Heteroclinic cycles in Hopfield networks

Learning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic pattern of the associated neural circuit. In this work we consider a class of network neuron models, known as Hopfield networks, with a learning rule which consists of transforming an information string to a coupling pattern. Within this class of models we study dynamic patterns, known as robust heteroclinic cycles, and establish a tight connection between their existence and the structure of the coupling

Heteroclinic cycles in Hopfield networks

International audienceLearning or memory formation are associated with the strengthening of the synaptic connections between neurons according to a pattern reflected by the input. According to this theory a retained memory sequence is associated to a dynamic pattern of the associated neural circuit. In this work we consider a class of network neuron models, known as Hopfield networks, with a learning rule which consists of transforming an information string to a coupling pattern. Within this class of models we study dynamic patterns, known as robust heteroclinic cycles, and establish a tight connection between their existence and the structure of the coupling

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA

Switching in heteroclinic networks

We study the dynamics near heteroclinic networks for which all eigenvalues of the linearization at the equilibria are real. A common connection and an assumption on the geometry of its incoming and outgoing directions exclude even the weakest forms of switching (i.e. along this connection). The form of the global transition maps, and thus the type of the heteroclinic cycle, plays a crucial role in this. We look at two examples in $\mathbb{R}^5$, the House and Bowtie networks, to illustrate complex dynamics that may occur when either of these conditions is broken. For the House network, there is switching along the common connection, while for the Bowtie network we find switching along a cycle

The Penicillin for the Emergency Department Outpatient treatment of CELLulitis (PEDOCELL) trial: update to the study protocol and detailed statistical analysis plan (SAP)

Background: Cellulitis is a painful, potentially serious, infectious process of the dermal and subdermal tissues and represents a significant disease burden. The statistical analysis plan (SAP) for the Penicillin for the Emergency Department Outpatient treatment of CELLulitis (PEDOCELL) trial is described here. The PEDOCELL trial is a multicentre, randomised, parallel-arm, double-blinded, non-inferiority clinical trial comparing the efficacy of flucloxacillin (monotherapy) with combination flucloxacillin/phenoxymethylpenicillin (dual therapy) for the outpatient treatment of cellulitis in the emergency department (ED) setting. To prevent outcome reporting bias, selective reporting and data-driven results, the a priori-defined, detailed SAP is presented here. Methods/design: Patients will be randomised to either orally administered flucloxacillin 500 mg four times daily and placebo or orally administered 500 mg of flucloxacillin four times daily and phenoxymethylpenicillin 500 mg four times daily. The trial consists of a 7-day intervention period and a 2-week follow-up period. Study measurements will be taken at four specific time points: at patient enrolment, day 2-3 after enrolment and commencing treatment (early clinical response (ECR) visit), day 8-10 after enrolment (end-of-treatment (EOT) visit) and day 14-21 after enrolment (test-of-cure (TOC) visit). The primary outcome measure is investigator-determined clinical response measured at the TOC visit. The secondary outcomes are as follows: lesion size at ECR, clinical treatment failure at each follow-up visit, adherence and persistence of trial patients with orally administered antibiotic therapy at EOT, health-related quality of life (HRQoL) and pharmacoeconomic assessments. The plan for the presentation and comparison of baseline characteristics and outcomes is described in this paper. Discussion: This trial aims to establish the non-inferiority of orally administered flucloxacillin monotherapy with orally administered flucloxacillin/phenoxymethylpenicillin dual therapy for the ED-directed outpatient treatment of cellulitis. In doing so, this trial will bridge a knowledge gap in this understudied and common condition and will be relevant to clinicians across several different disciplines. The SAP for the PEDOCELL trial was developed a priori in order to minimise analysis bias