Stochastic IMT (insulator-metal-transition) neurons: An interplay of thermal and threshold noise at bifurcation

Artificial neural networks can harness stochasticity in multiple ways to enable a vast class of computationally powerful models. Electronic implementation of such stochastic networks is currently limited to addition of algorithmic noise to digital machines which is inherently inefficient; albeit recent efforts to harness physical noise in devices for stochasticity have shown promise. To succeed in fabricating electronic neuromorphic networks we need experimental evidence of devices with measurable and controllable stochasticity which is complemented with the development of reliable statistical models of such observed stochasticity. Current research literature has sparse evidence of the former and a complete lack of the latter. This motivates the current article where we demonstrate a stochastic neuron using an insulator-metal-transition (IMT) device, based on electrically induced phase-transition, in series with a tunable resistance. We show that an IMT neuron has dynamics similar to a piecewise linear FitzHugh-Nagumo (FHN) neuron and incorporates all characteristics of a spiking neuron in the device phenomena. We experimentally demonstrate spontaneous stochastic spiking along with electrically controllable firing probabilities using Vanadium Dioxide (VO$_2$) based IMT neurons which show a sigmoid-like transfer function. The stochastic spiking is explained by two noise sources - thermal noise and threshold fluctuations, which act as precursors of bifurcation. As such, the IMT neuron is modeled as an Ornstein-Uhlenbeck (OU) process with a fluctuating boundary resulting in transfer curves that closely match experiments. As one of the first comprehensive studies of a stochastic neuron hardware and its statistical properties, this article would enable efficient implementation of a large class of neuro-mimetic networks and algorithms.Comment: Added sectioning, Figure 6, Table 1, and Section II.E Updated abstract, discussion and corrected typo

Relative distribution of pneumococcal serotypes among 468 pneumococcal strains isolated in prevaccine or vaccine era.

<p>The relative frequency of pneumococcal serotypes isolated from nasopharyngeal swabs before and after the introduction of the seven-valent conjugated polysaccharide vaccine for (<b>A</b>) swabs with one serotype only (prevaccine era n 106, vaccine era n 298), and (<b>B</b>) restricted to isolates from cocolonized samples (prevaccine era n 12, vaccine era n 52). For easier reading of the graph rare serotypes (prevalence <2%) were grouped as “others”. They included serotypes and/or serogroups 1, 8, 9 (except 9V), 10, 16, 17, 17F, 18 (except 18C), 20, 21, 28, 33, 34, 35, 38 and non-typeable isolates.</p

Serotype distribution among nasopharyngeal <i>S. pneumoniae</i> isolates.

<p><b>A.</b> Serotype distribution among nasopharyngeal isolates (n 468) of <i>S. pneumoniae</i> stratified according to the detection of cocolonization or single colonization with <i>S. pneumoniae</i> strains. The group “cocolonizing” includes the 64 isolates from cocolonized samples, for which a serotype could be determined. Serotypes with a relative frequency of less than 2% are summarized as “others”. They included serotypes/-groups 1, 8, 9 (except 9V), 10, 16, 17, 17F, 18 (except 18C), 20, 21, 28, 33, 34, 35, 38 and non-typeable isolates. The rate of rare serotypes (“others”) was significantly higher in cocolonized than in single colonized swabs (23.4% vs. 11.4%, p = 0.01), but difference in the frequency of individual serotypes (for example for the serotypes 11, 15, and 19F) did not reach statistical significance. <b>B.</b> Distribution of rare serotypes (group “other” in Figure 2A) in samples with or without cocolonization. The difference between the proportion of non-typeable strains in cocolonized samples (4.7%) and in those with a single strain (0.5%) was statistically significant (Fisher's exact test p = 0.02).</p

Ratio of strains present in cocolonized nasopharyngeal swabs.

<p>Strain ratios were determined from the peak heights in the chromatograms obtained by terminal-restriction fragment length polymorphism analysis (T-RFLP, as described in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0011638#s2" target="_blank">methods</a> section). The X-axis indicates the fold-higher presence of the more abundant strain. The three samples with three strains were excluded.</p

Univariate analysis of DNA quantity of <i>plyNCR</i> PCR products as a surrogate for pneumococcal colonization density in the nasopharynx.

a<p>No information was available about age for 7 patients.</p>b<p>PCV7 =  seven-valent conjugated pneumococcal vaccine.</p>c<p>This associations became statistically significant after adjustment for carriage of a serotype contained in PCV7 in a logistic regression model (p = 0.02).</p>d<p>Carriage of a serotype contained in the seven-valent conjugated pneumococcal vaccine; i.e. one of the following serotypes: 4, 6B, 9V, 14, 18C, 19F.</p><p>No information about vaccination status was available for 100 patients (8.9%). P-values compare the carriage of single or multiple strains of <i>S. pneumoniae</i> to no carriage.</p

Univariate analysis for factors associated with carriage of single or multiple strains of <i>Streptococcus pneumoniae</i>.

a<p>PCV7 = 7-valent conjugated pneumococcal polysaccharide vaccine.</p>b<p>No information was available about age for 7 patients.</p>c<p>No information was available about gender for 4 patients.</p>d<p>Antibiotic treatment during the 8 weeks before swab collection, no information was available for 108 patients (9.6%).</p>e<p>No information about current day care use was available for 152 patients (13.5%).</p>f<p>More than one otitis media episode during the past 12 months. No information was available about recurrent otitis media for 183 patients (16.3%).</p>g<p>Vaccination with the seven-valent conjugated pneumococcal vaccine.</p><p>No information about vaccination status was available for 100 patients (8.9%). P-value is for the comparison between carriage of single or multiple strains of <i>S. pneumoniae</i> versus no carriage.</p

Comparison between multiplex PCR and <i>plyNCR</i> RFLP/T-RFLP for the detection of multiple colonization in 141 nasopharyngeal swabs collected during study period 4 for which culture revealed growth of a pneumococcal strain.

<p>Multiplex PCR was performed on DNA extracted from frozen stocks of the primary culture plate. <i>plyNCR</i> RFLP and T-RFLP detected more episodes of multiple colonization than multiplex PCR positive and In 3 of the 8 cocolonization events not detected by multiplex PCR non-typeable pneumococcal strains were involved.</p

Prevalence of the most frequent bacterial taxa.

*<p>No data concerning day care for 10 children.</p>**<p>Data based on <i>Tsp509I</i> received TFs of 464 bp (<i>Haemophilus influenzae</i>), 518 bp (<i>Corynebacterium</i> spp.) 535 bp (<i>Moraxella</i> spp.), 665 bp (<i>Streptococcus</i> spp. 1) and 204 bp (<i>Streptococcus</i> spp. 2). <i>Streptococcus pneumoniae</i> and <i>pseudopneumoniae</i> are included in <i>Streptococcus</i> spp. 1 while other members of the Mitis group are included in <i>Streptococcus</i> spp. 2 (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052241#pone-0052241-t002" target="_blank">Table 2</a>).</p

DNA sequencing and subsequent taxa assignments of the most prevalent <i>Tsp509I</i> terminal fragments (TFs) derived from 15 samples with different T-RFLP patterns.

*<p><i>Streptococcus pneumoniae</i> and <i>pseudopneumoniae</i> are included in <i>Streptococcus</i> spp. 1 while other members of the Mitis group are included in <i>Streptococcus</i> spp. 2. Using the second restriction enzyme (<i>Hpy166II</i>) <i>Streptococcus</i> spp. 1 can be further divided into <i>S. pneumoniae</i> and <i>S. pseudopneumoniae</i> (see text).</p>**<p>Two different bacterial assignments were retrieved for TF with 148 base pairs (bp).</p

Additive Main Effects and Multiplicative Interaction Model (AMMI) analysis of bacterial T-RFLP data

<p><b>sets.</b> Using the software T-Rex (T-RFLP analysis Expedited) <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052241#pone.0052241-Culman1" target="_blank">[15]</a>, T-RFLP profiles were first analyzed individually and then grouped according to antibiotic exposure, vaccine season and vaccine status in the software R. The quadrates illustrate the centroids of the individual data points and represent the following: A) prevaccine era, not vaccinated, no antibiotic exposure. B) vaccine era, not vaccinated, no antibiotic exposure. C) vaccine era, vaccinated, no antibiotic exposure. A_ab) prevaccine era, not vaccinated, antibiotic exposure. B_ab) vaccine era, not vaccinated, antibiotic exposure. C_ab) vaccine era, vaccinated, antibiotic exposure. According to AMMI, antibiotic exposure (grey versus black) and vaccine season (A and A_ab versus others) significantly influences the microbiota (see text and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0052241#pone-0052241-t003" target="_blank">Table 3</a>).</p