Synthetic Aperture Radar (SAR) data processing

The available and optimal methods for generating SAR imagery for NASA applications were identified. The SAR image quality and data processing requirements associated with these applications were studied. Mathematical operations and algorithms required to process sensor data into SAR imagery were defined. The architecture of SAR image formation processors was discussed, and technology necessary to implement the SAR data processors used in both general purpose and dedicated imaging systems was addressed

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1

Quantum-Mechanical Histories and the Uncertainty Principle: I.Information-Theoretic Inequalities

This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories. We first consider histories characterized by position or momentum projections at two moments of time. Both exact and approximate (Gaussian) projections are studied. Shannon information is used as a measure of the uncertainty expressed in the probabilities for these histories. We derive a number of inequalities in which the uncertainty principle is expressed as a lower bound on the information of phase space distributions derived from the probabilities for two-time histories. We go on to consider histories characterized by position samplings at $n$ moments of time. We derive a lower bound on the information of the joint probability for $n$ position samplings. Similar bounds are derived for histories characterized by samplings of other variables. All lower bounds on the information of histories have the general form $\ln \left( V_H / V_S \right)$, where $V_H$ is a volume element of history space, which we define, and $V_S$ is the volume of that space probed by the projections. We thus obtain a concise and general form of the uncertainty principle referring directly to the histories description of the system, and making no reference to notions of phase space.Comment: 40 pages (revised uncorrupted version), Imperial College Preprint IC 92-93/2

Clinicopathological and prognostic significance of HER-2/neu and VEGF expression in colon carcinomas

<p>Abstract</p> <p>Background</p> <p>HER-2/neu and VEGF expression is correlated with disease behaviors in various cancers. However, evidence for their expression in colon cancer is rather contradictory both for the protein expression status and prognostic value. HER-2/neu is found to participate in VEGF regulation, and has known correlation with VEGF expression in some tumors. In this study, we investigated HER-2/neu and VEGF expression in Chinese colon patients and explored whether there was any correlation between their expression patterns.</p> <p>Methods</p> <p>HER-2/neu and VEGF were investigated immunohistochemically using tumor samples obtained from 317 colon cancer patients with all tumor stages. Correlation of the degree of staining with clinicopathological parameters and survival was investigated.</p> <p>Results</p> <p>Positive expression rates of HER-2/neu and VEGF in colon cancer were 15.5% and 55.5% respectively. HER-2/neu expression was significantly correlated with tumor size and distant metastases (<it>P </it>< 0.05), but was not an independent prognostic marker of survival <it>(P > 0.05)</it>. Expression of VEGF was significantly correlated with tumor size, tumor stage, lymph node metastases, and distant metastases (<it>P </it>< 0.05). The 5-year survival rate in patients with negative and positive VEGF expression was 70.2% and 61.9% respectively; the difference was not statistically significant <it>(P = 0.146)</it>. No correlation between HER-2/neu and VEGF expression was detected (<it>P = </it>0.151).</p> <p>Conclusions</p> <p>HER-2/neu and VEGF are not important prognostic markers of colon cancer. The present results do not support any association between HER2/neu and VEGF expression in this setting.</p

Dynamic Models of Language Evolution: The Linguistic Perspective

Language is probably the key defining characteristic of humanity, an immensely powerful tool which provides its users with an infinitely expressive means of representing their complex thoughts and reflections, and of successfully communicating them to others. It is the foundation on which human societies have been built and the means through which humanity’s unparalleled intellectual and technological achievements have been realized. Although we have a natural intuitive understanding of what a language is, the specification of a particular language is nevertheless remarkably difficult, if not impossible, to pin down precisely. All languages contain many separate yet integral systems which work interdependently to allow the expression of our thoughts and the interpretation of others’ expressions: each has, for instance, a set of basic meaningless sounds (e.g. [e], [l], [s]) which can be combined to make different meaningful words and parts of words (e.g. else, less, sell, -less ); these meaningful units can be combined to make complex words (e.g. spinelessness, selling ), and the words themselves can then be combined in very many complex ways into phrases, clauses and an infinite number of meaningful sentences; finally each of these sentences can be interpreted in dramatically different ways, depending on the contexts in which it is uttered and on who is doing the interpretation. Languages can be analysed at any of these different levels, which make up many of the sub-fields of linguistics, and the primary job of linguistic theorists is to try to explain the rules which best explain these complex combinations

Measurement of the mass difference m(D-s(+))-m(D+) at CDF II

We present a measurement of the mass difference m(D-s(+))-m(D+), where both the D-s(+) and D+ are reconstructed in the phipi(+) decay channel. This measurement uses 11.6 pb(-1) of data collected by CDF II using the new displaced-track trigger. The mass difference is found to be m(D-s(+))-m(D+)=99.41+/-0.38(stat)+/-0.21(syst) MeV/c(2)

A guide to the Choquard equation

We survey old and recent results dealing with the existence and properties of solutions to the Choquard type equations $$-\Delta u + V(x)u = \bigl(|x|^{-(N-\alpha)} * |u|^p\bigr)|u|^{p - 2} u \qquad \text{in $\mathbb{R}^N$},$$ and some of its variants and extensions.Comment: 39 page

Context, cognition and communication in language

Questions pertaining to the unique structure and organisation of language have a long history in the field of linguistics. In recent years, researchers have explored cultural evolutionary explanations, showing how language structure emerges from weak biases amplified over repeated patterns of learning and use. One outstanding issue in these frameworks is accounting for the role of context. In particular, many linguistic phenomena are said to to be context-dependent; interpretation does not take place in a void, and requires enrichment from the current state of the conversation, the physical situation, and common knowledge about the world. Modelling the relationship between language structure and context is therefore crucial for developing a cultural evolutionary approach to language. One approach is to use statistical analyses to investigate large-scale, cross-cultural datasets. However, due to the inherent limitations of statistical analyses, especially with regards to the inadequacy of these methods to test hypotheses about causal relationships, I argue that experiments are better suited to address questions pertaining to language structure and context. From here, I present a series of artificial language experiments, with the central aim being to test how manipulations to context influence the structure and organisation of language. Experiment 1 builds upon previous work in iterated learning and communication games through demonstrating that the emergence of optimal communication systems is contingent on the contexts in which languages are learned and used. The results show that language systems gradually evolve to only encode information that is informative for conveying the intended meaning of the speaker - resulting in markedly different systems of communication. Whereas Experiment 1 focused on how context influences the emergence of structure, Experiments 2 and 3 investigate under what circumstances do manipulations to context result in the loss of structure. While the results are inconclusive across these two experiments, there is tentative evidence that manipulations to context can disrupt structure, but only when interacting with other factors. Lastly, Experiment 4 investigates whether the degree of signal autonomy (the capacity for a signal to be interpreted without recourse to contextual information) is shaped by manipulations to contextual predictability: the extent to which a speaker can estimate and exploit contextual information a hearer uses in interpreting an utterance. When the context is predictable, speakers organise languages to be less autonomous (more context-dependent) through combining linguistic signals with contextual information to reduce effort in production and minimise uncertainty in comprehension. By decreasing contextual predictability, speakers increasingly rely on strategies that promote more autonomous signals, as these signals depend less on contextual information to discriminate between possible meanings. Overall, these experiments provide proof-of-concept for investigating the relationship between language structure and context, showing that the organisational principles underpinning language are the result of competing pressures from context, cognition, and communication