Optimization along Families of Periodic and Quasiperiodic Orbits in Dynamical Systems with Delay

This paper generalizes a previously-conceived, continuation-based optimization technique for scalar objective functions on constraint manifolds to cases of periodic and quasiperiodic solutions of delay-differential equations. A Lagrange formalism is used to construct adjoint conditions that are linear and homogenous in the unknown Lagrange multipliers. As a consequence, it is shown how critical points on the constraint manifold can be found through several stages of continuation along a sequence of connected one-dimensional manifolds of solutions to increasing subsets of the necessary optimality conditions. Due to the presence of delayed and advanced arguments in the original and adjoint differential equations, care must be taken to determine the degree of smoothness of the Lagrange multipliers with respect to time. Such considerations naturally lead to a formulation in terms of multi-segment boundary-value problems (BVPs), including the possibility that the number of segments may change, or that their order may permute, during continuation. The methodology is illustrated using the software package coco on periodic orbits of both linear and nonlinear delay-differential equations, keeping in mind that closed-form solutions are not typically available even in the linear case. Finally, we demonstrate optimization on a family of quasiperiodic invariant tori in an example unfolding of a Hopf bifurcation with delay and parametric forcing. The quasiperiodic case is a further original contribution to the literature on optimization constrained by partial differential BVPs.Comment: preprint, 17 pages, 9 figure

Galerkin approximations with embedded boundary conditions for retarded delay differential equations

Finite-dimensional approximations are developed for retarded delay differential equations (DDEs). The DDE system is equivalently posed as an initial-boundary value problem consisting of hyperbolic partial differential equations (PDEs). By exploiting the equivalence of partial derivatives in space and time, we develop a new PDE representation for the DDEs that is devoid of boundary conditions. The resulting boundary condition-free PDEs are discretized using the Galerkin method with Legendre polynomials as the basis functions, whereupon we obtain a system of ordinary differential equations (ODEs) that is a finite-dimensional approximation of the original DDE system. We present several numerical examples comparing the solution obtained using the approximate ODEs to the direct numerical simulation of the original non-linear DDEs. Stability charts developed using our method are compared to existing results for linear DDEs. The presented results clearly demonstrate that the equivalent boundary condition-free PDE formulation accurately captures the dynamic behaviour of the original DDE system and facilitates the application of control theory developed for systems governed by ODEs

Adaptive sparse Galerkin methods for vibrating continuous structures

Adaptive reduced-order methods are explored for simulating continuous vibrating structures. The Galerkin method is used to convert the governing partial differential equation (PDE)into a finite-dimensional system of ordinary differential equations (ODEs) whose solution approximates that of the original PDE. Sparse projections of the approximate ODE solution are then found at each integration time step by applying either the least absolute shrinkage and selection operator (lasso) or the optimal subset selection method. We apply the two projection schemes to the simulation of a vibrating Euler–Bernoulli beam subjected to nonlinear unilateral and bilateral spring forces. The subset selection approach is found to be superior for this application, as it generates a solution with similar sparsity but substantially lower error than the lasso

Mathematical Modeling and Stability Analysis of Delay Differential Equations

Finite-dimensional approximations are developed for retarded delay differential equations (DDEs). The DDE system is equivalently posed as an initial–boundary value problem consisting of hyperbolic partial differential equations (PDEs). By exploting the equivalence of partial derivatives in space and time, we develop a new PDE representation for the DDEs that is devoid of boundary conditions. The resulting boundary condition–free PDEs are discretized using the Galerkin method with Legendre polynomials as the basis functions, whereupon we obtain a system of ordinary differential equations (ODEs) that is a finite-dimensional approximation of the original DDE system

Our experience of forgotten double-J stents in a tertiary care center

Background: Double-J (DJ) stents have become an essential tool in the field of urology. Forgotten DJ stents are associated with significant morbidity and mortality, if not intervened timely. Aims and Objectives: In this study, we report our experience of forgotten stents related complications, along with its management and steps taken by us in preventing stent-related morbidity. Materials and Methods: We retrospectively analyzed the records of patients presented to the Department of Urology, Indira Gandhi Institute of Medical Sciences, Patna with forgotten or long-term retention of DJ stents from January 2021 to December 2022. All cases were reviewed for age, gender, symptoms, indication of stent insertion, duration of stent insertion, radiological images, and procedures performed for management. Results: The mean age of the patients was 49.23 years. The mean duration of the indwelling stent in situ was 16.61 months. Presenting complaint was flank pain, recurrent urinary tract infection, dysuria, hematuria, and irritative lower urinary tract symptoms. Common indications of indwelling stents were ureteroscopic lithotripsy, percutaneous nephrolithotomy, and Laparoscopic pyeloplasty. Cystoscopy, ureteroscopy, cystolithotripsy, percutaneous nephrolithotomy, and open surgery were done to extract the forgotten DJ stent. Conclusion: Forgotten DJ stents are a source of severe morbidity. Patients and relatives counseling before and after the procedure is necessary in reducing stent-related complications

Purple stem Brassica napus exhibits higher photosynthetic efficiency, antioxidant potential and anthocyanin biosynthesis related genes expression against drought stress

Purple-stem Brassica napus (B. napus) is a phenotype with unique color because of its high anthocyanins content. Anthocyanins are naturally occurring plant pigments that have antioxidants activity and play important role in plant defense against abiotic and biotic stresses. In the present study, drought induced effects on plants were investigated in hydroponically grown seedlings of green stem (GS) and purple stem (PS) genotypes of B. napus. The results of this study showed that the major function of anthocyanins accumulation during drought was to enhance the antioxidant capability and stress tolerance in B. napus plants. Our results showed that drought significantly inhibited the plant growth in terms of decreased biomass accumulation in both genotypes, although marked decline was observed in GS genotype. The reduction in photosynthetic attributes was more noticeable in the GS genotype, whereas the PS genotype showed better performance under drought stress. Under stressful conditions, both the genotype showed excessive accumulation of reactive oxygen species (ROS) and malondialdehyde (MDA), as well as higher levels of antioxidant enzymes activities. Under drought conditions, the GS genotype showed apparent damages on chloroplast deformation like in thylakoid membrane and grana structural distortion and fewer starch grains and bigger plastoglobuli. Moreover, during drought stress, the PS genotype exhibited maximum expression levels of anthocyanins biosynthesis genes and antioxidant enzymes accompanied by higher stress tolerance relative to GS genotype. Based on these findings, it can be concluded that GS genotype found more sensitive to drought stress than the PS genotype. Furthermore this research paper also provides practical guidance for plant biologists who are developing stress-tolerant crops by using anthocyanin biosynthesis or regulatory genes

Proximal Actuation of an Elastically Loaded Scissors Mechanism for the Leg Design of a Quadruped Robot

Spring Loaded Pantographs (SLPs) are frequently used in designing lightweight limbs for multi-legged robots. Quadruped robots that incorporate cable-pulled SLP legs have proven to be agile, robust and capable of conserving energy during their gait cycle. In such designs, the extension of the distal segments via the knee joint is dependent upon the length of the cable. In this article we propose the use of an Elastically Loaded Scissors Mechanism (ELS Mechanism or ELSM), which is a variant of the SLP. Driven by ’pulling’ onto the proximal joint of the scissors as opposed to the distal joint, this proposed leg utilizes the increased mechanical advantage of the scissors mechanism to ’amplify’ input angles to larger output displacement by the knee joint. Analysis and Simulations reveal that the proposed mechanism achieves increased motion speed as compared to the SLP mechanism. This, however, comes at the cost of higher load on the actuator which serves as an engineering trade-off. This is validated by experimentation using motion capture and load motor techniques of the SLP and ELS configurations in a physical quadruped robot

Chemical priming enhances plant tolerance to salt stress

Salt stress severely limits the productivity of crop plants worldwide and its detrimental effects are aggravated by climate change. Due to a significant world population growth, agriculture has expanded to marginal and salinized regions, which usually render low crop yield. In this context, finding methods and strategies to improve plant tolerance against salt stress is of utmost importance to fulfill food security challenges under the scenario of the ever-increasing human population. Plant priming, at different stages of plant development, such as seed or seedling, has gained significant attention for its marked implication in crop salt-stress management. It is a promising field relying on the applications of specific chemical agents which could effectively improve plant salt-stress tolerance. Currently, a variety of chemicals, both inorganic and organic, which can efficiently promote plant growth and crop yield are available in the market. This review summarizes our current knowledge of the promising roles of diverse molecules/compounds, such as hydrogen sulfide (H2S), molecular hydrogen, nitric oxide (NO), hydrogen peroxide (H2O2), melatonin, chitosan, silicon, ascorbic acid (AsA), tocopherols, and trehalose (Tre) as potential primers that enhance the salinity tolerance of crop plants

MGP Panel is a comprehensive targeted genomics panel for molecular profiling of multiple myeloma patients

PURPOSE: We designed a comprehensive multiple myeloma (MM) targeted sequencing panel to identify common genomic abnormalities in a single assay and validated it against known standards. EXPERIMENTAL DESIGN: The panel comprised 228 genes/exons for mutations, 6 regions for translocations, and 56 regions for copy number abnormalities (CNAs). Toward panel validation, targeted sequencing was conducted on 233 patient samples and further validated using clinical fluorescence in situ hybridization (FISH) (translocations), multiplex ligation probe analysis (MLPA) (CNAs), whole genome sequencing (WGS) (CNAs, mutations, translocations) or droplet digital PCR (ddPCR) of known standards (mutations). RESULTS: Canonical IgH translocations were detected in 43.2% of patients by sequencing, and aligned with FISH except for one patient. CNAs determined by sequencing and MLPA for 22 regions were comparable in 103 samples and concordance between platforms was R2=0.969. VAFs for 74 mutations were compared between sequencing and ddPCR with concordance of R2=0.9849. CONCLUSIONS: In summary, we have developed a targeted sequencing panel that is as robust or superior to FISH and WGS. This molecular panel is cost effective, comprehensive, clinically actionable and can be routinely deployed to assist risk stratification at diagnosis or post-treatment to guide sequencing of therapies