Mechanistic mathematical models: An underused platform for HPV research

Health economic modeling has become an invaluable methodology for the design and evaluation of clinical and public health interventions against the human papillomavirus (HPV) and associated diseases. At the same time, relatively little attention has been paid to a different yet complementary class of models, namely that of mechanistic mathematical models. The primary focus of mechanistic mathematical models is to better understand the intricate biologic mechanisms and dynamics of disease. Inspired by a long and successful history of mechanistic modeling in other biomedical fields, we highlight several areas of HPV research where mechanistic models have the potential to advance the field. We argue that by building quantitative bridges between biologic mechanism and population level data, mechanistic mathematical models provide a unique platform to enable collaborations between experimentalists who collect data at different physical scales of the HPV infection process. Through such collaborations, mechanistic mathematical models can accelerate and enhance the investigation of HPV and related diseases

Thermal quantum electrodynamics of nonrelativistic charged fluids

The theory relevant to the study of matter in equilibrium with the radiation field is thermal quantum electrodynamics (TQED). We present a formulation of the theory, suitable for non relativistic fluids, based on a joint functional integral representation of matter and field variables. In this formalism cluster expansion techniques of classical statistical mechanics become operative. They provide an alternative to the usual Feynman diagrammatics in many-body problems which is not perturbative with respect to the coupling constant. As an application we show that the effective Coulomb interaction between quantum charges is partially screened by thermalized photons at large distances. More precisely one observes an exact cancellation of the dipolar electric part of the interaction, so that the asymptotic particle density correlation is now determined by relativistic effects. It has still the $r^{-6}$ decay typical for quantum charges, but with an amplitude strongly reduced by a relativistic factor.Comment: 32 pages, 0 figures. 2nd versio

Link and subgraph likelihoods in random undirected networks with fixed and partially fixed degree sequence

The simplest null models for networks, used to distinguish significant features of a particular network from {\it a priori} expected features, are random ensembles with the degree sequence fixed by the specific network of interest. These "fixed degree sequence" (FDS) ensembles are, however, famously resistant to analytic attack. In this paper we introduce ensembles with partially-fixed degree sequences (PFDS) and compare analytic results obtained for them with Monte Carlo results for the FDS ensemble. These results include link likelihoods, subgraph likelihoods, and degree correlations. We find that local structural features in the FDS ensemble can be reasonably well estimated by simultaneously fixing only the degrees of few nodes, in addition to the total number of nodes and links. As test cases we use a food web, two protein interaction networks (\textit{E. coli, S. cerevisiae}), the internet on the autonomous system (AS) level, and the World Wide Web. Fixing just the degrees of two nodes gives the mean neighbor degree as a function of node degree, $_k$, in agreement with results explicitly obtained from rewiring. For power law degree distributions, we derive the disassortativity analytically. In the PFDS ensemble the partition function can be expanded diagrammatically. We obtain an explicit expression for the link likelihood to lowest order, which reduces in the limit of large, sparse undirected networks with $L$ links and with $k_{\rm max} \ll L$ to the simple formula $P(k,k') = kk'/(2L + kk')$. In a similar limit, the probability for three nodes to be linked into a triangle reduces to the factorized expression $P_{\Delta}(k_1,k_2,k_3) = P(k_1,k_2)P(k_1,k_3)P(k_2,k_3)$.Comment: 17 pages, includes 11 figures; first revision: shortened to 14 pages (7 figures), added discussion of subgraph counts, deleted discussion of directed network

Totally nonpositive completions on partial matrices

An n £ n real matrix is said to be totally no positive if every minor is no positive. In this paper, we are interested in totally no positive completion problems, that is, does A partial totally no positive matrix have a totally no positive matrix completion? This Problem has, in general, a negative answer. Therefore, we analyze the question: for which Labelled graphs G does every partial totally no positive matrix, whose associated graph is G, have a totally no positive completion? Here we study the mentioned problem when G Is a choral graph or an undirected cycle.Spanish DGI grant number BFM2001-0081-C03-02 and Generalitat Valenciana GRUPOS03/062Fundação para a Ciência e a Tecnologia (FCT

Impact of coverage-dependent marginal costs on optimal HPV vaccination strategies

AbstractThe effectiveness of vaccinating males against the human papillomavirus (HPV) remains a controversial subject. Many existing studies conclude that increasing female coverage is more effective than diverting resources into male vaccination. Recently, several empirical studies on HPV immunization have been published, providing evidence of the fact that marginal vaccination costs increase with coverage. In this study, we use a stochastic agent-based modeling framework to revisit the male vaccination debate in light of these new findings. Within this framework, we assess the impact of coverage-dependent marginal costs of vaccine distribution on optimal immunization strategies against HPV. Focusing on the two scenarios of ongoing and new vaccination programs, we analyze different resource allocation policies and their effects on overall disease burden. Our results suggest that if the costs associated with vaccinating males are relatively close to those associated with vaccinating females, then coverage-dependent, increasing marginal costs may favor vaccination strategies that entail immunization of both genders. In particular, this study emphasizes the necessity for further empirical research on the nature of coverage-dependent vaccination costs

Families with infants: a general approach to solve hard partition problems

We introduce a general approach for solving partition problems where the goal is to represent a given set as a union (either disjoint or not) of subsets satisfying certain properties. Many NP-hard problems can be naturally stated as such partition problems. We show that if one can find a large enough system of so-called families with infants for a given problem, then this problem can be solved faster than by a straightforward algorithm. We use this approach to improve known bounds for several NP-hard problems as well as to simplify the proofs of several known results. For the chromatic number problem we present an algorithm with $O^*((2-\varepsilon(d))^n)$ time and exponential space for graphs of average degree $d$. This improves the algorithm by Bj\"{o}rklund et al. [Theory Comput. Syst. 2010] that works for graphs of bounded maximum (as opposed to average) degree and closes an open problem stated by Cygan and Pilipczuk [ICALP 2013]. For the traveling salesman problem we give an algorithm working in $O^*((2-\varepsilon(d))^n)$ time and polynomial space for graphs of average degree $d$. The previously known results of this kind is a polyspace algorithm by Bj\"{o}rklund et al. [ICALP 2008] for graphs of bounded maximum degree and an exponential space algorithm for bounded average degree by Cygan and Pilipczuk [ICALP 2013]. For counting perfect matching in graphs of average degree~$d$ we present an algorithm with running time $O^*((2-\varepsilon(d))^{n/2})$ and polynomial space. Recent algorithms of this kind due to Cygan, Pilipczuk [ICALP 2013] and Izumi, Wadayama [FOCS 2012] (for bipartite graphs only) use exponential space.Comment: 18 pages, a revised version of this paper is available at http://arxiv.org/abs/1410.220