Steady state and (bi-) stability evaluation of simple protease signalling networks

Signal transduction networks are complex, as are their mathematical models. Gaining a deeper understanding requires a system analysis. Important aspects are the number, location and stability of steady states. In particular, bistability has been recognised as an important feature to achieve molecular switching. This paper compares different model structures and analysis methods particularly useful for bistability analysis. The biological applications include proteolytic cascades as, for example, encountered in the apoptotic signalling pathway or in the blood clotting system. We compare three model structures containing zero-order, inhibitor and cooperative ultrasensitive reactions, all known to achieve bistability. The combination of phase plane and bifurcation analysis provides an illustrative and comprehensive understanding of how bistability can be achieved and indicates how robust this behaviour is. Experimentally, some so-called “inactive” components were shown to have a residual activity. This has been mostly ignored in mathematical models. Our analysis reveals that bistability is only mildly affected in the case of zero-order or inhibitor ultrasensitivity. However, the case where bistability is achieved by cooperative ultrasensitivity is severely affected by this perturbation

Open Shop Scheduling with Synchronization

In this paper, we study open shop scheduling problems with synchronization. This model has the same features as the classical open shop model, where each of the n jobs has to be processed by each of the m machines in an arbitrary order. Unlike the classical model, jobs are processed in synchronous cycles, which means that the m operations of the same cycle start at the same time. Within one cycle, machines which process operations with smaller processing times have to wait until the longest operation of the cycle is finished before the next cycle can start. Thus, the length of a cycle is equal to the maximum processing time of its operations. In this paper, we continue the line of research started by Weiß et al. (Discrete Appl Math 211:183–203, 2016). We establish new structural results for the two-machine problem with the makespan objective and use them to formulate an easier solution algorithm. Other versions of the problem, with the total completion time objective and those which involve due dates or deadlines, turn out to be NP-hard in the strong sense, even for m=2 machines. We also show that relaxed models, in which cycles are allowed to contain less than m jobs, have the same complexity status

MR motility imaging in Crohn's disease improves lesion detection compared with standard MR imaging

Objective: To evaluate retrospectively in patients with Crohn's disease (CD) if magnetic resonance (MR) motility alterations correlate with CD typical lesions leading to an increased detection rate. Methods: Forty patients with histologically proven CD underwent MR enterography (MRE), including coronal cine sequences (cine MRE), in addition to the standard CD MR protocol. Two blinded readings were performed with and without cine MRE. Locations presenting motility alterations on the cine sequences were analysed on standard MRE for CD-related lesions. This was compared with a second reading using the standard clinical MRE protocol alone. Results: The number of lesions localised by cine MRE and identified on standard MRE compared with standard MRE alone were 35/24 for wall thickening (p = 0.002), 24/20 for stenoses (p = 0.05), 17/11 for wall layering (p = 0.02), 5/3 for mucosal ulcers (p = 0.02) and 21/17 for the comb sign (p = 0.05). Overall, cine MRE detected 35 more CD-specific findings than standard MRE alone (124/89; p = 0.007) and significantly more patients with CD-relevant MR findings (34/28; p = 0.03). Conclusion: CD lesions seem to be associated with motility changes and this leads to an increased lesion detection rate compared with standard-MRE imaging alon

Adductor insertion avulsion syndrome, "thigh splints”: relevance of radiological follow-up

We present a case of chronic osteomyelitis in a 13-year-old girl which was originally diagnosed as adductor insertion avulsion syndrome ("thigh splints”) on the basis of the clinical presentation, patient history, initial radiographs and MRI examination. However, at follow-up with persistent pain and altered radiographic and MRI appearances, surgical biopsy was indicated. Histopathological findings confirmed a bone abscess. This case underlines the necessity of clinical follow-up and imaging in certain patients with apparent thigh splint

Opening up the Quantum Three-Box Problem with Undetectable Measurements

One of the most striking features of quantum mechanics is the profound effect exerted by measurements alone. Sophisticated quantum control is now available in several experimental systems, exposing discrepancies between quantum and classical mechanics whenever measurement induces disturbance of the interrogated system. In practice, such discrepancies may frequently be explained as the back-action required by quantum mechanics adding quantum noise to a classical signal. Here we implement the 'three-box' quantum game of Aharonov and Vaidman in which quantum measurements add no detectable noise to a classical signal, by utilising state-of-the-art control and measurement of the nitrogen vacancy centre in diamond. Quantum and classical mechanics then make contradictory predictions for the same experimental procedure, however classical observers cannot invoke measurement-induced disturbance to explain this discrepancy. We quantify the residual disturbance of our measurements and obtain data that rule out any classical model by > 7.8 standard deviations, allowing us for the first time to exclude the property of macroscopic state-definiteness from our system. Our experiment is then equivalent to a Kochen-Spekker test of quantum non-contextuality that successfully addresses the measurement detectability loophole

Composite-pulse magnetometry with a solid-state quantum sensor

The sensitivity of quantum magnetometers is challenged by control errors and, especially in the solid-state, by their short coherence times. Refocusing techniques can overcome these limitations and improve the sensitivity to periodic fields, but they come at the cost of reduced bandwidth and cannot be applied to sense static (DC) or aperiodic fields. Here we experimentally demonstrate that continuous driving of the sensor spin by a composite pulse known as rotary-echo (RE) yields a flexible magnetometry scheme, mitigating both driving power imperfections and decoherence. A suitable choice of RE parameters compensates for different scenarios of noise strength and origin. The method can be applied to nanoscale sensing in variable environments or to realize noise spectroscopy. In a room-temperature implementation based on a single electronic spin in diamond, composite-pulse magnetometry provides a tunable trade-off between sensitivities in the microT/sqrt(Hz) range, comparable to those obtained with Ramsey spectroscopy, and coherence times approaching T1

MR motility imaging in Crohn's disease improves lesion detection compared with standard MR imaging

To evaluate retrospectively in patients with Crohn's disease (CD) if magnetic resonance (MR) motility alterations correlate with CD typical lesions leading to an increased detection rate

Demonstration of entanglement-by-measurement of solid state qubits

Projective measurements are a powerful tool for manipulating quantum states. In particular, a set of qubits can be entangled by measurement of a joint property such as qubit parity. These joint measurements do not require a direct interaction between qubits and therefore provide a unique resource for quantum information processing with well-isolated qubits. Numerous schemes for entanglement-by-measurement of solid-state qubits have been proposed, but the demanding experimental requirements have so far hindered implementations. Here we realize a two-qubit parity measurement on nuclear spins in diamond by exploiting the electron spin of a nitrogen-vacancy center as readout ancilla. The measurement enables us to project the initially uncorrelated nuclear spins into maximally entangled states. By combining this entanglement with high-fidelity single-shot readout we demonstrate the first violation of Bells inequality with solid-state spins. These results open the door to a new class of experiments in which projective measurements are used to create, protect and manipulate entanglement between solid-state qubits.Comment: 6 pages, 4 figure