On the Adjoint Operator in Photoacoustic Tomography

Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from coupled physics" technique, in which the image contrast is due to optical absorption, but the information is carried to the surface of the tissue as ultrasound pulses. Many algorithms and formulae for PAT image reconstruction have been proposed for the case when a complete data set is available. In many practical imaging scenarios, however, it is not possible to obtain the full data, or the data may be sub-sampled for faster data acquisition. In such cases, image reconstruction algorithms that can incorporate prior knowledge to ameliorate the loss of data are required. Hence, recently there has been an increased interest in using variational image reconstruction. A crucial ingredient for the application of these techniques is the adjoint of the PAT forward operator, which is described in this article from physical, theoretical and numerical perspectives. First, a simple mathematical derivation of the adjoint of the PAT forward operator in the continuous framework is presented. Then, an efficient numerical implementation of the adjoint using a k-space time domain wave propagation model is described and illustrated in the context of variational PAT image reconstruction, on both 2D and 3D examples including inhomogeneous sound speed. The principal advantage of this analytical adjoint over an algebraic adjoint (obtained by taking the direct adjoint of the particular numerical forward scheme used) is that it can be implemented using currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems

Concept design of a fast sail assisted feeder container ship

An environmentally sustainable fast sail-assisted feeder-container ship concept, with a maximum speed of 25 knots, has been developed for the 2020 South East Asian and Caribbean container markets. The use of low-carbon and zero-sulphur fuel (liquefied natural gas) and improvements in operational efficiency (cargo handling and scheduling) mean predicted Green house gas emissions should fall by 42% and 40% in the two selected operational regions. The adoption of a Multi-wing sail system reduces power requirement by up to 6% at the lower ship speed of 15 knots. The predicted daily cost savings are respectively 27% and 33% in South East Asian and the Caribbean regions.Two hull forms with a cargo capacity of 1270TEU utilising different propulsion combinations were initially developed to meet operational requirements. Analysis & tank testing of different hydrodynamic phenomena has enabled identification of efficiency gains for each design. The final propulsion chosen is a contra-rotating podded drive arrangement. Wind tunnel testing improved Multi-wing sail performance by investigating wing spacing, wing stagger and sail-container interactions. The associated lift coefficient was increased by 32%. Whilst savings in sail-assisted power requirement are lower than initially predicted an unexpected identified benefit was motion damping.The fast feeder-container ship is a proposed as a viable future method of container transhipment

Popularity-Driven Networking

We investigate the growth of connectivity in a network. In our model, starting with a set of disjoint nodes, links are added sequentially. Each link connects two nodes, and the connection rate governing this random process is proportional to the degrees of the two nodes. Interestingly, this network exhibits two abrupt transitions, both occurring at finite times. The first is a percolation transition in which a giant component, containing a finite fraction of all nodes, is born. The second is a condensation transition in which the entire system condenses into a single, fully connected, component. We derive the size distribution of connected components as well as the degree distribution, which is purely exponential throughout the evolution. Furthermore, we present a criterion for the emergence of sudden condensation for general homogeneous connection rates.Comment: 5 pages, 2 figure

Preparation and characterization of electrolytic alumina deposit on austenitic stainless steel

Conversion coating modified by alumina has been studied as a way for improving the resistance to thermal oxidation of an austenitic stainless steel. Conversion coating, characterized by a particular morphology and strong interfacial adhesion with the substrate, facilitate the electrochemical deposition of ceramic layers and enhance their adhesion to the substrate. The influence of the current density and treatment time on alumina deposit was studied using statistical experimental designs like Doehlert uniform shell design. After heating, coatings present a continuous composition gradient with refractory compounds at the surface. The behavior at high temperature (1000 8C) of the alumina coating was investigated. The presence of alumina increases the oxidation resistance of an austenitic stainless steel at 1000 8C. The morphology and the chemical composition of the deposit are analyzed. Results on the thermal stability of coating on austenitic stainless steel are presented

A Learned Born Series for Highly-Scattering Media

A new method for solving the wave equation is presented, called the learned Born series (LBS), which is derived from a convergent Born Series but its components are found through training. The LBS is shown to be significantly more accurate than the convergent Born series for the same number of iterations, in the presence of high contrast scatterers, while maintaining a comparable computational complexity. The LBS is able to generate a reasonable prediction of the global pressure field with a small number of iterations, and the errors decrease with the number of learned iterations.Comment: 6 pages, 1 figur

A Helmholtz equation solver using unsupervised learning: Application to transcranial ultrasound

Transcranial ultrasound therapy is increasingly used for the non-invasive treatment of brain disorders. However, conventional numerical wave solvers are currently too computationally expensive to be used online during treatments to predict the acoustic field passing through the skull (e.g., to account for subject-specific dose and targeting variations). As a step towards real-time predictions, in the current work, a fast iterative solver for the heterogeneous Helmholtz equation in 2D is developed using a fully-learned optimizer. The lightweight network architecture is based on a modified UNet that includes a learned hidden state. The network is trained using a physics-based loss function and a set of idealized sound speed distributions with fully unsupervised training (no knowledge of the true solution is required). The learned optimizer shows excellent performance on the test set, and is capable of generalization well outside the training examples, including to much larger computational domains, and more complex source and sound speed distributions, for example, those derived from x-ray computed tomography images of the skull.Comment: 23 pages, 13 figure

Rank Statistics in Biological Evolution

We present a statistical analysis of biological evolution processes. Specifically, we study the stochastic replication-mutation-death model where the population of a species may grow or shrink by birth or death, respectively, and additionally, mutations lead to the creation of new species. We rank the various species by the chronological order by which they originate. The average population N_k of the kth species decays algebraically with rank, N_k ~ M^{mu} k^{-mu}, where M is the average total population. The characteristic exponent mu=(alpha-gamma)/(alpha+beta-gamma)$ depends on alpha, beta, and gamma, the replication, mutation, and death rates. Furthermore, the average population P_k of all descendants of the kth species has a universal algebraic behavior, P_k ~ M/k.Comment: 4 pages, 3 figure

Testing systems of identical components

We consider the problem of testing sequentially the components of a multi-component reliability system in order to figure out the state of the system via costly tests. In particular, systems with identical components are considered. The notion of lexicographically large binary decision trees is introduced and a heuristic algorithm based on that notion is proposed. The performance of the heuristic algorithm is demonstrated by computational results, for various classes of functions. In particular, in all 200 random cases where the underlying function is a threshold function, the proposed heuristic produces optimal solutions

A Method of Intervals for the Study of Diffusion-Limited Annihilation, A + A --> 0

We introduce a method of intervals for the analysis of diffusion-limited annihilation, A+A -> 0, on the line. The method leads to manageable diffusion equations whose interpretation is intuitively clear. As an example, we treat the following cases: (a) annihilation in the infinite line and in infinite (discrete) chains; (b) annihilation with input of single particles, adjacent particle pairs, and particle pairs separated by a given distance; (c) annihilation, A+A -> 0, along with the birth reaction A -> 3A, on finite rings, with and without diffusion.Comment: RevTeX, 13 pages, 4 figures, 1 table. References Added, and some other minor changes, to conform with final for

Increasing water cycle extremes in California and in relation to ENSO cycle under global warming

Since the winter of 2013–2014, California has experienced its most severe drought in recorded history, causing statewide water stress, severe economic loss and an extraordinary increase in wildfires. Identifying the effects of global warming on regional water cycle extremes, such as the ongoing drought in California, remains a challenge. Here we analyse large-ensemble and multi-model simulations that project the future of water cycle extremes in California as well as to understand those associations that pertain to changing climate oscillations under global warming. Both intense drought and excessive flooding are projected to increase by at least 50% towards the end of the twenty-first century; this projected increase in water cycle extremes is associated with a strengthened relation to El Niño and the Southern Oscillation (ENSO)—in particular, extreme El Niño and La Niña events that modulate California’s climate not only through its warm and cold phases but also its precursor patterns