Ultimate periodicity of b-recognisable sets : a quasilinear procedure

It is decidable if a set of numbers, whose representation in a base b is a regular language, is ultimately periodic. This was established by Honkala in 1986. We give here a structural description of minimal automata that accept an ultimately periodic set of numbers. We then show that it can verified in linear time if a given minimal automaton meets this description. This thus yields a O(n log(n)) procedure for deciding whether a general deterministic automaton accepts an ultimately periodic set of numbers.Comment: presented at DLT 201

A complementary view on the growth of directory trees

Trees are a special sub-class of networks with unique properties, such as the level distribution which has often been overlooked. We analyse a general tree growth model proposed by Klemm {\em et. al.} (2005) to explain the growth of user-generated directory structures in computers. The model has a single parameter $q$ which interpolates between preferential attachment and random growth. Our analysis results in three contributions: First, we propose a more efficient estimation method for $q$ based on the degree distribution, which is one specific representation of the model. Next, we introduce the concept of a level distribution and analytically solve the model for this representation. This allows for an alternative and independent measure of $q$. We argue that, to capture real growth processes, the $q$ estimations from the degree and the level distributions should coincide. Thus, we finally apply both representations to validate the model with synthetically generated tree structures, as well as with collected data of user directories. In the case of real directory structures, we show that $q$ measured from the level distribution are incompatible with $q$ measured from the degree distribution. In contrast to this, we find perfect agreement in the case of simulated data. Thus, we conclude that the model is an incomplete description of the growth of real directory structures as it fails to reproduce the level distribution. This insight can be generalised to point out the importance of the level distribution for modeling tree growth.Comment: 16 pages, 7 figure

Origins of power-law degree distribution in the heterogeneity of human activity in social networks

The probability distribution of number of ties of an individual in a social network follows a scale-free power-law. However, how this distribution arises has not been conclusively demonstrated in direct analyses of people's actions in social networks. Here, we perform a causal inference analysis and find an underlying cause for this phenomenon. Our analysis indicates that heavy-tailed degree distribution is causally determined by similarly skewed distribution of human activity. Specifically, the degree of an individual is entirely random - following a "maximum entropy attachment" model - except for its mean value which depends deterministically on the volume of the users' activity. This relation cannot be explained by interactive models, like preferential attachment, since the observed actions are not likely to be caused by interactions with other people.Comment: 23 pages, 5 figure

Googling the brain: discovering hierarchical and asymmetric network structures, with applications in neuroscience

Hierarchical organisation is a common feature of many directed networks arising in nature and technology. For example, a well-defined message-passing framework based on managerial status typically exists in a business organisation. However, in many real-world networks such patterns of hierarchy are unlikely to be quite so transparent. Due to the nature in which empirical data is collated the nodes will often be ordered so as to obscure any underlying structure. In addition, the possibility of even a small number of links violating any overall “chain of command” makes the determination of such structures extremely challenging. Here we address the issue of how to reorder a directed network in order to reveal this type of hierarchy. In doing so we also look at the task of quantifying the level of hierarchy, given a particular node ordering. We look at a variety of approaches. Using ideas from the graph Laplacian literature, we show that a relevant discrete optimization problem leads to a natural hierarchical node ranking. We also show that this ranking arises via a maximum likelihood problem associated with a new range-dependent hierarchical random graph model. This random graph insight allows us to compute a likelihood ratio that quantifies the overall tendency for a given network to be hierarchical. We also develop a generalization of this node ordering algorithm based on the combinatorics of directed walks. In passing, we note that Google’s PageRank algorithm tackles a closely related problem, and may also be motivated from a combinatoric, walk-counting viewpoint. We illustrate the performance of the resulting algorithms on synthetic network data, and on a real-world network from neuroscience where results may be validated biologically

Comparison of White Blood Cell Scintigraphy, FDG PET/CT and MRI in Suspected Diabetic Foot Infection:Results of a Large Retrospective Multicenter Study

Diabetic foot infections (DFIs) represent one of the most frequent and disabling morbidities of longstanding diabetes; therefore, early diagnosis is mandatory. The aim of this multicenter retrospective study was to compare the diagnostic accuracy of white blood cell scintigraphy (WBC), 18F-fluorodeoxyglucose positron emission tomography/computed tomography ((18F) FDG PET/CT), and Magnetic Resonance Imaging (MRI) in patients with suspected DFI. Images and clinical data from 251 patients enrolled by five centers were collected in order to calculate the sensitivity, specificity, and accuracy of WBC, FDG, and MRI in diagnosing osteomyelitis (OM), soft-tissue infection (STI), and Charcot osteoarthropathy. In OM, WBC acquired following the European Society of Nuclear Medicine (EANM) guidelines was more specific and accurate than MRI (91.9% vs. 70.7%, p < 0.0001 and 86.2% vs. 67.1%, p = 0.003, respectively). In STI, both FDG and WBC achieved a significantly higher specificity than MRI (97.9% and 95.7% vs. 83.6%, p = 0.04 and p = 0.018, respectively). In Charcot, both MRI and WBC demonstrated a significantly higher specificity and accuracy than FDG (88.2% and 89.3% vs. 62.5%, p = 0.0009; 80.3% and 87.9% vs. 62.1%, p < 0.02, respectively). Moreover, in Charcot, WBC was more specific than MRI (89.3% vs. 88.2% p < 0.0001). Given the limitations of a retrospective study, WBC using EANM guidelines was shown to be the most reliable imaging modality to differentiate between OM, STI, and Charcot in patients with suspected DFI

Structure-guided design and optimization of small molecules targeting the protein-protein interaction between the von hippel-lindau (VHL) E3 ubiquitin ligase and the hypoxia inducible factor (HIF) alpha subunit with in vitro nanomolar affinities

E3 ubiquitin ligases are attractive targets in the ubiquitin-proteasome system, however, the development of small-molecule ligands has been rewarded with limited success. The von Hippel-Lindau protein (pVHL) is the substrate recognition subunit of the VHL E3 ligase that targets HIF-1α for degradation. We recently reported inhibitors of the pVHL:HIF-1α interaction, however they exhibited moderate potency. Herein, we report the design and optimization, guided by X-ray crystal structures, of a ligand series with nanomolar binding affinities

Theories for influencer identification in complex networks

In social and biological systems, the structural heterogeneity of interaction networks gives rise to the emergence of a small set of influential nodes, or influencers, in a series of dynamical processes. Although much smaller than the entire network, these influencers were observed to be able to shape the collective dynamics of large populations in different contexts. As such, the successful identification of influencers should have profound implications in various real-world spreading dynamics such as viral marketing, epidemic outbreaks and cascading failure. In this chapter, we first summarize the centrality-based approach in finding single influencers in complex networks, and then discuss the more complicated problem of locating multiple influencers from a collective point of view. Progress rooted in collective influence theory, belief-propagation and computer science will be presented. Finally, we present some applications of influencer identification in diverse real-world systems, including online social platforms, scientific publication, brain networks and socioeconomic systems.Comment: 24 pages, 6 figure

Effective-Range Expansion of the Neutron-Deuteron Scattering Studied by a Quark-Model Nonlocal Gaussian Potential

The S-wave effective range parameters of the neutron-deuteron (nd) scattering are derived in the Faddeev formalism, using a nonlocal Gaussian potential based on the quark-model baryon-baryon interaction fss2. The spin-doublet low-energy eigenphase shift is sufficiently attractive to reproduce predictions by the AV18 plus Urbana three-nucleon force, yielding the observed value of the doublet scattering length and the correct differential cross sections below the deuteron breakup threshold. This conclusion is consistent with the previous result for the triton binding energy, which is nearly reproduced by fss2 without reinforcing it with the three-nucleon force.Comment: 21 pages, 6 figures and 6 tables, submitted to Prog. Theor. Phy

Transethnic meta-analysis of rare coding variants in PLCG2, ABI3, and TREM2 supports their general contribution to Alzheimer's disease

Rare coding variants in TREM2, PLCG2, and ABI3 were recently associated with the susceptibility to Alzheimer's disease (AD) in Caucasians. Frequencies and AD-associated effects of variants differ across ethnicities. To start filling the gap on AD genetics in South America and assess the impact of these variants across ethnicity, we studied these variants in Argentinian population in association with ancestry. TREM2 (rs143332484 and rs75932628), PLCG2 (rs72824905), and ABI3 (rs616338) were genotyped in 419 AD cases and 486 controls. Meta-analysis with European population was performed. Ancestry was estimated from genome-wide genotyping results. All variants show similar frequencies and odds ratios to those previously reported. Their association with AD reach statistical significance by meta-analysis. Although the Argentinian population is an admixture, variant carriers presented mainly Caucasian ancestry. Rare coding variants in TREM2, PLCG2, and ABI3 also modulate susceptibility to AD in populations from Argentina, and they may have a European heritage.Acknowledgements: This work was supported by grants from the International Society for Neurochemistry (ISN) and Alexander von Humboldt Foundation (to M.C.D.); Agencia Nacional de Promoción Científica y Tecnológica (PBIT/09 2013, PICT-2015-0285 and PICT-2016-4647 to L.M.; PICT-2014-1537 to M.C.D.); GENMED Labex and JPND PERADES grant; and JPND EADB grant (German Federal Ministry of Education and Research, BMBF: 01ED1619A)

Voice-based assessments of trustworthiness, competence, and warmth in blind and sighted adults

The study of voice perception in congenitally blind individuals allows researchers rare insight into how a lifetime of visual deprivation affects the development of voice perception. Previous studies have suggested that blind adults outperform their sighted counterparts in low-level auditory tasks testing spatial localization and pitch discrimination, as well as in verbal speech processing; however, blind persons generally show no advantage in nonverbal voice recognition or discrimination tasks. The present study is the first to examine whether visual experience influences the development of social stereotypes that are formed on the basis of nonverbal vocal characteristics (i.e., voice pitch). Groups of 27 congenitally or early-blind adults and 23 sighted controls assessed the trustworthiness, competence, and warmth of men and women speaking a series of vowels, whose voice pitches had been experimentally raised or lowered. Blind and sighted listeners judged both men’s and women’s voices with lowered pitch as being more competent and trustworthy than voices with raised pitch. In contrast, raised-pitch voices were judged as being warmer than were lowered-pitch voices, but only for women’s voices. Crucially, blind and sighted persons did not differ in their voice-based assessments of competence or warmth, or in their certainty of these assessments, whereas the association between low pitch and trustworthiness in women’s voices was weaker among blind than sighted participants. This latter result suggests that blind persons may rely less heavily on nonverbal cues to trustworthiness compared to sighted persons. Ultimately, our findings suggest that robust perceptual associations that systematically link voice pitch to the social and personal dimensions of a speaker can develop without visual input