A tube-based robust MPC for duty-cycled rotation needle steering systems with bounded disturbances

In this paper, we aim to design the trajectory tracking controller for variable curvature duty-cycled rotation flexible needles with a tube-based model predictive control approach. A non-linear model is adopted according to the kinematic characteristics of the flexible needle and a bicycle method. The modeling error is assumed to be an unknown but bounded disturbance. The non-linear model is transformed to a discrete time form for the benefit of predictive controller design. From the application perspective, the flexible needle system states and control inputs are bounded within a robust invariant set when subject to disturbance. Then, the tube-based model predictive control is designed for the system with bounded state vector and inputs. Finally, the simulation experiments are carried out with tube-based model predictive control and proportional integral derivative controller based on the particle swarm optimisation method. The simulation results show that the tube-based model predictive control method is more robust and it leads to much smaller tracking errors in different scenarios.

Bounded States for Breathers–Soliton and Breathers of Sine–Gordon Equation

The Wronskians solutions to the sine-Gordon (sG) equation that can provide interaction of different kinds of solutions are revisited. A novel expression N-soliton solution with a nonzero background is presented which is used to construct the soliton and breather solutions. Due to the existences of abundant structures of the solitons and breathers, it is possible to search for the coherent structures, or bounded states of solitons and breathers. By introducing the velocity resonant conditions, the sG equation is proved to possess the bounded state for breathers-soliton, or breather-soliton molecules (BSMs) and the bounded state for breathers, or breather molecules (BMs) by different parameters selections. In addition, an approximately bounded state for solitons is demonstrated. The interesting thing is the interactions among the BSMs, BMs and solitons, breathers may be nonelastic by the particular meaning the sizes of the BSMs and BMs change.

Card-Based Cryptography Meets Formal Verification

Card-based cryptography provides simple and practicable protocols for performing secure multi-party computation with just a deck of cards. For the sake of simplicity, this is often done using cards with only two symbols, e.g., $$\clubsuit $$ ♣ and $$\heartsuit $$ ♡ . Within this paper, we also target the setting where all cards carry distinct symbols, catering for use-cases with commonly available standard decks and a weaker indistinguishability assumption. As of yet, the literature provides for only three protocols and no proofs for non-trivial lower bounds on the number of cards. As such complex proofs (handling very large combinatorial state spaces) tend to be involved and error-prone, we propose using formal verification for finding protocols and proving lower bounds. In this paper, we employ the technique of software bounded model checking (SBMC), which reduces the problem to a bounded state space, which is automatically searched exhaustively using a SAT solver as a backend. Our contribution is threefold: (a) we identify two protocols for converting between different bit encodings with overlapping bases, and then show them to be card-minimal. This completes the picture of tight lower bounds on the number of cards with respect to runtime behavior and shuffle properties of conversion protocols. For computing AND, we show that there is no protocol with finite runtime using four cards with distinguishable symbols and fixed output encoding, and give a four-card protocol with an expected finite runtime using only random cuts. (b) We provide a general translation of proofs for lower bounds to a bounded model checking framework for automatically finding card- and run-minimal (i.e., the protocol has a run of minimal length) protocols and to give additional confidence in lower bounds. We apply this to validate our method and, as an example, confirm our new AND protocol to have its shortest run for protocols using this number of cards. (c) We extend our method to also handle the case of decks on symbols $$\clubsuit $$ ♣ and $$\heartsuit $$ ♡ , where we show run-minimality for two AND protocols from the literature.

Assessment of the PETase Conformational Changes Induced by Poly(ethylene terephthalate) Binding

Recently, a bacterium strain of Ideonella sakaiensis was identified with the uncommon ability to degrade the poly(ethylene terephthalate) (PET). The PETase from I. sakaiensis strain 201-F6 catalyzes the hydrolysis of PET converting it to mono(2-hydroxyethyl) terephthalic acid (MHET), bis(2-hydroxyethyl)-TPA (BHET), and terephthalic acid (TPA). Despite the potential of this enzyme for mitigation or elimination of environmental contaminants, one of the limitations of the use of PETase for PET degradation is the fact that it acts only at moderate temperature due to its low thermal stability. Besides, molecular details of the main interaction of PET in the active site of PETase remains unclear. Herein, molecular docking and molecular dynamics (MD) simulations were applied to analyze structural changes of PETase induced by PET binding. Results from the essential dynamics revealed that β1-β2 connecting loop is very flexible. This Loop is located far from the active site of PETase and we suggest that it can be considered for mutagenesis in order to increase the thermal stability of PETase. The free energy landscape (FEL) demonstrates that the main change in the transition between the unbounded to the bounded state is associated with β7-α5 connecting loop, where the catalytic residue Asp206 is located. Overall, the present study provides insights into the molecular binding mechanism of PET into the PETase structure and a computational strategy for mapping flexible regions of this enzyme, which can be useful for the engineering of more efficient enzymes for recycling the plastic polymers using biological systems.

Model Checking Finite-Horizon Markov Chains with Probabilistic Inference

We revisit the symbolic verification of Markov chains with respect to finite horizon reachability properties. The prevalent approach iteratively computes step-bounded state reachability probabilities. By contrast, recent advances in probabilistic inference suggest symbolically representing all horizon-length paths through the Markov chain. We ask whether this perspective advances the state-of-the-art in probabilistic model checking. First, we formally describe both approaches in order to highlight their key differences. Then, using these insights we develop Rubicon, a tool that transpiles Prism models to the probabilistic inference tool . Finally, we demonstrate better scalability compared to probabilistic model checkers on selected benchmarks. All together, our results suggest that probabilistic inference is a valuable addition to the probabilistic model checking portfolio, with Rubicon as a first step towards integrating both perspectives.

Boundaries at play

Summary In this paper, we model the left-bounded state reading and the true reflexive reading of the se clitic in the Spanish psychological domain. We argue that a lexical analysis of se provides us with a more accurate description of the different classes of psychological verbs that occur with the clitic. We provide a unified analysis where the use of the two readings of se are modeled by means of lexical rules. We take the morphologically simple but semantically more complex basic items (e.g. asustar ‘frighten’) as input of the lexical rules, getting as the output a morphologically more complex but semantically simpler verb (e.g asustarse ‘get frightened’). The analysis for psych verbs correctly allows only those verbs assigning accusative to the experiencer or the stimulus to combine with se, hence preventing dative verbs from entering the lexical rules. The analysis also demonstrates how to account for punctual and non-punctual readings of psych verbs with se incorporating ‘boundaries’ into the type hierarchy of eventualities.

Dynamic positioning for underactuated surface vessel via L1 adaptive backstepping control

This paper is concerned with the problem that fast-transient response and excellent robustness cannot be satisfied simultaneously in the process of dynamic positioning (DP) for underactuated surface vessel (USV) in shallow water. By combing the improved L1 adaptive control with backstepping method, a novel control scheme is designed, which can ensure a fast adaptation with a guaranteed smooth transient response without any overshoot and chattering phenomenon. System uncertainties and disturbances are estimated by the nonlinear observer. Moreover, the optimized extremum seeking control (ESC) is employed to reduce energy consumption under environmental disturbances. Rigorous theoretical analysis shows that all closed-loop signals are bounded-input bounded-state. Simulation and sea test results are presented to illustrate the effectiveness and the robustness of the proposed strategy under the condition of external disturbances and parametric uncertainties.

A Marginal Adjustment Rank Histogram Filter for Non-Gaussian Ensemble Data Assimilation

An extension to standard ensemble Kalman filter algorithms that can improve performance for non-Gaussian prior distributions, non-Gaussian likelihoods, and bounded state variables is described. The algorithm exploits the capability of the rank histogram filter (RHF) to represent arbitrary prior distributions for observed variables. The rank histogram algorithm can be applied directly to state variables to produce posterior marginal ensembles without the need for regression that is part of standard ensemble filters. These marginals are used to adjust the marginals obtained from a standard ensemble filter that uses regression to update state variables. The final posterior ensemble is obtained by doing an ordered replacement of the posterior marginal ensemble values from a standard ensemble filter with the values obtained from the rank histogram method applied directly to state variables; the algorithm is referred to as the Marginal Adjustment Rank Histogram Filter (MARHF). Applications to idealized bivariate problems and low-order dynamical systems show that the MARHF can produce better results than standard ensemble methods for priors that are non-Gaussian. Like the original RHF, the MARHF can also make use of arbitrary non-Gaussian observation likelihoods. The MARHF also has advantages for problems with bounded state variables, for instance the concentration of an atmospheric tracer. Bounds can be automatically respected in the posterior ensembles. With an efficient implementation of the MARHF, the additional cost has better scaling than the standard RHF.