Euler-Bessel and Euler-Fourier Transforms

We consider a topological integral transform of Bessel (concentric isospectral sets) type and Fourier (hyperplane isospectral sets) type, using the Euler characteristic as a measure. These transforms convert constructible \zed-valued functions to continuous $\real$-valued functions over a vector space. Core contributions include: the definition of the topological Bessel transform; a relationship in terms of the logarithmic blowup of the topological Fourier transform; and a novel Morse index formula for the transforms. We then apply the theory to problems of target reconstruction from enumerative sensor data, including localization and shape discrimination. This last application utilizes an extension of spatially variant apodization (SVA) to mitigate sidelobe phenomena

Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

Dianthracenylazatrioxa[8]circulene: synthesis, characterization and application in OLEDs

A soluble, green-blue fluorescent, pi-extended azatrioxa[8]circulene was synthesized by oxidative condensation of a 3,6-dihydroxycarbazole and 1,4-anthraquinone by using benzofuran scaffolding. This is the first circulene to incorporate anthracene within its carbon framework. Solvent-dependent fluorescence and bright green electroluminescence accompanied by excimer emission are the key optical properties of this material. The presence of sliding pi-stacked columns in the single crystal of dianthracenylazatrioxa[8]circulene is found to cause a very high electron-hopping rate, thus making this material a promising n-type organic semiconductor with an electron mobility predicted to be around 2.26 cm(2) V-1 s(-1). The best organic light-emitting diode (OLED) device based on the dianthracenylazatrioxa[8]circulene fluorescent emitter has a brightness of around 16 000 Cd m(-2) and an external quantum efficiency of 3.3 %. Quantum dot-based OLEDs were fabricated by using dianthracenylazatrioxa[8]circulene as a host matrix material.Peer reviewe

In vitro culture with gemcitabine augments death receptor and NKG2D ligand expression on tumour cells

Much effort has been made to try to understand the relationship between chemotherapeutic treatment of cancer and the immune system. Whereas much of that focus has been on the direct effect of chemotherapy drugs on immune cells and the release of antigens and danger signals by malignant cells killed by chemotherapy, the effect of chemotherapy on cells surviving treatment has often been overlooked. In the present study, tumour cell lines: A549 (lung), HCT116 (colon) and MCF-7 (breast), were treated with various concentrations of the chemotherapeutic drugs cyclophosphamide, gemcitabine (GEM) and oxaliplatin (OXP) for 24 hours in vitro. In line with other reports, GEM and OXP upregulated expression of the death receptor CD95 (fas) on live cells even at sub-cytotoxic concentrations. Further investigation revealed that the increase in CD95 in response to GEM sensitised the cells to fas ligand treatment, was associated with increased phosphorylation of stress activated protein kinase/c-Jun N-terminal kinase and that other death receptors and activatory immune receptors were co-ordinately upregulated with CD95 in certain cell lines. The upregulation of death receptors and NKG2D ligands together on cells after chemotherapy suggest that although the cells have survived preliminary treatment with chemotherapy they may now be more susceptible to immune cell-mediated challenge. This re-enforces the idea that chemotherapy-immunotherapy combinations may be useful clinically and has implications for the make-up and scheduling of such treatments

Optimization of supply diversity for the self-assembly of simple objects in two and three dimensions

The field of algorithmic self-assembly is concerned with the design and analysis of self-assembly systems from a computational perspective, that is, from the perspective of mathematical problems whose study may give insight into the natural processes through which elementary objects self-assemble into more complex ones. One of the main problems of algorithmic self-assembly is the minimum tile set problem (MTSP), which asks for a collection of types of elementary objects (called tiles) to be found for the self-assembly of an object having a pre-established shape. Such a collection is to be as concise as possible, thus minimizing supply diversity, while satisfying a set of stringent constraints having to do with the termination and other properties of the self-assembly process from its tile types. We present a study of what we think is the first practical approach to MTSP. Our study starts with the introduction of an evolutionary heuristic to tackle MTSP and includes results from extensive experimentation with the heuristic on the self-assembly of simple objects in two and three dimensions. The heuristic we introduce combines classic elements from the field of evolutionary computation with a problem-specific variant of Pareto dominance into a multi-objective approach to MTSP.Comment: Minor typos correcte

Vicious Walkers and Hook Young Tableaux

We consider a generalization of the vicious walker model. Using a bijection map between the path configuration of the non-intersecting random walkers and the hook Young diagram, we compute the probability concerning the number of walker's movements. Applying the saddle point method, we reveal that the scaling limit gives the Tracy--Widom distribution, which is same with the limit distribution of the largest eigenvalues of the Gaussian unitary ensemble.Comment: 23 pages, 5 figure

On the partial connection between random matrices and interacting particle systems

In the last decade there has been increasing interest in the fields of random matrices, interacting particle systems, stochastic growth models, and the connections between these areas. For instance, several objects appearing in the limit of large matrices arise also in the long time limit for interacting particles and growth models. Examples of these are the famous Tracy-Widom distribution functions and the Airy_2 process. The link is however sometimes fragile. For example, the connection between the eigenvalues in the Gaussian Orthogonal Ensembles (GOE) and growth on a flat substrate is restricted to one-point distribution, and the connection breaks down if we consider the joint distributions. In this paper we first discuss known relations between random matrices and the asymmetric exclusion process (and a 2+1 dimensional extension). Then, we show that the correlation functions of the eigenvalues of the matrix minors for beta=2 Dyson's Brownian motion have, when restricted to increasing times and decreasing matrix dimensions, the same correlation kernel as in the 2+1 dimensional interacting particle system under diffusion scaling limit. Finally, we analyze the analogous question for a diffusion on (complex) sample covariance matrices.Comment: 31 pages, LaTeX; Added a section concerning the Markov property on space-like path

Second order analysis of geometric functionals of Boolean models

This paper presents asymptotic covariance formulae and central limit theorems for geometric functionals, including volume, surface area, and all Minkowski functionals and translation invariant Minkowski tensors as prominent examples, of stationary Boolean models. Special focus is put on the anisotropic case. In the (anisotropic) example of aligned rectangles, we provide explicit analytic formulae and compare them with simulation results. We discuss which information about the grain distribution second moments add to the mean values.Comment: Chapter of the forthcoming book "Tensor Valuations and their Applications in Stochastic Geometry and Imaging" in Lecture Notes in Mathematics edited by Markus Kiderlen and Eva B. Vedel Jensen. (The second version mainly resolves minor LaTeX problems.

Statistical mechanics of voting

Decision procedures aggregating the preferences of multiple agents can produce cycles and hence outcomes which have been described heuristically as `chaotic'. We make this description precise by constructing an explicit dynamical system from the agents' preferences and a voting rule. The dynamics form a one dimensional statistical mechanics model; this suggests the use of the topological entropy to quantify the complexity of the system. We formulate natural political/social questions about the expected complexity of a voting rule and degree of cohesion/diversity among agents in terms of random matrix models---ensembles of statistical mechanics models---and compute quantitative answers in some representative cases.Comment: 9 pages, plain TeX, 2 PostScript figures included with epsf.tex (ignore the under/overfull \vbox error messages