The complexity of dynamics in small neural circuits

Mean-field theory is a powerful tool for studying large neural networks. However, when the system is composed of a few neurons, macroscopic differences between the mean-field approximation and the real behavior of the network can arise. Here we introduce a study of the dynamics of a small firing-rate network with excitatory and inhibitory populations, in terms of local and global bifurcations of the neural activity. Our approach is analytically tractable in many respects, and sheds new light on the finite-size effects of the system. In particular, we focus on the formation of multiple branching solutions of the neural equations through spontaneous symmetry-breaking, since this phenomenon increases considerably the complexity of the dynamical behavior of the network. For these reasons, branching points may reveal important mechanisms through which neurons interact and process information, which are not accounted for by the mean-field approximation.Comment: 34 pages, 11 figures. Supplementary materials added, colors of figures 8 and 9 fixed, results unchange

Stationary-State Statistics of a Binary Neural Network Model with Quenched Disorder

We study the statistical properties of the stationary firing-rate states of a neural network model with quenched disorder. The model has arbitrary size, discrete-time evolution equations and binary firing rates, while the topology and the strength of the synaptic connections are randomly generated from known, generally arbitrary, probability distributions. We derived semi-analytical expressions of the occurrence probability of the stationary states and the mean multistability diagram of the model, in terms of the distribution of the synaptic connections and of the external stimuli to the network. Our calculations rely on the probability distribution of the bifurcation points of the stationary states with respect to the external stimuli, which can be calculated in terms of the permanent of special matrices, according to extreme value theory. While our semi-analytical expressions are exact for any size of the network and for any distribution of the synaptic connections, we also specialized our calculations to the case of statistically-homogeneous multi-population networks. In the specific case of this network topology, we calculated analytically the permanent, obtaining a compact formula that outperforms of several orders of magnitude the Balasubramanian-Bax-Franklin-Glynn algorithm. To conclude, by applying the Fisher-Tippett-Gnedenko theorem, we derived asymptotic expressions of the stationary-state statistics of multi-population networks in the large-network-size limit, in terms of the Gumbel (double exponential) distribution. We also provide a Python implementation of our formulas and some examples of the results generated by the code.Comment: 30 pages, 6 figures, 2 supplemental Python script

Identifying priority areas for spatial management of mixed fisheries using ensemble of multi‐species distribution models

Spatial fisheries management is widely used to reduce overfishing, rebuild stocks, and protect biodiversity. However, the effectiveness and optimization of spatial measures depend on accurately identifying ecologically meaningful areas, which can be difficult in mixed fisheries. To apply a method generally to a range of target species, we devel- oped an ensemble of species distribution models (e-SDM) that combines general ad- ditive models, generalized linear mixed models, random forest, and gradient-boosting machine methods in a training and testing protocol. The e-SDM was used to integrate density indices from two scientific bottom trawl surveys with the geopositional data, relevant oceanographic variables from the three-dimensional physical-biogeochemi- cal operational model, and fishing effort from the vessel monitoring system. The de- termined best distributions for juveniles and adults are used to determine hot spots of aggregation based on single or multiple target species. We applied e-SDM to juvenile and adult stages of 10 marine demersal species representing 60% of the total demer- sal landings in the central areas of the Mediterranean Sea. Using the e-SDM results, hot spots of aggregation and grounds potentially more selective were identified for each species and for the target species group of otter trawl and beam trawl fisheries. The results confirm the ecological appropriateness of existing fishery restriction areas and support the identification of locations for new spatial management measures

Identifying priority areas for spatial management of mixed fisheries using ensemble of multi‐species distribution models

Spatial fisheries management is widely used to reduce overfishing, rebuild stocks, and protect biodiversity. However, the effectiveness and optimization of spatial measures depend on accurately identifying ecologically meaningful areas, which can be difficult in mixed fisheries. To apply a method generally to a range of target species, we developed an ensemble of species distribution models (e-SDM) that combines general additive models, generalized linear mixed models, random forest, and gradient-boosting machine methods in a training and testing protocol. The e-SDM was used to integrate density indices from two scientific bottom trawl surveys with the geopositional data, relevant oceanographic variables from the three-dimensional physical-biogeochemical operational model, and fishing effort from the vessel monitoring system. The determined best distributions for juveniles and adults are used to determine hot spots of aggregation based on single or multiple target species. We applied e-SDM to juvenile and adult stages of 10 marine demersal species representing 60% of the total demersal landings in the central areas of the Mediterranean Sea. Using the e-SDM results, hot spots of aggregation and grounds potentially more selective were identified for each species and for the target species group of otter trawl and beam trawl fisheries. The results confirm the ecological appropriateness of existing fishery restriction areas and support the identification of locations for new spatial management measures

Clinical utility of Next Generation Sequencing of plasma cell-free DNA for the molecular profiling of patients with NSCLC at diagnosis and disease progression

Background: The present study evaluates the utility of NGS analysis of circulating free DNA (cfDNA), which incorporates small amounts of tumor DNA (ctDNA), at diagnosis or at disease progression (PD) in NSCLC patients. Methods: Comprehensive genomic profiling on cfDNA by NGS were performed in NSCLC patients at diagnosis (if tissue was unavailable/insufficient) or at PD to investigate potential druggable molecular aberrations. Blood samples were collected as routinary diagnostic procedures, DNA was extracted, and the NextSeq 550 Illumina platform was used to run the Roche Avenio ctDNA Expanded Kit for molecular analyses. Gene variants were classified accordingly to the ESCAT score. Results: A total of 106 patients were included in this study; 44 % of cases were requested because of tissue unavailability at the diagnosis and 56 % were requested at the PD. At least one driver alteration was observed in 62 % of cases at diagnosis. Driver druggable variants classified as ESCAT level I were detected in 34 % of patients, including ALK-EML4, ROS1-CD74, EGFR, BRAF, KRAS p.G12C, PI3KCA. In the PD group, most patients were EGFR-positive, progressing to a first line-therapy. Sixty-three percent of patients had at least one driver alteration detected in blood and 17 % of patients had a known biological mechanism of resistance allowing further therapeutic decisions. Conclusions: The present study confirms the potential of liquid biopsy to detect tumour molecular heterogeneity in NSCLC patients at the diagnosis and at PD, demonstrating that a significant number of druggable mutations and mechanisms of resistance can be detected by NGS analysis on ctDNA

Modelli di distribuzione spaziale per specie demersali per il management spaziale, valutazione e previsione in mare Adriatico e Ionio

I modelli di distribuzione di specie (SDMs) sono ampiamente utilizzati in ecologia, specialmente nel contesto marino negli ultimi decenni. Qui, in particolare, parliamo della scienza della pesca. Sappiamo che le specie demersali sono molto importanti per la gestione della pesca e dell'ecosistema marino, e un numero crescente di studi sottolinea l'importanza della gestione dello spazio per la ricostituzione degli stock e la protezione delle risorse dell'ecosistema e della biodiversità. Gli SDMs potrebbero aiutare nella gestione della pesca nelle operazioni spaziali. In questo studio, mi sono concentrato su diversi aspetti della distribuzione delle specie e ho definito una procedura per sviluppare un insieme di modelli che combinano diversi approcci modellistici. Ho utilizzato i modelli additivi generalizzati, il random forest e il metodo Gradient Boosted per dieci specie di pesci demersali, due stadi di vita (pesce adulto e giovanile) e due diversi indici, ovvero chilogrammi per km2 (kg/km2) e numero di individui per km2 (n/km2). Ho utilizzato i dati di due indagini condotte in Adriatico e Ionio: Mediterranean International Trawl Survey (MEDITS) e Sole Monitoring (SOLEMON). Nello specifico: • Ho analizzato gli indici di biomassa (kg/km2) per nasello, sogliola, canocchie, triglie e seppie utilizzando un set di modelli additivi generalizzati (GAM) con e senza variabili abiotiche. I risultati evidenziano che il modello geostatistico per la stima della distribuzione delle diverse specie demersali è migliorato quando sono incluse ulteriori variabili ambientali (variabili oceanografiche). • Ho analizzato gli indici di densità (n/km2) definendo una procedura per sviluppare un insieme di modelli (ensemble model), ottenuti combinando 5 diversi approcci. Ho implementato training spaziale per valutare le migliori prestazioni di 9 modelli attraverso una serie di indicatori statistici. Questi modelli includono una diversa combinazione di covariate, a partire dal modello più semplice (profondità, anno e variabili spaziotemporali) a quello più complesso (includendo anche variabili oceanografiche e sforzo di pesca). I risultati evidenziano il miglioramento (minore differenza tra dati modellati e osservati) per il modello con variabili ambientali, utilizzando come caso di studio il nasello Europeo (Merluccius merluccius) nei mari Adriatico e Ionio. • Ho utilizzato l’ensemble model (e-SDM) che combina i modelli additivi generali, il random forest e i Gradient Boosted per determinare l'hot spot di aggregazione per giovani e adulti di dieci specie demersali, utilizzando indici di densità (n/ km2) derivati da MEDITS e SOLEMON, e dati geo-referenziatii (profondità, latitudine, longitudine e mese), variabili oceanografiche 3D rilevanti (temperatura, salinità, clorofilla-a, nutrienti disciolti e ossigeno, particolato di carbonio organico, pH) e sforzo di pesca (dal sistema di monitoraggio delle navi). • Ho utilizzato l’ensemble model (e-SDM) per valutare la distribuzione futura di dieci specie demersali nell'area di studio, identificando aree di aggregazione per quattro diversi scenari (2012, 2018, 2035 e 2050) e due fasi di vita (adulti e giovanilie). Ho stimato le distribuzioni future di hot spot di aggregazione, distribuzione della densità e centro di gravità per le 10 specie nell'area di studio. I risultati consentono di prevedere le aree guadagnate e perse nelle future condizioni climatiche IPCC RCP 8.5, ponendo le basi per determinare i potenziali spostamenti per le dieci specie.Species distribution models (SDMs) are widely used in ecology, especially in the marine context in recent decades. Here we are talking about fisheries science in particular. We know that demersal species are very important for fisheries management and the marine ecosystem, and a growing number of studies emphasize the importance of spatial management for rebuilding stocks and protecting ecosystem resources and biodiversity. SDMs could assist fisheries management in spatial operations. In this study, I focused on different aspects of species distribution and defined a procedure to develop an ensemble of models combining different modeling approaches. I combined Generalized Additive Models, Random Forest, and the Gradient Boosted method for ten ground fish species, two life stages (adult and juvenile fish), and two different indices such as kilograms per km2 (kg/km2) and number of individuals per km2 (n/km2). I used data from two surveys conducted in the Adriatic and Ionian Seas: Mediterranean International Trawl Survey (MEDITS) and Sole Monitoring (SOLEMON). Specifically: - I analyzed biomass indices (kg/km2) for European hake, common sole, mantis shrimp, red mullet, and common cuttlefish using a set of Generalized Additive Models (GAMs) with and without abiotic variables. The results highlight that the geostatistical model for estimating the distribution of different demersal species based on trawl data is improved when additional environmental variables are included (oceanographic variables). - I analyzed the density index (n/km2) defining an original procedure to develop an ensemble of models, obtained by combining 5 different approaches. I implemented spatial training and test data sets to evaluate the best performance of 9 models through a set of indicators. These models include a different combination of covariates, starting with the simplest model (depth, year, and spatiotemporal variables) to the most complex one (including also oceanographic variables and effort). The results highlight the improvement (smaller difference between modelled and observed data) for the model with environmental variables, using as a case study European hake (Merluccius merluccius) in the Adriatic and Ionian Seas. - I used the ensemble of Species Distribution Models (e-SDM) that combines General Additive Models, random forest, and gradient-boosting machine methods to determine the hot spot of aggregation for juveniles and adults of ten demersal species, using density indexes (n/km2) derived from MEDITS and SOLEMON, and geopositional data (depth, latitude, longitude, and month), relevant 3D oceanographic variables (temperature, salinity, chlorophyll-a, dissolved nutrients and oxygen, particulate organic carbon, pH) and fishing effort (from Vessel Monitoring System). - I used ensemble-species distributions models (e-SDM) to evaluate the future distribution of ten demersal species in the area of study, identifying areas of aggregation for four different scenarios (2012, 2018, 2035, and 2050) and two life stages. I estimated the foreseen future modifications of hot spot of aggregation, density distribution, and center of gravity for the 10 species in the area of study by GSA (Geographic Sub Area, 17, 18, and 19). The results allow to predict gained and lost areas in future IPCC RCP 8.5 climate conditions, setting basis for determining potential range shifts for the ten species

A Formalism for Evaluating Analytically the Cross-Correlation Structure of a Firing-Rate Network Model

International audienceWe introduce a new formalism for evaluating analytically the cross-correlation structure of a finite-size firing-rate network with recurrent connections. The analysis performs a first-order perturbative expansion of neural activity equations that include three different sources of randomness: the background noise of the membrane potentials, their initial conditions, and the distribution of the recurrent synaptic weights. This allows the analytical quantification of the relationship between anatomical and functional connectivity, i.e. of how the synaptic connections determine the statistical dependencies at any order among different neurons. The technique we develop is general, but for simplicity and clarity we demonstrate its efficacy by applying it to the case of synaptic connections described by regular graphs. The analytical equations so obtained reveal previously unknown behaviors of recurrent firing-rate networks, especially on how correlations are modified by the external input, by the finite size of the network, by the density of the anatomical connections and by correlation in sources of randomness. In particular, we show that a strong input can make the neurons almost independent, suggesting that functional connectivity does not depend only on the static anatomical connectivity, but also on the external inputs. Moreover we prove that in general it is not possible to find a mean-field description à la Sznitman of the network, if the anatomical connections are too sparse or our three sources of variability are correlated. To conclude, we show a very counterintuitive phenomenon, which we call stochastic synchronization, through which neurons become almost perfectly correlated even if the sources of randomness are independent. Due to its ability to quantify how activity of individual neurons and the correlation among them depends upon external inputs, the formalism introduced here can serve as a basis for exploring analytically the computational capability of population codes expressed by recurrent neural networks