On the foundations of cancer modelling: selected topics, speculations, & perspectives

This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution

Estimating three-demensional energy transfer in isotropic turbulence

To obtain an estimate of the spectral transfer function that indicates the rate of decay of energy, an x-wire probe was set at a fixed position, and two single wire probes were set at a number of locations in the same plane perpendicular to the mean flow in the wind tunnel. The locations of the single wire probes are determined by pseudo-random numbers (Monte Carlo). Second order spectra and cross spectra are estimated. The assumption of isotropy relative to second order spectra is examined. Third order spectra are also estimated corresponding to the positions specified. A Monte Carlo Fourier transformation of the downstream bispectra corresponding to integration across the plane perpendicular to the flow is carried out assuming isotropy. Further integration is carried out over spherical energy shells

Fast computation of MadGraph amplitudes on graphics processing unit (GPU)

Continuing our previous studies on QED and QCD processes, we use the graphics processing unit (GPU) for fast calculations of helicity amplitudes for general Standard Model (SM) processes. Additional HEGET codes to handle all SM interactions are introduced, as well assthe program MG2CUDA that converts arbitrary MadGraph generated HELAS amplitudess(FORTRAN) into HEGET codes in CUDA. We test all the codes by comparing amplitudes and cross sections for multi-jet srocesses at the LHC associated with production of single and double weak bosonss a top-quark pair, Higgs boson plus a weak boson or a top-quark pair, and multisle Higgs bosons via weak-boson fusion, where all the heavy particles are allowes to decay into light quarks and leptons with full spin correlations. All the helicity amplitudes computed by HEGET are found to agree with those comsuted by HELAS within the expected numerical accuracy, and the cross sections obsained by gBASES, a GPU version of the Monte Carlo integration program, agree wish those obtained by BASES (FORTRAN), as well as those obtained by MadGraph. The performance of GPU was over a factor of 10 faster than CPU for all processes except those with the highest number of jets.Comment: 37 pages, 12 figure

Compositional changes on GaN surfaces under low-energy ion bombardment studied by synchrotron-based spectroscopies

We have investigated compositional changes on GaNsurfaces under Ar-ion bombardment using synchrotron-based high-resolution x-rayphotoemission (PES) and near-edge x-ray absorption fine structure(NEXAFS)spectroscopy. The low-energy ion bombardment of GaN produces a Ga-rich surface layer which transforms into a metallic Ga layer at higher bombarding energies. At the same time, the photoemissionspectra around N 1s core levels reveal the presence of both uncoordinated nitrogen and nitrogen interstitials, which we have analyzed in more details by x-rayabsorption measurements at N K edge. We have demonstrated that PES and NEXAFS provide a powerful combination for studying the compositional changes on GaNsurfaces. A mechanism for the relocation and loss of nitrogen during ion bombardment in agreement with some recent experimental and theoretical studies of defect formation in GaN has been proposed.P.N.K.D. is grateful for the financial support of the Australian Research Council

Evidence for a quantum phase transition in electron-doped Pr2−x_{2-x}Cex_{x}CuO4−δ_{4-\delta} from Thermopower measurements

The evidence for a quantum phase transition under the superconducting dome in the high-$T_c$ cuprates has been controversial. We report low temperature normal state thermopower(S) measurements in electron-doped Pr$_{2-x}$Ce$_{x}$CuO$_{4-\delta}$ as a function of doping (x from 0.11 to 0.19). We find that at 2K both S and S/T increase dramatically from x=0.11 to 0.16 and then saturate in the overdoped region. This behavior has a remarkable similarity to previous Hall effect results in Pr$_{2-x}$Ce$_{x}$CuO$_{4-\delta}$ . Our results are further evidence for an antiferromagnetic to paramagnetic quantum phase transition in electron-doped cuprates near x=0.16.Comment: 4 pages, 5 figure

Long-Term Global Market Correlations

In this paper we examine the correlation structure of the major world equity markets over 150 years. We find that correlations vary considerably through time and are highest during periods of economic and financial integration such as the late 19th and 20th centuries. Our analysis suggests that the diversification benefits to global investing are not constant, and that they are currently low compared to the rest of capital market history. We decompose the diversification benefits into two parts: a component that is due to variation in the average correlation across markets, and a component that is due to the variation in the investment opportunity set. There are periods, like the last two decades, in which the opportunity set expands dramatically, and the benefits to diversification are driven primarily by the existence of marginal markets. For other periods, such as the two decades following World War II, risk reduction is due to low correlations among the major national markets. From this, we infer that periods of globalization have both benefits and drawbacks for international investors. They expand the opportunity set, but diversification relies increasingly on investment in emerging markets.

Classification of Multipartite Entanglement via Negativity Fonts

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state - the negativity fonts. If K-way negativity fonts with non zero determinants exist, then selective partial transposition of a pure state, involving K of the N qubits (K leq N) yields an operator with negative eigevalues, identifying K-body correlations in the state. Expansion of GPT interms of K-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states, based on underlying structure of global partial transpose of canonical state, are proposed. Number of N-partite entanglement types for an N qubit system is found to be 2^{N-1}-N+2, while the number of major entanglement classes is 2^{N-1}-1. Major classes for three and four qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical state.Comment: 5 pages, No figures, Corrected typo

Anomalous thermopower and Nernst effect in CeCoIn5\rm CeCoIn_5: entropy-current loss in precursor state

The heavy-electron superconductor CeCoIn$_5$ exhibits a puzzling precursor state above its superconducting critical temperature at $T_c$ = 2.3 K. The thermopower and Nernst signal are anomalous. Below 15 K, the entropy current of the electrons undergoes a steep decrease reaching $\sim$0 at $T_c$. Concurrently, the off-diagonal thermoelectric current $\alpha_{xy}$ is enhanced. The delicate sensitivity of the zero-entropy state to field implies phase coherence over large distances. The prominent anomalies in the thermoelectric current contrast with the relatively weak effects in the resistivity and magnetization.Comment: 5 figures, 4 page