODUCTION: Sternal fractures are rare with 3-8 % out of the total number of trauma cases mostly caused by direct impact to the anterior chest wall. Most cases described are due to motor vehicle crash either caused by direct impact to the steering wheel or by the seat belt. Fractures mainly occur to the sternal body. Only rarely are cases of manubrium fractures described in literature, for example, in relationship with a direct impact to the shoulder which caused an oblique fracture near to the sternoclavicular joint. Three patients with profoundly dislocated oblique manubrium fracture were admitted to our Level I Trauma Center in 2012 and 2013. Those patients suffered from instability of the upper sternum and the shoulder girdle. MATERIAL AND METHODS: Between January 2012 and October 2013, a total of 538 trauma patients were admitted to the emergency room and received whole body CT-scan. They were analysed retrospectively for sternal fractures. In cases of instability and dislocation, fracture stabilisation was performed by anterior plating through a medial approach using low profile titanium plates (MatrixRib®). RESULTS: Seventy-nine (14.7 %) patients showed sternal fracture, out of which 13 (2.4 %) patients showed a fracture of manubrium, ten caused by seatbelt. In three cases stabilization was performed. Follow up showed sufficient consolidation without complications. DISCUSSION: A total of 16.5 % of sternal fractures were localized at the manubrium, mostly caused by seat belt. Fractures without significant dislocation seemed to be stable and healed well under conservative treatment. Dislocation in this region leads to unstable shoulder girdle. Anterior plating provides sufficient stabilisation and allowed consolidation.

Observation of a Fragmented, Strongly Interacting Fermi Gas.

We study the emergence of a fragmented state in a strongly interacting Fermi gas subject to a tunable disorder. We investigate its properties using a combination of high-resolution in situ imaging and conductance measurements. The fragmented state exhibits saturated density modulations, a strongly reduced density percolation threshold, lower than the average density, and a resistance equal to that of a noninteracting Fermi gas in the same potential landscape. The transport measurements further indicate that this state is connected to the superfluid state as disorder is reduced. We propose that the fragmented state consists of unpercolated islands of bound pairs, whose binding energy is enhanced by the disorder.

Superfluidity with disorder in a thin film of quantum gas.

We investigate the properties of a strongly interacting superfluid gas of (6)Li(2) Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.

The significance of a concomitant clavicle fracture in flail chest patients: incidence, concomitant injuries, and outcome of 12,348 polytraumata from the TraumaRegister DGU®.

PURPOSE: Isolated clavicle fractures (CF) rarely show complications, but their influence in the thorax trauma of the seriously injured still remains unclear. Some authors associate CF with a higher degree of chest injuries; therefore, the clavicle is meant to be a gatekeeper of the thorax. METHODS: A retrospective analysis of the TraumaRegister DGU® (project 2017-10) was carried out involving the years 2009-2016 (ISS ≥ 16, primary admission to a trauma center). Cohort formation: unilateral and bilateral flail chest injuries (FC), respectively, with and without a concomitant CF. RESULTS: 73,141 patients (26.5% female) met the inclusion criteria and 12,348 had flail chest injuries (FC; 20.0% CF; 67.7% monolateral FC), 25,425 other rib fractures (17.7% CF), and 35,368 had no rib fractures (6.5% CF). On average, monolateral FC patients were 56.0 ± 17.9 years old and bilateral FC patients were 57.7 ± 19 years old. The ISS in unilateral and bilateral FC were 29.1 ± 11.7 and 42.2 ± 12.9 points, respectively. FC with a CF occurred more frequently with bicycle and motorbike injuries in monolateral FC and pedestrians in bilateral FC injuries and less frequently due to falls. Patients with a CF in addition to a FC had longer hospital and ICU stays, underwent artificially respiration for longer periods, and died less often than patients without a CF. The effects were highly significant in bilateral FC. CF indicates more relevant concomitant injuries of the lung, scapula, and spinal column. Moreover, CF was associated with more injuries of the extremities in monolateral CF. CONCLUSION: Due to the relevance of a concomitant CF fracture in FC, diagnostics should focus on finding CFs or rule them out. Combined costoclavicular injuries are associated with a significantly higher degree of thoracic injuries and longer hospital stays.

Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases.

Quantum computing crucially relies on the ability to efficiently characterize the quantum states output by quantum hardware. Conventional methods which probe these states through direct measurements and classically computed correlations become computationally expensive when increasing the system size. Quantum neural networks tailored to recognize specific features of quantum states by combining unitary operations, measurements and feedforward promise to require fewer measurements and to tolerate errors. Here, we realize a quantum convolutional neural network (QCNN) on a 7-qubit superconducting quantum processor to identify symmetry-protected topological (SPT) phases of a spin model characterized by a non-zero string order parameter. We benchmark the performance of the QCNN based on approximate ground states of a family of cluster-Ising Hamiltonians which we prepare using a hardware-efficient, low-depth state preparation circuit. We find that, despite being composed of finite-fidelity gates itself, the QCNN recognizes the topological phase with higher fidelity than direct measurements of the string order parameter for the prepared states.

Osteosynthesis or arthroplasty of fractures near the knee joint in geriatric patients - a clinical-economical comparison. / Osteosynthetische oder endoprothetische Versorgung kniegelenksnaher Frakturen beim geriatrischen Patienten ­ ein klinisch-gesundheitsökonomischer Vergleich.

BACKGROUND: The treatment of fractures of the tibial plateau or distal femur often represents a severe problem in geriatric patients. In particular, complex fracture types and concomitant severe osteoporosis are confronted with inferior results following internal fixation. Therefore, primary arthroplasty is increasingly propagated for such particular cases. PATIENTS, MATERIALS AND METHODS: In 16 patients suffering from fractures of the distal femur or tibial plateau were treated either by internal fixation (n = 8) or primary arthroplasty (n = 8). The outcome of each case was retrospectively analysed according to clinical and economic criteria. RESULTS: In the investigated geriatric patients, primary arthroplasty was significantly superior to internal fixation regarding mobilisation and range of motion without being inferior in cost-effectiveness. CONCLUSION: Compared to internal fixation, primary arthroplasty represents an efficient and cost-effective therapeutical option for the treatment of complex fractures of the distal femur or tibial plateau of the elderly patient.

Emergency department thoracotomy of severely injured patients: an analysis of the TraumaRegister DGU®.

AIM OF THE STUDY: Emergency department thoracotomy (EDT) may be the last chance for survival in some severe thoracic trauma. This study investigates a representative collective with the aim to compare the findings in Europe to the international experience. Moreover, the influence of different levels of trauma care is investigated. METHODS: All emergency thoracotomies in patients with an ISS ≥ 9 from TR-DGU (2009-2014) within the first 60 min after arrival were identified. EDTs were identified separately, and mini thoracotomies and drainage systems were excluded. RESULTS: 99,013 patients with sufficient data were observed. 1736 (1.8%) received thoracotomy during their hospital stay. 887 patients had a thoracotomy within the first hour in the emergency department (ED). 52.5% were treated in supraregional trauma centers (STC), 36.4% in regional (RTC) and 11.0% in local trauma centers (LTC). The mortality rates were 39.4% (STC), 20.9% (RTC) and 20.8% (LTC). The overall mortality rate showed no significant differences for blunt (28.2%) and penetrating trauma (31.3%). In case of cardiac arrest in the ED, a survival rate of 4.8% for blunt trauma and 20.7% for penetrating trauma was determined if EDT was carried out. Those patients showed a higher rate in severe thoracic organ injuries due to penetrating trauma but less extrathoracic injuries. CONCLUSION: Just over half of EDTs were performed in STC. Emergency room resuscitation followed by EDT had survival rates of 4.8% and 20.7% for blunt and penetrating trauma patients, respectively.