Vertex Components Research Articles

Node-Level Community Detection within Edge Exchangeable Models for Interaction Processes

Scientists are increasingly interested in discovering community structure from modern relational data arising on large-scale social networks. While many methods have been proposed for learning community structure, few account for the fact that these modern networks arise from processes of interactions in the population. We introduce block edge exchangeable models (BEEM) for the study of interaction networks with latent node-level community structure. The block vertex components model (B-VCM) is derived as a canonical example. Several theoretical and practical advantages over traditional vertex-centric approaches are highlighted. In particular, BEEMs allow for sparse degree structure and power-law degree distributions within communities. Our theoretical analysis bounds the misspecification rate of block assignments while supporting simulations show the properties of the network can be recovered. A computationally tractable Gibbs algorithm is derived. We demonstrate the proposed model using post-comment interaction data from Talklife, a large-scale online peer-to-peer support network, and contrast the learned communities from those using standard algorithms including degree-corrected stochastic block models, popularity-adjusted block models, and weighted stochastic block models. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.

Molecular plasticity of herpesvirus nuclear egress analysed in situ.

The viral nuclear egress complex (NEC) allows herpesvirus capsids to escape from the nucleus without compromising the nuclear envelope integrity. The NEC lattice assembles on the inner nuclear membrane and mediates the budding of nascent nucleocapsids into the perinuclear space and their subsequent release into the cytosol. Its essential role makes it a potent antiviral target, necessitating structural information in the context of a cellular infection. Here we determined structures of NEC-capsid interfaces in situ using electron cryo-tomography, showing a substantial structural heterogeneity. In addition, while the capsid is associated with budding initiation, it is not required for curvature formation. By determining the NEC structure in several conformations, we show that curvature arises from an asymmetric assembly of disordered and hexagonally ordered lattice domains independent of pUL25 or other viral capsid vertex components. Our results advance our understanding of the mechanism of nuclear egress in the context of a living cell.

Current noise and Keldysh vertex function of an Anderson impurity in the Fermi-liquid regime

We present a complete microscopic Fermi-liquid description for next-to-leading order transport through an Anderson impurity under a finite bias voltage $V$. It is applicable to multilevel quantum dots without particle-hole or time-reversal symmetry and is constructed based on the nonequilibrium Keldysh formalism, taking into account the current conservation between electrons in the impurity levels and the conduction bands. Specifically, we derive the formula for the current noise generated in the steady flow up to terms of order ${(eV)}^{3}$ at zero temperature $T=0$. To this end, we calculate the Keldysh vertex functions ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\sigma}{\ensuremath{\sigma}}^{\ensuremath{'}};{\ensuremath{\sigma}}^{\ensuremath{'}}\ensuremath{\sigma}}^{{\ensuremath{\nu}}_{1}{\ensuremath{\nu}}_{2};{\ensuremath{\nu}}_{3}{\ensuremath{\nu}}_{4}}(\ensuremath{\omega},{\ensuremath{\omega}}^{\ensuremath{'}};{\ensuremath{\omega}}^{\ensuremath{'}},\ensuremath{\omega})$, which depend on branches ${\ensuremath{\nu}}_{1},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{2},\phantom{\rule{4pt}{0ex}}{\ensuremath{\nu}}_{3}$, and ${\ensuremath{\nu}}_{4}$ of the time-loop contour and on spin degrees of freedom $\ensuremath{\sigma}$ and ${\ensuremath{\sigma}}^{\ensuremath{'}}$, up to linear order terms with respect to $eV$, $T$, and frequencies $\ensuremath{\omega}$ and ${\ensuremath{\omega}}^{\ensuremath{'}}$. The coefficients of these linear order terms are determined by a set of the parameters, defined with respect to the equilibrium ground state: the phase shift, static susceptibilities, and nonlinear three-body susceptibilities of the impurity electrons. The low-energy expressions of the vertex components are shown to satisfy the Ward identities with the Keldysh Green's functions expanded up to terms of order ${\ensuremath{\omega}}^{2}$, ${(eV)}^{2}$, and ${T}^{2}$. We also find that the imaginary part of the Ward identities can be described in terms of the $eV$-dependent collision integrals for a single-quasiparticle excitation and that for a single quasiparticle-quasihole pair excitation. These collision integrals ensure the current conservation of the next-to-leading order Fermi-liquid transport due to the quasiparticles with a finite damping rate.

Effects of Electron Correlation inside Disordered Crystals

We propose a novel approach for characterising the electron spectrum of disordered crystals constructed from a Hamiltonian of electrons as well as phonons and a diagram approach for Green’s function. The system’s electronic states were modelled by means of the multi-band, tight-binding approach. The system’s Hamiltonian is described based on the electron wave functions at the field of the atom nucleus. Our novel approach incorporates the long-range Coulomb interplay of electrons located in different lattice positions. Explicit interpretations of Green’s functions are derived using a diagram method. Equations are obtained for the vertex components for the mass operators of the electron–electron as well aselectron–phonon interplays. A system of equations for the spectrum of elementary excitations in the crystal is obtained, in which the vertex components for the mass operators of electron–electron as well as electron–phonon interplays are renormalised. Thismakes it possible to perform numerical computationsfor the system’s energy spectrum with a predetermined accuracy. In contrast to other approaches in which electron correlations are only taken into account in the limiting cases of an infinitely large and infinitesimal electron density, in this method, electron correlations are described in the general case of an arbitrary density. We obtained the cluster expansion of the density of states (DOS) of the disordered systems. We demonstrate that the addition of the electron-scattering mechanismsto the clusters is decreasing. This happens due to a growing number of positions in the cluster, which hang ontothe small parameter. The computing exactness is fixed by a small parameter for cluster expansion of Green’s functions of electrons as well as phonons.

Hierarchical Network Models for Exchangeable Structured Interaction Processes

Network data often arises via a series of structured interactions among a population of constituent elements. E-mail exchanges, for example, have a single sender followed by potentially multiple receivers. Scientific articles, on the other hand, may have multiple subject areas and multiple authors. We introduce a statistical model, termed the Pitman-Yor hierarchical vertex components model (PY-HVCM), that is well suited for structured interaction data. The proposed PY-HVCM effectively models complex relational data by partial pooling of local information via a latent, shared population-level distribution. The PY-HCVM is a canonical example of hierarchical vertex components models—a subfamily of models for exchangeable structured interaction-labeled networks, that is, networks invariant to interaction relabeling. Theoretical analysis and supporting simulations provide clear model interpretation, and establish global sparsity and power law degree distribution. A computationally tractable Gibbs sampling algorithm is derived for inferring sparsity and power law properties of complex networks. We demonstrate the model on both the Enron e-mail dataset and an ArXiv dataset, showing goodness of fit of the model via posterior predictive validation.

Propositional Frame-Based Analysis of the Semantics of Proverbs of the Russian and Chinese Languages (Based on Frame Father – Son)

Propositional frame-based modeling is one of the most effective methods of cognitive linguistics. This method considers the interaction between the semantic and cognitive aspects of units of two typologically different languages, e.g. Russian and Chinese, in order to study the way language structures and reflects human knowledge and experience. Propositional structures are the same for all languages, but they are implemented differently in every language. The authors used the propositional frame-based analysis to identify universal and specific aspects in the semantics of proverbs based on frame father – son, which is an important fragment of the Russian and Chinese linguistic world view. The cognitive potential of paroemiological units is enormous: proverbs reflect historical, cultural, linguistic, and extralinguistic cognitive experience. Cognitivists define experience as one’s knowledge about stereotypical situations, stored in one’s mind as frames. A frame is a collection of vertex ("top") and terminal ("low") components. Vertex components are formed by concepts that are valid in relation to the stereotypical situation of the frame. As a result, they are clearly structured and constant. The "low level" is not constant, and its terminals are variable. The semantics of the proverbs in question were represented by frames. The meanings of their components formed a common and complex situation. Knowledge about this situation made it possible to perceive the meaning of each proverb in a holistic way. The proverbs could be interpreted as units that activate a certain cognitive context about the content and structure of the concepts father and son in Russian and Chinese.

Edge Exchangeable Models for Interaction Networks

ABSTRACTMany modern network datasets arise from processes of interactions in a population, such as phone calls, email exchanges, co-authorships, and professional collaborations. In such interaction networks, the edges comprise the fundamental statistical units, making a framework for edge-labeled networks more appropriate for statistical analysis. In this context, we initiate the study of edge exchangeable network models and explore its basic statistical properties. Several theoretical and practical features make edge exchangeable models better suited to many applications in network analysis than more common vertex-centric approaches. In particular, edge exchangeable models allow for sparse structure and power law degree distributions, both of which are widely observed empirical properties that cannot be handled naturally by more conventional approaches. Our discussion culminates in the Hollywood model, which we identify here as the canonical family of edge exchangeable distributions. The Hollywood model is computationally tractable, admits a clear interpretation, exhibits good theoretical properties, and performs reasonably well in estimation and prediction as we demonstrate on real network datasets. As a generalization of the Hollywood model, we further identify the vertex components model as a nonparametric subclass of models with a convenient stick breaking construction.

Adaptive synchronization of coupled harmonic oscillators under switching topology

This paper investigates the adaptive synchronization for coupled harmonic oscillators with switching topology. Edge-based adaptive control protocols are proposed for both leaderless and leader-following synchronization for coupled harmonic oscillators with switching topology. Using Lyapunov stability theory, by parting the topology graph into connected components (containing at least two connected vertices) and isolated vertex components (containing a isolated vertex), full distributed adaptive synchronization conditions are obtained, which can guarantee that the synchronization conditions do not require any global information except a mild connection assumption. Finally numerical simulations are presented to illustrate the theoretical findings.

Пропозиционально-семантическая организация гнёзд однокоренных слов с вершинными компонентами отец, папа в русском языке (на материале лексикографических источников)

The present study is carried out in the course of cognitive word formation of the Russian language. The author, noting the axiological nature of word formation, pays close attention to the internal (propositional-semantic) organization of the same root word families - one of its complex units. The object of study in the work are the same root word families with the vertex components otets , papa , each of which demonstrates the angles of understanding of the culturally significant fragment of the world in the minds of the Russian people. The source of the same-root vocabulary selected for the analysis within two families are the dictionary materials. Reference to lexicographic works and application of the method of propositional-frame modeling allow, firstly, to establish a set of same-root lexemes, united by the vertices otets , papa ; secondly, to determine the semantic volume and word-formation capabilities of the vertex components otets , papa ; thirdly, to trace the features of the implementation of multidimensional semantics of the vertex components otets , papa in the semantic structure of same-root derived lexemes within the boundaries of the considered families through identification of propositional structures. It is established that the propositional-semantic organization of families of same-root words is set by the meaning-generating potential of the top components and highlights the actual, culturally significant, aspects of the perception of father in the consciousness of the Russian people. It is concluded that the same-root lexemes within the comparative families reveal different semantic specialization, which reflects the system of knowledge and ideas of modern Russian speakers.

Vespucci: A Free, Cross-Platform Tool for Spectroscopic Data Analysis and Imaging

Vespucci is a software application developed for imaging and analysis of hyperspectral datasets. Vespucci offers several advantages over other software packages, including a simple user interface with a small learning curve, no cost, and less restrictive licensing. Vespucci expands several analysis techniques including univariate imaging, principal components analysis, partial-least-squares regression, and vertex components analysis with endmember extraction, and k-means clustering. Additionally, Vespucci can perform a number of useful data-processing operations, including filtering, normalization, baseline correction, and background subtraction. Datasets that consist of spatial or temporal data with a corresponding digital signal, including spectroscopic images, mass spectrometric images, and X-ray diffraction data can be processed in this software. A few use cases for Raman and surface-enhanced Raman spectroscopies are provided. Vespucci is written in C++ and makes use of the MLPACK [3], Armadillo [9], Qt, and QCustomPlot libraries. Vespucci is a graphically-driven package that is designed with ease-of-use in mind and is equally capable to other available tools. Vespucci’s capabilities are extended by interfaces to Octave and R to allow existing research code to be run from a common environment. Additionally, Vespucci’s C++ classes can be used to construct more specialized programs when an application programming interface (API) is desired. The source code and a Windows binary distribution can be accessed at https://github.com/dpfoose/Vespucci.

Thermo-magnetic behavior of the quark-gluon vertex

The thermo-magnetic corrections to the quark-gluon vertex in the presence of a weak magnetic field are calculated in the frame of the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy calculated within the same approximation. It turns out that only the longitudinal vertex components get modified. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. The effective thermo-magnetic quark-gluon coupling shows a decreasing behavior as function of the field strength. This result supports the observation that the behavior of the effective quark-gluon coupling in the presence of a magnetic field is an important ingredient in order to understand the inverse magnetic catalysis phenomenon recently observed in the lattice QCD simulations.

Finite temperature quark-gluon vertex with a magnetic field in the hard thermal loop approximation

We compute the thermo-magnetic correction to the quark-gluon vertex in the presence of a weak magnetic field within the Hard Thermal Loop approximation. The vertex satisfies a QED-like Ward identity with the quark self-energy. The only vertex components that get modified are the longitudinal ones. The calculation provides a first principles result for the quark anomalous magnetic moment at high temperature in a weak magnetic field. We extract the effective thermo-magnetic quark-gluon coupling and show that this decreases as a function of the field strength. The result supports the idea that the properties of the effective quark-gluon coupling in the presence of a magnetic field are an important ingredient to understand the inverse magnetic catalysis phenomenon.

Perceiving monetary loss as due to inequity reduces behavioral and cortical responses to pain

Studies indicate that physical and social pain may share some mechanisms and neural correlates. Nothing is known, however, on whether the neural activity in the nociceptive system, as indexed by laser-evoked potentials (LEPs), is modified when suffering the consequences of a conspecific violating social norms. To explore this issue, we created an interaction scenario where participants could gain money by performing a time-estimation task. On each win-trial, another player connected online could arbitrarily decide to keep the participant's pay-off for him- or herself. Thus, participants knew that monetary loss could occur because of their own failure in performing the task or because of the inequitable behavior of another individual. Moreover, participants were asked to play for themselves or on behalf of a third party. In reality, the win/loss events were entirely decided by an ad hoc programmed computer. At the end of the interaction, participants reported if they believed the game-playing interaction was real. Results showed that the loss due to the opponent's inequitable behavior brought about a reduction both in pain intensity self-reports and in the amplitude of LEPs' components (i.e., N2, N2/P2, P2a, P2b). Importantly, both the behavioral and neurophysiological effects were found in the participants who believed their deserved payoff was stolen by their opponent. Furthermore, reduction of vertex components was present only when the inequitable behavior was directed toward the self. These results suggest that, far from being a private experience, pain perception might be modulated by the social saliency of interpersonal interactions.

46. Late and ultralate laser-evoked potentials using a laser YAG stimulator

Laser-evoked potentials (LEPs) currently represent the most reliable and widely used method of investigating the Ad-fibre pathways in the diagnosis of neuropathic pain. The aim of our study was to investigate the usefulness of a new laser evoked simulator and its application in clinical neurophysiology. Using the Tm:YAG laser simulator ( λ 1.9 μm) we recorded LEPs after face, hand, and foot bilateral stimulation in 30 normal subjects. We performed late and ultralate LEPs recordings using two different setting of stimuli for C – fibers and for A delta – fibers. We measured the perceptive threshold, latency and amplitude of the main vertex components, and their side-to-side differences. We also studied the correlations between LEP data and age and body height, as well as gender differences. In all normal subjects we obtained a N2P2 complex at the vertex after both A delta and C stimuli. Laser perceptive threshold increased and LEP amplitude decreased from face to foot ( P < 0.005). The amplitude correlated with age ( P < 0.001. LEP data did not significantly differ between genders ( P < O0.3). This study provides the usefulness of a new laser simulator able to obtain also at the foot reliable ultralate C Leps. We collect normative values for the main LEP data and their absolute and side-to-side limits, confirming the physiological differences assessed in Literature for others Laser stimulators. Our preliminary data may help to improve the clinical application of late and ultralate LEPs as a diagnostic tool in clinical practice.

Evoked potentials to nociceptive stimuli delivered by CO 2 or Nd:YAP lasers

Objective This study compares the amplitude, latency, morphology, scalp topography and intracranial generators of laser-evoked potentials (LEPs) to CO 2 and Nd:YAP laser stimuli. Methods LEPs were assessed in 11 healthy subjects (6 men, mean age 39 ± 10 years) using a 32-channel acquisition system. Laser stimuli were delivered on the dorsum of both hands (intensity slightly above pain threshold), and permitted to obtain lateralised (N1) and vertex components (N2-P2) with similar scalp distribution for both types of lasers. Results The N1-YAP had similar latencies but significantly higher amplitudes relative to N1-CO 2. The N2-P2 complex showed earlier latencies, higher amplitudes (N2) and more synchronised responses when using Nd:YAP stimulation. The distribution of intracranial generators assessed with source localization analyses (sLORETA) was similar for Nd:YAP and CO 2 lasers. The insular, opercular, and primary sensorimotor cortices were active during the N1 time-window, whereas the anterior midcingulate, supplementary motor areas and mid-anterior insulae were active concomitant to the N2-P2 complex. Conclusions Earlier latencies and larger amplitudes recorded when using Nd:YAP pulses suggest a more synchronized nociceptive afferent volley with this type of laser. Significance This, together with its handy utilization due to optic fibre transmission, may favour the use of Nd:YAP lasers in clinical settings.

Laser-evoked potentials: normative values

Objective: Laser-evoked potentials (LEPs) currently represent the most reliable and widely agreed method of investigating the Aδ-fibre pathways. Many studies dealt with the usefulness of LEPs in peripheral and central nervous system diseases. We aimed at gaining normative values for LEP data. Methods: Using a CO 2 laser stimulator we recorded LEPs after face, hand, and foot stimulation in 100 normal subjects. We measured the perceptive threshold, latency and amplitude of the main vertex components, and their side-to-side differences. We also studied the correlations between LEP data and age and body height, as well as gender differences. Results: Laser perceptive threshold increased and LEP amplitude decreased from face to foot ( P<0.0001). The latency of hand and foot-LEPs correlated significantly with body height ( P<0.0001). The amplitude, though not the latency, correlated with age ( P<0.0001). LEP data did not significantly differ between genders ( P>0.1). Conclusions: This study provides normative values for the main LEP data and their absolute and side-to-side limits, highlighting the physiological differences related to, body height, age, gender and stimulation site. Significance: Our data may help to improve the clinical reliability of LEPs as a diagnostic tool.

Gating of the vertex somatosensory and auditory evoked potential P50 and the correlation to skin conductance orienting response in healthy men

A defect in auditory evoked potential (AEP) P50 gating supports the theory of information-processing deficits in schizophrenia. The relationship between gating of the mid-latency evoked potentials (EP) in the somatosensory and the auditory modalities has not been studied together before. In schizophrenia, we might expect the processing deficits to act on multiple modalities. We have examined the gating of median nerve somatosensory EP (SEP) following paired stimulation identical to the AEP P50 gating paradigm using interstimulus intervals (ISI) of 500, 750 and 1000 ms and the correlation of gating to the skin conductance orienting response (SCOR) in 20 healthy men. We measured mid-latency vertex components (SEP: P50, N65, P85 and N100; AEP: P30, N45, P50 and N80). The gating was most pronounced at ISI 500 ms where the SEP P50 and N100 gating were 0.59 and 0.37, respectively, as compared to a gating of 0.61 in P30, 0.33 in P50 and 0.45 in N80 in the AEP. Repetition effects in the two modalities were not correlated. AEP P50 gating was correlated to skin conductance level (SCL). The combination of recording repetition effects on the mid-latency EP in two modalities could provide a method for investigating if deficits of information processing in schizophrenia are cross-modal.

Sensory gating of auditory evoked potentials in rats: effects of repetitive stimulation and the interstimulus interval

In the P50 gating or conditioning–testing (C–T) paradigm, the P50 response, a small positive midlatency (∼50 ms after stimulus onset) component of the human auditory evoked potential (AEP), is reduced towards the second click (S2) as compared to the response to the first click (S1). This phenomenon is called sensory gating. The putative function of sensory gating is thought to protect subjects from being flooded by irrelevant stimuli. Comparative studies have been done in rats in order to elucidate the underlying neural substrate of sensory gating. However, for a direct comparison of rat and human AEP components, it is imperative for both components to show similar characteristics. The amount of sensory gating in humans is dependent on repetitive stimulation and the interstimulus interval (ISI). In the present study effects of repetitive stimulation (Experiment 1) and various ISIs (Experiment 2) were determined on rat AEP components. The results demonstrate that gating is not limited to a restricted cortical area or a single midlatency component and that repetitive stimulation and ISI affect gating of several rat AEP components. Components such as the vertex P17 and N22 show a decrease in gating within several S1–S2 presentations, mainly due to a decrease in amplitude to S1 (Experiment 1). Gating for vertex components (such as the P17, N22 and N50) is ISI dependent (Experiment 2), but there is no interval in the 200–600 ms range at which optimal gating occurs. The ISI effects on gating are due to an increase of the amplitude to S2. The results have implications for the discussion about the rat homologue of the human P50.

Graph characterising polynomials

The discovery of a complete set of invariants for graphs, or equivalently, a graph characterising polynomial has been a long outstanding problem in graph theory. In 1980 Balasubrahmanian and Parthasarathy introduced the bivariate permanent polynomial and the frame polynomial and conjectured that these are graph characterising polynomials. In this paper we show that these conjectures imply the Graph Reconstruction Conjectures and suggest a possible approach to settle the bivariate permanent polynomial conjecture using Mnukhin's (Acta Applicandae Mathematicae 29 (1992) 83–117) characterisation of a complete set of graph invariants. We also address the problem of determining the number of single vertex components of a graph from its permanent polynomial.

The sense of effort without peripheral feedback in a subject with a large fibre peripheral sensory neuropathy

This study compares the amplitude, latency, morphology, scalp topography and intracranial generators of laser-evoked potentials (LEPs) to CO2 and Nd:YAP laser stimuli.LEPs were assessed in 11 healthy subjects (6 men, mean age 39 ± 10 years) using a 32-channel acquisition system. Laser stimuli were delivered on the dorsum of both hands (intensity slightly above pain threshold), and permitted to obtain lateralised (N1) and vertex components (N2-P2) with similar scalp distribution for both types of lasers.The N1-YAP had similar latencies but significantly higher amplitudes relative to N1-CO2. The N2-P2 complex showed earlier latencies, higher amplitudes (N2) and more synchronised responses when using Nd:YAP stimulation. The distribution of intracranial generators assessed with source localization analyses (sLORETA) was similar for Nd:YAP and CO2 lasers. The insular, opercular, and primary sensorimotor cortices were active during the N1 time-window, whereas the anterior midcingulate, supplementary motor areas and mid-anterior insulae were active concomitant to the N2-P2 complex.Earlier latencies and larger amplitudes recorded when using Nd:YAP pulses suggest a more synchronized nociceptive afferent volley with this type of laser.This, together with its handy utilization due to optic fibre transmission, may favour the use of Nd:YAP lasers in clinical settings.