A 4D-Var Method with Flow-Dependent Background Covariances for the Shallow-Water Equations

The 4D-Var method for filtering partially observed nonlinear chaotic dynamical systems consists of finding the maximum a-posteriori (MAP) estimator of the initial condition of the system given observations over a time window, and propagating it forward to the current time via the model dynamics. This method forms the basis of most currently operational weather forecasting systems. In practice the optimization becomes infeasible if the time window is too long due to the non-convexity of the cost function, the effect of model errors, and the limited precision of the ODE solvers. Hence the window has to be kept sufficiently short, and the observations in the previous windows can be taken into account via a Gaussian background (prior) distribution. The choice of the background covariance matrix is an important question that has received much attention in the literature. In this paper, we define the background covariances in a principled manner, based on observations in the previous $b$ assimilation windows, for a parameter $b\ge 1$. The method is at most $b$ times more computationally expensive than using fixed background covariances, requires little tuning, and greatly improves the accuracy of 4D-Var. As a concrete example, we focus on the shallow-water equations. The proposed method is compared against state-of-the-art approaches in data assimilation and is shown to perform favourably on simulated data. We also illustrate our approach on data from the recent tsunami of 2011 in Fukushima, Japan.Comment: 32 pages, 5 figure

On the Navier-Stokes Equations with Stochastic Lie Transport

We prove the existence and uniqueness of maximal solutions to the 3D SALT (Stochastic Advection by Lie Transport, [Holm arXiv:1410.8311]) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain respectively. The current work partners the paper [Goodair et al, arXiv:2209.09137] as an application of the abstract framework presented there, justifying the results first announced in [Goodair, arXiv:2202.09242v2]. In particular this represents the first well-posedness result for a fluid equation perturbed by a general transport type noise on a bounded domain

The Zero Viscosity Limit of Stochastic Navier-Stokes Flows

We introduce an analogue to Kato's Criterion regarding the inviscid convergence of stochastic Navier-Stokes flows to the strong solution of the deterministic Euler equation. Our assumptions cover additive, multiplicative and transport type noise models. This is achieved firstly for the typical noise scaling of $\nu^\frac{1}{2}$, before considering a new parameter which approaches zero with viscosity but at a potentially different rate. We determine the implications of this for our criterion and clarify a sense in which the scaling by $\nu^\frac{1}{2}$ is optimal. To enable the analysis we prove the existence of probabilistically weak, analytically weak solutions to a general stochastic Navier-Stokes Equation on a bounded domain with no-slip boundary condition in three spatial dimensions, as well as the existence and uniqueness of probabilistically strong, analytically weak solutions in two dimensions. The criterion applies for these solutions in both two and three dimensions, with some technical simplifications in the 2D case

Existence and Uniqueness of Maximal Solutions to SPDEs with Applications to Viscous Fluid Equations

We present two criteria to conclude that a stochastic partial differential equation (SPDE) posseses a unique maximal strong solution. This paper provides the full details of the abstract well-posedness results first given in arXiv:2202.09242v2, and partners a paper which rigorously addresses applications to the 3D SALT (Stochastic Advection by Lie Transport) Navier-Stokes Equation in velocity and vorticity form, on the torus and the bounded domain respectively. Each criterion has its corresponding set of assumptions and can be applied to viscous fluid equations with additive, multiplicative or a general transport type noise.Comment: 58 page

Polymeric scaffolds as building blocks for nanomaterials with biomedical applications

Functional polymers are emerging as strong candidates for a variety of biomedical applications, but progress in this field is slow due to the difficulties associated with the synthesis of libraries of polymers. Polymeric scaffolds facilitate the rapid synthesis of such functional polymers by employing click chemistries as a tool for post-polymerisation modification. Acrylic and acetylene based polyhydrazides have been explored as potential scaffolds for the in situ screening of functionalised polymers for biomedical applications. Poly(acryloyl hydrazide) was prepared from commercially available starting materials using RAFT polymerisation in a three step synthesis, and its postpolymerisation modification using a variety of hydrophilic and hydrophobic aldehydes was investigated. Biocompatible solvents and reaction conditions were determined such that the postpolymerisation modification could be achieved with good yields or better. The applicability of the scaffold was shown during the in situ screening of functional polymers for siRNA delivery, which required no isolation or purification of candidate polymers. Poly(4-ethynylbenzohydrazide) was synthesised using rhodium catalysed polymerisation conditions, towards achieving a helical polymer scaffold. Despite the lack of solubility in aqueous solvents, the stability and post-polymerisation modification was analysed in a variety of conditions, opening the possibility of synthesising biodegradable mimics to naturally occurring helical moieties

Poly(acryloyl hydrazide), a versatile scaffold for the preparation of functional polymers: synthesis and post-polymerisation modification

Here we present the synthesis and post-polymerisation modification of poly(acryloyl hydrazide), a versatile scaffold for the preparation of functional polymers: poly(acryloyl hydrazide) was prepared from commercially available starting materials in a three step synthesis on a large scale, in good yields and high purity. Our synthetic approach included the synthesis of a Boc-protected acryloyl hydrazide, the preparation of polymers via RAFT polymerisation and the deprotection of the corresponding Boc-protected poly(acryloyl hydrazide). Post-polymerisation modification of poly(acryloyl hydrazide) was then demonstrated using a range of conditions for both hydrophilic and hydrophobic aldehydes. These experiments demonstrate the potential of poly(acryloyl hydrazide) as a scaffold in the synthesis of functional polymers, in particular those applications where in situ screening of the activity of the functionalised polymers may be required (e.g. biological applications)This work was supported by the Royal Society, U.K (IE130688) and the Wellcome Trust (177ISSFPP). F. F.-T. thanks the Birmingham Science City and the European Regional Development Fund, the Royal Society (RG140273), and the University of Birmingham (John Evans Fellowship). J. M. thanks funding from MINECO (CTQ2014-59646-R, RYC-2013-1378) the Xunta de Galicia (ED431G/09 and 2016-AD031) and the ERC (Stg-DYNAP-677786)S

TurboTag: Lookup Filtering to Reduce Coherence Directory Power

On-chip coherence directories of today’s multi-core systems are not energy efficient. Coherence directories dissipate a significant fraction of their power on unnecessary lookups when running commercial server and scientific workloads. These workloads have large working sets that are beyond the reach of on-chip caches of modern processors. Limited to capturing a small part of the working set, private caches retain cache blocks only for a short period of time before replacing them with new blocks. Moreover, coherence enforcement is a known performance bottleneck of multi-threaded software, hence data-sharing in optimized high-performance software is minimal. Consequently, the majority of the accesses to the coherence directory find no sharers in the directory because the data are not available in the on-chip private caches, effectively wasting power on the coherence checks. To improve energy-efficiency for future many-core systems, we propose TurboTag, a filtering mechanism to eliminate needless directory lookups. We analyze full-system traces of server and scientific workloads and find that over 69% of accesses to the directory find no sharers and can be entirely avoided. Taking advantage of this behavior, TurboTag achieves a 58% reduction in the directory’s dynamic power consumption

Different-Length Hydrazone Activated Polymers for Plasmid DNA Condensation and Cellular Transfection

The recent advances in genetic engineering demand the development of conceptually new methods to prepare and identify efficient vectors for the intracellular delivery of different nucleotide payloads ranging from short single-stranded oligonucleotides to larger plasmid double-stranded circular DNAs. Although many challenges still have to be overcome, polymers hold great potential for intracellular nucleotide delivery and gene therapy. We here develop and apply the postpolymerization modification of polyhydrazide scaffolds, with different degree of polymerization, for the preparation of amphiphilic polymeric vehicles for the intracellular delivery of a circular plasmid DNA. The hydrazone formation reactions with a mixture of cationic and hydrophobic aldehydes proceed in physiologically compatible aqueous conditions, and the resulting amphiphilic polyhydrazones are directly combined with the biological cargo without any purification step. This methodology allowed the preparation of stable polyplexes with a suitable size and zeta potential to achieve an efficient encapsulation and intracellular delivery of the DNA cargo. Simple formulations that performed with efficiencies and cell viabilities comparable to the current gold standard were identified. Furthermore, the internalization mechanism was studied via internalization experiments in the presence of endocytic inhibitors and fluorescence microscopy. The results reported here confirmed that the polyhydrazone functionalization is a suitable strategy for the screening and identification of customized polymeric vehicles for the delivery of different nucleotide cargosThis work was partially supported by the Spanish Agencia Estatal de Investigación (AEI) [CTQ2014-59646-R, CTQ2016-78423-R, SAF2017-89890-R], the Xunta de Galicia (ED431G/09, ED431C 2017/25 and 2016-AD031), the ERDF, Royal Society U.K (IE130688 and RG140273), and the Wellcome Trust (177ISSFPP). J.M. received a Ramón y Cajal (RYC-2013-13784), an ERC Starting Investigator Grant (DYNAP-677786), and a Young Investigator Grant from the Human Frontier Science Research Program (RGY0066/2017). F. F.-T. thanks the Birmingham Science City and the European Regional Development Fund, and the University of Birmingham (John Evans Fellowship). J.M.P. thanks the Spanish Agencia Estatal de Investigación (AEI) for his research contractS