Controlling surface morphologies by time-delayed feedback

We propose a new method to control the roughness of a growing surface, via a time-delayed feedback scheme. As an illustration, we apply this method to the Kardar-Parisi-Zhang equation in 1+1 dimensions and show that the effective growth exponent of the surface width can be stabilized at any desired value in the interval [0.25,0.33], for a significant length of time. The method is quite general and can be applied to a wide range of growth phenomena. A possible experimental realization is suggested.Comment: 4 pages, 3 figure

An error bound for model reduction of Lur'e-type systems

In general, existing model reduction techniques for stable nonlinear systems lack a guarantee on stability of the reduced-order model, as well as an error bound. In this paper, a model reduction procedure for absolutely stable Lur’e-type systems is presented, where conditions to ensure absolute stability of the reduced-order model as well as an error bound are given. The proposed model reduction procedure exploits linear model reduction techniques for the reduction of the linear part of the Lur’e-type system. Hence, the proposed model reduction strategy is computationally attractive. Moreover, both stability and the error bound for the obtained reduced-order model hold for an entire class of nonlinearities. The results are illustrated by application to a nonlinear mechanical system

Direct Visualization of Single Nuclear Pore Complex Proteins Using Genetically-Encoded Probes for DNA-PAINT

The nuclear pore complex (NPC) is one of the largest and most complex protein assemblies in the cell and, among other functions, serves as the gatekeeper of nucleocytoplasmic transport. Unraveling its molecular architecture and functioning has been an active research topic for decades with recent cryogenic electron microscopy and super-resolution studies advancing our understanding of the architecture of the NPC complex. However, the specific and direct visualization of single copies of NPC proteins is thus far elusive. Herein, we combine genetically-encoded self-labeling enzymes such as SNAP-tag and HaloTag with DNA-PAINT microscopy. We resolve single copies of nucleoporins in the human Y-complex in three dimensions with a precision of circa 3 nm, enabling studies of multicomponent complexes on the level of single proteins in cells using optical fluorescence microscopy

Multidisciplinary decision-making in older patients with cancer, does it differ from younger patients?

Background: In order to tailor treatment to the individual patient, it is important to take the patients context and preferences into account, especially for older patients. We assessed the quality of information used in the decision-making process in different oncological MDTs and compared this for older (>70 years) and younger patients. Patients and methods: Cross-sectional observations of oncological MDTs were performed, using an observation tool in a University Hospital. Primary outcome measures were quality of input of information into the discussion for older and younger patients. Secondary outcomes were the contribution of different team members, discussion time for each case and whether or not a treatment decision was formulated. Results: Five-hundred and three cases were observed. The median patient age was 63 year, 32% were >70. In both age groups quality of patient-centered information (psychosocial information and patient's view) was poor. There was no difference in quality of information between older and younger patients, only for comorbidities the quality of information for older patients was better. There was no significant difference in the contributions by team members, discussion time (median 3.54 min) or number of decision reached (87.5%). Conclusion: For both age groups, we observed a lack of patient-centered information. The only difference between the age groups was for information on comorbidities. There were also no differences in contributions by different team members, case discussion time or number of decisions. Decision-making in the observed oncological MDTs was mostly based on medical technical information. (c) 2021 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/)

Ferromagnetic phase transition in a Heisenberg fluid: Monte Carlo simulations and Fisher corrections to scaling

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling (FSS) technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent $\alpha$. The appearance of such new corrections to scaling is a general feature of systems with constraints.Comment: 12 pages, 2 figures; submitted to Phys. Rev. Let

A reduced complexity numerical method for optimal gate synthesis

Although quantum computers have the potential to efficiently solve certain problems considered difficult by known classical approaches, the design of a quantum circuit remains computationally difficult. It is known that the optimal gate design problem is equivalent to the solution of an associated optimal control problem, the solution to which is also computationally intensive. Hence, in this article, we introduce the application of a class of numerical methods (termed the max-plus curse of dimensionality free techniques) that determine the optimal control thereby synthesizing the desired unitary gate. The application of this technique to quantum systems has a growth in complexity that depends on the cardinality of the control set approximation rather than the much larger growth with respect to spatial dimensions in approaches based on gridding of the space, used in previous literature. This technique is demonstrated by obtaining an approximate solution for the gate synthesis on $SU(4)$- a problem that is computationally intractable by grid based approaches.Comment: 8 pages, 4 figure

Decoherence Control in Open Quantum System via Classical Feedback

In this work we propose a novel strategy using techniques from systems theory to completely eliminate decoherence and also provide conditions under which it can be done so. A novel construction employing an auxiliary system, the bait, which is instrumental to decoupling the system from the environment is presented. Our approach to decoherence control in contrast to other approaches in the literature involves the bilinear input affine model of quantum control system which lends itself to various techniques from classical control theory, but with non-trivial modifications to the quantum regime. The elegance of this approach yields interesting results on open loop decouplability and Decoherence Free Subspaces(DFS). Additionally, the feedback control of decoherence may be related to disturbance decoupling for classical input affine systems, which entails careful application of the methods by avoiding all the quantum mechanical pitfalls. In the process of calculating a suitable feedback the system has to be restructured due to its tensorial nature of interaction with the environment, which is unique to quantum systems. The results are qualitatively different and superior to the ones obtained via master equations. Finally, a methodology to synthesize feedback parameters itself is given, that technology permitting, could be implemented for practical 2-qubit systems to perform decoherence free Quantum Computing.Comment: 17 pages, 4 Fig

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

A comparison of model reduction techniques from structural dynamics, numerical mathematics and systems and control

In this paper, popular model reduction techniques from the fields of structural dynamics, numerical mathematics and systems and control are reviewed and compared. The motivation for such a comparison stems from the fact the model reduction techniques in these fields have been developed fairly independently. In addition, the insight obtained by the comparison allows for making a motivated choice for a particular model reduction technique, on the basis of the desired objectives and properties of the model reduction problem. In particular, a detailed review is given on mode displacement techniques, moment matching methods and balanced truncation, whereas important extensions are outlined briefly. In addition, a qualitative comparison of these methods is presented, hereby focussing both on theoretical and computational aspects. Finally, the differences are illustrated on a quantitative level by means of application of the model reduction techniques to a common example