Cliques in High-Dimensional Geometric Inhomogeneous Random Graphs

A recent trend in the context of graph theory is to bring theoretical analyses closer to empirical observations, by focusing the studies on random graph models that are used to represent practical instances. There, it was observed that geometric inhomogeneous random graphs (GIRGs) yield good representations of complex real-world networks, by expressing edge probabilities as a function that depends on (heterogeneous) vertex weights and distances in some underlying geometric space that the vertices are distributed in. While most of the parameters of the model are understood well, it was unclear how the dimensionality of the ground space affects the structure of the graphs. In this paper, we complement existing research into the dimension of geometric random graph models and the ongoing study of determining the dimensionality of real-world networks, by studying how the structure of GIRGs changes as the number of dimensions increases. We prove that, in the limit, GIRGs approach non-geometric inhomogeneous random graphs and present insights on how quickly the decay of the geometry impacts important graph structures. In particular, we study the expected number of cliques of a given size as well as the clique number and characterize phase transitions at which their behavior changes fundamentally. Finally, our insights help in better understanding previous results about the impact of the dimensionality on geometric random graphs

A simple statistic for determining the dimensionality of complex networks

Detecting the dimensionality of graphs is a central topic in machine learning. While the problem has been tackled empirically as well as theoretically, existing methods have several drawbacks. On the one hand, empirical tools are computationally heavy and lack theoretical foundation. On the other hand, theoretical approaches do not apply to graphs with heterogeneous degree distributions, which is often the case for complex real-world networks. To address these drawbacks, we consider geometric inhomogeneous random graphs (GIRGs) as a random graph model, which captures a variety of properties observed in practice. These include a heterogeneous degree distribution and non-vanishing clustering coefficient, which is the probability that two random neighbours of a vertex are adjacent. In GIRGs, $n$ vertices are distributed on a $d$-dimensional torus and weights are assigned to the vertices according to a power-law distribution. Two vertices are then connected with a probability that depends on their distance and their weights. Our first result shows that the clustering coefficient of GIRGs scales inverse exponentially with respect to the number of dimensions, when the latter is at most logarithmic in $n$. This gives a first theoretical explanation for the low dimensionality of real-world networks observed by Almagro et. al. [Nature '22]. Our second result is a linear-time algorithm for determining the dimensionality of a given GIRG. We prove that our algorithm returns the correct number of dimensions with high probability when the input is a GIRG. As a result, our algorithm bridges the gap between theory and practice, as it not only comes with a rigorous proof of correctness but also yields results comparable to that of prior empirical approaches, as indicated by our experiments on real-world instances

A Strategic Routing Framework and Algorithms for Computing Alternative Paths

Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin-destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines. Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case

A strategic routing framework and algorithms for computing alternative paths

Traditional navigation services find the fastest route for a single driver. Though always using the fastest route seems desirable for every individual, selfish behavior can have undesirable effects such as higher energy consumption and avoidable congestion, even leading to higher overall and individual travel times. In contrast, strategic routing aims at optimizing the traffic for all agents regarding a global optimization goal. We introduce a framework to formalize real-world strategic routing scenarios as algorithmic problems and study one of them, which we call Single Alternative Path (SAP), in detail. There, we are given an original route between a single origin-destination pair. The goal is to suggest an alternative route to all agents that optimizes the overall travel time under the assumption that the agents distribute among both routes according to a psychological model, for which we introduce the concept of Pareto-conformity. We show that the SAP problem is NP-complete, even for such models. Nonetheless, assuming Pareto-conformity, we give multiple algorithms for different variants of SAP, using multi-criteria shortest path algorithms as subroutines. Moreover, we prove that several natural models are in fact Pareto-conform. The implementation and evaluation of our algorithms serve as a proof of concept, showing that SAP can be solved in reasonable time even though the algorithms have exponential running time in the worst case

Metabolic manipulation in chronic heart failure: study protocol for a randomised controlled trial

<p>Abstract</p> <p>Background</p> <p>Heart failure is a major cause of morbidity and mortality in society. Current medical therapy centres on neurohormonal modulation with angiotensin converting enzyme inhibitors and β-blockers. There is growing evidence for the use of metabolic manipulating agents as adjunctive therapy in patients with heart failure. We aim to determine the effect of perhexiline on cardiac energetics and alterations in substrate utilisation in patients with non-ischaemic dilated cardiomyopathy.</p> <p>Methods</p> <p>A multi-centre, prospective, randomised double-blind, placebo-controlled trial of 50 subjects with non-ischaemic dilated cardiomyopathy recruited from University Hospital Birmingham NHS Foundation Trust and Cardiff and Vale NHS Trust. Baseline investigations include magnetic resonance spectroscopy to assess cardiac energetic status, echocardiography to assess left ventricular function and assessment of symptomatic status. Subjects are then randomised to receive 200 mg perhexiline maleate or placebo daily for 4 weeks with serum drug level monitoring. All baseline investigations will be repeated at the end of the treatment period. A subgroup of patients will undergo invasive investigations with right and left heart catheterisation to calculate respiratory quotient, and mechanical efficiency. The primary endpoint is an improvement in the phosphocreatine to adenosine triphosphate ratio at 4 weeks. Secondary end points are: i) respiratory quotient; ii) mechanical efficiency; iii) change in left ventricular (LV) function.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT00841139">NCT00841139</a></p> <p>ISRCTN: <a href="http://www.controlled-trials.com/ISRCTN2887836">ISRCTN2887836</a></p

Vitalism and the Resistance to Experimentation on Life in the Eighteenth Century

There is a familiar opposition between a ‘Scientific Revolution’ ethos and practice of experimentation, including experimentation on life, and a ‘vitalist’ reaction to this outlook. The former is often allied with different forms of mechanism – if all of Nature obeys mechanical laws, including living bodies, ‘iatromechanism’ should encounter no obstructions in investigating the particularities of animal-machines – or with more chimiatric theories of life and matter, as in the ‘Oxford Physiologists’. The latter reaction also comes in different, perhaps irreducibly heterogeneous forms, ranging from metaphysical and ethical objections to the destruction of life, as in Margaret Cavendish, to more epistemological objections against the usage of instruments, the ‘anatomical’ outlook and experimentation, e.g. in Locke and Sydenham. But I will mainly focus on a third anti-interventionist argument, which I call ‘vitalist’ since it is often articulated in the writings of the so-called Montpellier Vitalists, including their medical articles for the Encyclopédie. The vitalist argument against experimentation on life is subtly different from the metaphysical, ethical and epistemological arguments, although at times it may borrow from any of them. It expresses a Hippocratic sensibility – understood as an artifact of early modernity, not as some atemporal trait of medical thought – in which Life resists the experimenter, or conversely, for the experimenter to grasp something about Life, it will have to be without torturing or radically intervening in it. I suggest that this view does not have to imply that Nature is something mysterious or sacred; nor does the vitalist have to attack experimentation on life in the name of some ‘vital force’ – which makes it less surprising to find a vivisectionist like Claude Bernard sounding so close to the vitalists

Identification and Classification of Hubs in Brain Networks

Brain regions in the mammalian cerebral cortex are linked by a complex network of fiber bundles. These inter-regional networks have previously been analyzed in terms of their node degree, structural motif, path length and clustering coefficient distributions. In this paper we focus on the identification and classification of hub regions, which are thought to play pivotal roles in the coordination of information flow. We identify hubs and characterize their network contributions by examining motif fingerprints and centrality indices for all regions within the cerebral cortices of both the cat and the macaque. Motif fingerprints capture the statistics of local connection patterns, while measures of centrality identify regions that lie on many of the shortest paths between parts of the network. Within both cat and macaque networks, we find that a combination of degree, motif participation, betweenness centrality and closeness centrality allows for reliable identification of hub regions, many of which have previously been functionally classified as polysensory or multimodal. We then classify hubs as either provincial (intra-cluster) hubs or connector (inter-cluster) hubs, and proceed to show that lesioning hubs of each type from the network produces opposite effects on the small-world index. Our study presents an approach to the identification and classification of putative hub regions in brain networks on the basis of multiple network attributes and charts potential links between the structural embedding of such regions and their functional roles

Evaluation of epidermal growth factor receptor mutation status in serum DNA as a predictor of response to gefitinib (IRESSA)

The aim of this study was to evaluate the usefulness of EGFR mutation status in serum DNA as a means of predicting a benefit from gefitinib (IRESSA) therapy in Japanese patients with non-small cell lung cancer (NSCLC). We obtained pairs of tumour and serum samples from 42 patients treated with gefitinib. EGFR mutation status was determined by a direct sequencing method and by Scorpion Amplification Refractory Mutation System (ARMS) technology. EGFR mutations were detected in the tumour samples of eight patients and in the serum samples of seven patients. EGFR mutation status in the tumours and serum samples was consistent in 39 (92.9%) of the 42 pairs. EGFR mutations were strong correlations between both EGFR mutation status in the tumour samples and serum samples and objective response to gefitinib (P<0.001). Median progression-free survival time was significantly longer in the patients with EGFR mutations than in the patients without EGFR mutations (194 vs 55 days, P=0.016, in tumour samples; 174 vs 58 days, P=0.044, in serum samples). The results suggest that it is feasible to use serum DNA to detect EGFR mutation, and that it's potential as a predictor of response to, and survival on gefitinib is worthy of further evaluation

Omega-3 fatty acids in high-risk cardiovascular patients: a meta-analysis of randomized controlled trials

<p>Abstract</p> <p>Background</p> <p>Multiple randomized controlled trials (RCTs) have examined the cardiovascular effects of omega-3 fatty acids and have provided unexplained conflicting results. A meta-analysis of these RCTs to estimate efficacy and safety and potential sources of heterogeneity may be helpful.</p> <p>Methods</p> <p>The Cochrane library, MEDLINE, and EMBASE were systematically searched to identify all interventional trials of omega-3 fatty acids compared to placebo or usual diet in high-risk cardiovascular patients. The primary outcome was all-cause mortality and secondary outcomes were coronary restenosis following percutaneous coronary intervention and safety. Meta-analyses were carried out using Bayesian random-effects models, and heterogeneity was examined using meta-regression.</p> <p>Results</p> <p>A total of 29 RCTs (n = 35,144) met our inclusion criteria, with 25 reporting mortality and 14 reporting restenosis. Omega-3 fatty acids were not associated with a statistically significant decreased mortality (relative risk [RR] = 0.88, 95% Credible Interval [CrI] = 0.64, 1.03) or with restenosis prevention (RR = 0.89, 95% CrI = 0.72, 1.06), though the probability of some benefit remains high (0.93 and 0.90, respectively). However in meta-regressions, there was a >90% probability that larger studies and those with longer follow-up were associated with smaller benefits. No serious safety issues were identified.</p> <p>Conclusions</p> <p>Although not reaching conventional statistical significance, the evidence to date suggests that omega-3 fatty acids may result in a modest reduction in mortality and restenosis. However, caution must be exercised in interpreting these benefits as results were attenuated in higher quality studies, suggesting that bias may be at least partially responsible. Additional high quality studies are required to clarify the role of omega-3 fatty acid supplementation for the secondary prevention of cardiovascular disease.</p