Synthesis of a PID-controller of a trim robust control system of an autonomous underwater vehicle

Autonomous underwater vehicles are often used for performing scientific, emergency or other types of missions under harsh conditions and environments, which can have non-stable, variable parameters. So, the problem of developing autonomous underwater vehicle motion control systems, capable of operating properly in random environments, is highly relevant. The paper is dedicated to the synthesis of a PID-controller of a trim robust control system, capable of keeping an underwater vehicle stable during a translation at different angles of attack. In order to synthesize the PID-controller, two problems were solved: a new method of synthesizing a robust controller was developed and a mathematical model of an underwater vehicle motion process was derived. The newly developed mathematical model structure is simpler than others due to acceptance of some of the system parameters as interval ones. The synthesis method is based on a system poles allocation approach and allows providing the necessary transient process quality in a considered system

Global stabilization of fixed points using predictive control

We analyze the global stability properties of some methods of predictive control. We particularly focus on the optimal control function introduced by de Sousa Vieira and Lichtenberg [Phys. Rev. E54, 1200 (1996)]. We rigorously prove that it is possible to use this method for the global stabilization of a discrete system xn+1=f(xn) into a positive equilibrium for a class of maps commonly used in population dynamics. Moreover, the controlledsystem is globally stable for all values of the control parameter for which it is locally asymptotically stable. Our study highlights the difficulty of obtaining global stability results for other methods of predictive control, where higher iterations of f are used in the control scheme.Ministerio de Ciencia e InnovaciónFondo Europeo de Desarrollo Regiona

Molecular-orbital-free algorithm for excited states in time-dependent perturbation theory

A non-linear conjugate gradient optimization scheme is used to obtain excitation energies within the Random Phase Approximation (RPA). The solutions to the RPA eigenvalue equation are located through a variational characterization using a modified Thouless functional, which is based upon an asymmetric Rayleigh quotient, in an orthogonalized atomic orbital representation. In this way, the computational bottleneck of calculating molecular orbitals is avoided. The variational space is reduced to the physically-relevant transitions by projections. The feasibility of an RPA implementation scaling linearly with system size, N, is investigated by monitoring convergence behavior with respect to the quality of initial guess and sensitivity to noise under thresholding, both for well- and ill-conditioned problems. The molecular- orbital-free algorithm is found to be robust and computationally efficient providing a first step toward a large-scale, reduced complexity calculation of time-dependent optical properties and linear response. The algorithm is extensible to other forms of time-dependent perturbation theory including, but not limited to, time-dependent Density Functional theory.Comment: 9 pages, 7 figure

A stochastic approximation algorithm with multiplicative step size modification

An algorithm of searching a zero of an unknown function \vphi : \, \R \to \R is considered: $\, x_{t} = x_{t-1} - \gamma_{t-1} y_t$,\, $t=1,\ 2,\ldots$, where $y_t = \varphi(x_{t-1}) + \xi_t$ is the value of \vphi measured at $x_{t-1}$ and $\xi_t$ is the measurement error. The step sizes \gam_t > 0 are modified in the course of the algorithm according to the rule: \, \gamma_t = \min\{u\, \gamma_{t-1},\, \mstep\} if $y_{t-1} y_t > 0$, and $\gamma_t = d\, \gamma_{t-1}$, otherwise, where $0 < d < 1 0$. That is, at each iteration \gam_t is multiplied either by $u$ or by $d$, provided that the resulting value does not exceed the predetermined value \mstep. The function \vphi may have one or several zeros; the random values $\xi_t$ are independent and identically distributed, with zero mean and finite variance. Under some additional assumptions on \vphi, $\xi_t$, and \mstep, the conditions on $u$ and $d$ guaranteeing a.s. convergence of the sequence $\{ x_t \}$, as well as a.s. divergence, are determined. In particular, if $\P (\xi_1 > 0) = \P (\xi_1 < 0) = 1/2$ and $\P (\xi_1 = x) = 0$ for any $x \in \R$, one has convergence for $ud 1$. Due to the multiplicative updating rule for \gam_t, the sequence $\{ x_t \}$ converges rapidly: like a geometric progression (if convergence takes place), but the limit value may not coincide with, but instead, approximates one of the zeros of \vphi. By adjusting the parameters $u$ and $d$, one can reach arbitrarily high precision of the approximation; higher precision is obtained at the expense of lower convergence rate

Topological entropy of a stiff ring polymer and its connection to DNA knots

We discuss the entropy of a circular polymer under a topological constraint. We call it the {\it topological entropy} of the polymer, in short. A ring polymer does not change its topology (knot type) under any thermal fluctuations. Through numerical simulations using some knot invariants, we show that the topological entropy of a stiff ring polymer with a fixed knot is described by a scaling formula as a function of the thickness and length of the circular chain. The result is consistent with the viewpoint that for stiff polymers such as DNAs, the length and diameter of the chains should play a central role in their statistical and dynamical properties. Furthermore, we show that the new formula extends a known theoretical formula for DNA knots.Comment: 14pages,11figure

The Pure Virtual Braid Group Is Quadratic

If an augmented algebra K over Q is filtered by powers of its augmentation ideal I, the associated graded algebra grK need not in general be quadratic: although it is generated in degree 1, its relations may not be generated by homogeneous relations of degree 2. In this paper we give a sufficient criterion (called the PVH Criterion) for grK to be quadratic. When K is the group algebra of a group G, quadraticity is known to be equivalent to the existence of a (not necessarily homomorphic) universal finite type invariant for G. Thus the PVH Criterion also implies the existence of such a universal finite type invariant for the group G. We apply the PVH Criterion to the group algebra of the pure virtual braid group (also known as the quasi-triangular group), and show that the corresponding associated graded algebra is quadratic, and hence that these groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies corrected, reflecting suggestions made by the referee of the published version of the pape

Gradient methods for problems with inexact model of the objective

We consider optimization methods for convex minimization problems under inexact information on the objective function. We introduce inexact model of the objective, which as a particular cases includes inexact oracle [19] and relative smoothness condition [43]. We analyze gradient method which uses this inexact model and obtain convergence rates for convex and strongly convex problems. To show potential applications of our general framework we consider three particular problems. The first one is clustering by electorial model introduced in [49]. The second one is approximating optimal transport distance, for which we propose a Proximal Sinkhorn algorithm. The third one is devoted to approximating optimal transport barycenter and we propose a Proximal Iterative Bregman Projections algorithm. We also illustrate the practical performance of our algorithms by numerical experiments

Combinations of Host- and Virus-Targeting Antiviral Drugs Confer Synergistic Suppression of SARS-CoV-2

Three directly acting antivirals (DAAs) demonstrated substantial reduction in COVID-19 hospitalizations and deaths in clinical trials. However, these agents did not completely prevent severe illness and are associated with cases of rebound illness and viral shedding. Combination regimens can enhance antiviral potency, reduce the emergence of drug-resistant variants, and lower the dose of each component in the combination. Concurrently targeting virus entry and virus replication offers opportunities to discover synergistic drug combinations. While combination antiviral drug treatments are standard for chronic RNA virus infections, no antiviral combination therapy has been approved for SARS-CoV-2. Here, we demonstrate that combining host-targeting antivirals (HTAs) that target TMPRSS2 and hence SARS-CoV-2 entry, with the DAA molnupiravir, which targets SARS-CoV-2 replication, synergistically suppresses SARS-CoV-2 infection in Calu-3 lung epithelial cells. Strong synergy was observed when molnupiravir, an oral drug, was combined with three TMPRSS2 (HTA) oral or inhaled inhibitors: camostat, avoralstat, or nafamostat. The combination of camostat plus molnupiravir was also effective against the beta and delta variants of concern. The pyrimidine biosynthesis inhibitor brequinar combined with molnupiravir also conferred robust synergistic inhibition. These HTA+DAA combinations had similar potency to the synergistic all-DAA combination of molnupiravir plus nirmatrelvir, the protease inhibitor found in paxlovid. Pharmacodynamic modeling allowed estimates of antiviral potency at all possible concentrations of each agent within plausible therapeutic ranges, suggesting possible in vivo efficacy. The triple combination of camostat, brequinar, and molnupiravir further increased antiviral potency. These findings support the development of HTA+DAA combinations for pandemic response and preparedness. IMPORTANCE Imagine a future viral pandemic where if you test positive for the new virus, you can quickly take some medicines at home for a few days so that you do not get too sick. To date, only single drugs have been approved for outpatient use against SARS-CoV-2, and we are learning that these have some limitations and may succumb to drug resistance. Here, we show that combinations of two oral drugs are better than the single ones in blocking SARS-CoV-2, and we use mathematical modeling to show that these drug combinations are likely to work in people. We also show that a combination of three oral drugs works even better at eradicating the virus. Our findings therefore bode well for the development of oral drug cocktails for at home use at the first sign of an infection by a coronavirus or other emerging viral pathogens.Peer reviewe

Heritability of DNA-damage-induced apoptosis and its relationship with age in lymphocytes from female twins

Apoptosis is a physiological form of cell death important in normal processes such as morphogenesis and the functioning of the immune system. In addition, defects in the apoptotic process play a major role in a number of important areas of disease, such as autoimmune diseases and cancer. DNA-damage-induced apoptosis plays a vital role in the maintenance of genomic stability by the removal of damaged cells. Previous studies of the apoptotic response (AR) to radiation-induced DNA damage of lymphoid cells from individuals carrying germline TP53 mutations have demonstrated a defective AR compared with normal controls. We have also previously demonstrated that AR is reduced as individuals age. Results from the current study on 108 twins aged 18–80 years confirm these earlier findings that the AR of lymphoid cells to DNA damage is significantly reduced with increasing age. In addition this twin study shows, for the first time, that DNA-damage-induced AR has a strong degree of heritability of 81% (95% confidence interval 67–89%). The vital role of DNA-damage-induced apoptosis in maintaining genetic stability, its relationship with age and its strong heritability underline the importance of this area of biology and suggest areas for further study