Finite difference approximations for a size-structured population model with distributed states in the recruitment

In this paper we consider a size-structured population model where individuals may be recruited into the population at different sizes. First and second order finite difference schemes are developed to approximate the solution of the mathematical model. The convergence of the approximations to a unique weak solution with bounded total variation is proved. We then show that as the distribution of the new recruits become concentrated at the smallest size, the weak solution of the distributed states-at-birth model converges to the weak solution of the classical Gurtin-McCamy-type size-structured model in the weak$^*$ topology. Numerical simulations are provided to demonstrate the achievement of the desired accuracy of the two methods for smooth solutions as well as the superior performance of the second-order method in resolving solution-discontinuities. Finally we provide an example where supercritical Hopf-bifurcation occurs in the limiting single state-at-birth model and we apply the second-order numerical scheme to show that such bifurcation occurs in the distributed model as well

Tumor detection and elimination by a targeted gallium corrole

Sulfonated gallium(III) corroles are intensely fluorescent macrocyclic compounds that spontaneously assemble with carrier proteins to undergo cell entry. We report in vivo imaging and therapeutic efficacy of a tumor-targeted corrole noncovalently assembled with a heregulin-modified protein directed at the human epidermal growth factor receptor (HER). Systemic delivery of this protein-corrole complex results in tumor accumulation, which can be visualized in vivo owing to intensely red corrole fluorescence. Targeted delivery in vivo leads to tumor cell death while normal tissue is spared. These findings contrast with the effects of doxorubicin, which can elicit cardiac damage during therapy and required direct intratumoral injection to yield similar levels of tumor shrinkage compared with the systemically delivered corrole. The targeted complex ablated tumors at >5 times a lower dose than untargeted systemic doxorubicin, and the corrole did not damage heart tissue. Complexes remained intact in serum and the carrier protein elicited no detectable immunogenicity. The sulfonated gallium(III) corrole functions both for tumor detection and intervention with safety and targeting advantages over standard chemotherapeutic agents

One-vortex moduli space and Ricci flow

The metric on the moduli space of one abelian Higgs vortex on a surface has a natural geometrical evolution as the Bradlow parameter, which determines the vortex size, varies. It is shown by various arguments, and by calculations in special cases, that this geometrical flow has many similarities to Ricci flow.Comment: 20 page

Sensitivity analysis of circadian entrainment in the space of phase response curves

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input--output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations.Comment: 22 pages, 8 figures. Correction of a mistake in Definition 2.1. arXiv admin note: text overlap with arXiv:1206.414

The Algebro-Geometric Solutions for the Ruijsenaars-Toda Hierarchy

We provide a detailed treatment of Ruijsenaars-Toda (RT) hierarchy with special emphasis on its the theta function representation of all algebro-geometric solutions. The basic tools involve hyperelliptic curve $\mathcal{K}_p$ associated with the Burchnall-Chaundy polynomial, Dubrovin-type equations for auxiliary divisors and associated trace formulas. With the help of a foundamental meromorphic function $\phi$, Baker-Akhiezer vector $\Psi$ on $\mathcal{K}_p$, the complex-valued algebro-geometric solutions of RT hierarchy are derived.Comment: 49 pages. arXiv admin note: substantial text overlap with arXiv:nlin/0702058, arXiv:nlin/0611055 by other author

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]>>1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale

A Mechanistic Study of Tumor-Targeted Corrole Toxicity

HerGa is a self-assembled tumor-targeted particle that bears both tumor detection and elimination activities in a single, two-component complex (Agadjanian et al. Proc. Natl. Acad. Sci. U.S.A.2009, 106, 6105–6110). Given its multifunctionality, HerGa (composed of the fluorescent cytotoxic corrole macrocycle, S2Ga, noncovalently bound to the tumor-targeted cell penetration protein, HerPBK10) has the potential for high clinical impact, but its mechanism of cell killing remains to be elucidated, and hence is the focus of the present study. Here we show that HerGa requires HerPBK10-mediated cell entry to induce toxicity. HerGa (but not HerPBK10 or S2Ga alone) induced mitochondrial membrane potential disruption and superoxide elevation, which were both prevented by endosomolytic-deficient mutants, indicating that cytosolic exposure is necessary for corrole-mediated cell death. A novel property discovered here is that corrole fluorescence lifetime acts as a pH indicator, broadcasting the intracellular microenvironmental pH during uptake in live cells. This feature in combination with two-photon imaging shows that HerGa undergoes early endosome escape during uptake, avoiding compartments of pH < 6.5. Cytoskeletal disruption accompanied HerGa-mediated mitochondrial changes whereas oxygen scavenging reduced both events. Paclitaxel treatment indicated that HerGa uptake requires dynamic microtubules. Unexpectedly, low pH is insufficient to induce release of the corrole from HerPBK10. Altogether, these studies identify a mechanistic pathway in which early endosomal escape enables HerGa-induced superoxide generation leading to cytoskeletal and mitochondrial damage, thus triggering downstream cell death

Non-polynomial Worst-Case Analysis of Recursive Programs

We study the problem of developing efficient approaches for proving worst-case bounds of non-deterministic recursive programs. Ranking functions are sound and complete for proving termination and worst-case bounds of nonrecursive programs. First, we apply ranking functions to recursion, resulting in measure functions. We show that measure functions provide a sound and complete approach to prove worst-case bounds of non-deterministic recursive programs. Our second contribution is the synthesis of measure functions in nonpolynomial forms. We show that non-polynomial measure functions with logarithm and exponentiation can be synthesized through abstraction of logarithmic or exponentiation terms, Farkas' Lemma, and Handelman's Theorem using linear programming. While previous methods obtain worst-case polynomial bounds, our approach can synthesize bounds of the form $\mathcal{O}(n\log n)$ as well as $\mathcal{O}(n^r)$ where $r$ is not an integer. We present experimental results to demonstrate that our approach can obtain efficiently worst-case bounds of classical recursive algorithms such as (i) Merge-Sort, the divide-and-conquer algorithm for the Closest-Pair problem, where we obtain $\mathcal{O}(n \log n)$ worst-case bound, and (ii) Karatsuba's algorithm for polynomial multiplication and Strassen's algorithm for matrix multiplication, where we obtain $\mathcal{O}(n^r)$ bound such that $r$ is not an integer and close to the best-known bounds for the respective algorithms.Comment: 54 Pages, Full Version to CAV 201

Characteristics of Ramachandran maps of L-alanine diamides as computed by various molecular mechanics, semiempirical and ab initio MO methods. A search for primary standard of peptide conformational stability

The optimized geometries and relative energies obtained by four force field and two semi-empirical methods were compared with ab initio results computed for formyl-L-alaninamide. Not all methods yielded the same number of minimum energy conformers. Furthermore, while the optimized geometries of the conformers found were comparable, the computed relative energies varied substantially. Also, the force field calculations produced Ramachandran maps that did not even have the appearance of the ab initio Ramachandran map. Correlating the ab initio relative energies (Delta E) or free energy (Delta G) with the log of relative populations, In(p(x)/p(gamma L)), led to linear relationships from which four conformers deviated; two of them (alpha(L) and epsilon(L)) were overly destabilized and two of them (gamma(L) and gamma(D)) were over-stabilized. It is suggested that, after such deviations are corrected, a primary standard may be obtained that might be useful in further investigations related to force-field parametrization as well as protein folding. (C) 1998 Elsevier Science B.V. All rights reserved

Hydrogen bond network topology in liquid water and methanol: a graph theory approach

Networks are increasingly recognized as important building blocks of various systems in nature and society. Water is known to possess an extended hydrogen bond network, in which the individual bonds are broken in the sub-picosecond range and still the network structure remains intact. We investigated and compared the topological properties of liquid water and methanol at various temperatures using concepts derived within the framework of graph and network theory (neighbour number and cycle size distribution, the distribution of local cyclic and local bonding coefficients, Laplacian spectra of the network, inverse participation ratio distribution of the eigenvalues and average localization distribution of a node) and compared them to small world and Erdős–Rényi random networks. Various characteristic properties (e.g. the local cyclic and bonding coefficients) of the network in liquid water could be reproduced by small world and/or Erdős–Rényi networks, but the ring size distribution of water is unique and none of the studied graph models could describe it. Using the inverse participation ratio of the Laplacian eigenvectors we characterized the network inhomogeneities found in water and showed that similar phenomena can be observed in Erdős–Rényi and small world graphs. We demonstrated that the topological properties of the hydrogen bond network found in liquid water systematically change with the temperature and that increasing temperature leads to a broader ring size distribution. We applied the studied topological indices to the network of water molecules with four hydrogen bonds, and showed that at low temperature (250 K) these molecules form a percolated or nearly-percolated network, while at ambient or high temperatures only small clusters of four-hydrogen bonded water molecules exist