Using nonequilibrium fluctuation theorems to understand and correct errors in equilibrium and nonequilibrium discrete Langevin dynamics simulations

Common algorithms for computationally simulating Langevin dynamics must discretize the stochastic differential equations of motion. These resulting finite time step integrators necessarily have several practical issues in common: Microscopic reversibility is violated, the sampled stationary distribution differs from the desired equilibrium distribution, and the work accumulated in nonequilibrium simulations is not directly usable in estimators based on nonequilibrium work theorems. Here, we show that even with a time-independent Hamiltonian, finite time step Langevin integrators can be thought of as a driven, nonequilibrium physical process. Once an appropriate work-like quantity is defined -- here called the shadow work -- recently developed nonequilibrium fluctuation theorems can be used to measure or correct for the errors introduced by the use of finite time steps. In particular, we demonstrate that amending estimators based on nonequilibrium work theorems to include this shadow work removes the time step dependent error from estimates of free energies. We also quantify, for the first time, the magnitude of deviations between the sampled stationary distribution and the desired equilibrium distribution for equilibrium Langevin simulations of solvated systems of varying size. While these deviations can be large, they can be eliminated altogether by Metropolization or greatly diminished by small reductions in the time step. Through this connection with driven processes, further developments in nonequilibrium fluctuation theorems can provide additional analytical tools for dealing with errors in finite time step integrators.Comment: 11 pages, 4 figure

25th annual computational neuroscience meeting: CNS-2016

The same neuron may play different functional roles in the neural circuits to which it belongs. For example, neurons in the Tritonia pedal ganglia may participate in variable phases of the swim motor rhythms [1]. While such neuronal functional variability is likely to play a major role the delivery of the functionality of neural systems, it is difficult to study it in most nervous systems. We work on the pyloric rhythm network of the crustacean stomatogastric ganglion (STG) [2]. Typically network models of the STG treat neurons of the same functional type as a single model neuron (e.g. PD neurons), assuming the same conductance parameters for these neurons and implying their synchronous firing [3, 4]. However, simultaneous recording of PD neurons shows differences between the timings of spikes of these neurons. This may indicate functional variability of these neurons. Here we modelled separately the two PD neurons of the STG in a multi-neuron model of the pyloric network. Our neuron models comply with known correlations between conductance parameters of ionic currents. Our results reproduce the experimental finding of increasing spike time distance between spikes originating from the two model PD neurons during their synchronised burst phase. The PD neuron with the larger calcium conductance generates its spikes before the other PD neuron. Larger potassium conductance values in the follower neuron imply longer delays between spikes, see Fig. 17.Neuromodulators change the conductance parameters of neurons and maintain the ratios of these parameters [5]. Our results show that such changes may shift the individual contribution of two PD neurons to the PD-phase of the pyloric rhythm altering their functionality within this rhythm. Our work paves the way towards an accessible experimental and computational framework for the analysis of the mechanisms and impact of functional variability of neurons within the neural circuits to which they belong

GIGAswitch System: A High-Performance Packet-Switching Platform

The GIGAswitch system is a high-performance packet-switching platform built on a 36-port 100 Mb/s crossbar switching fabric. The crossbar is data link independent and is capable of making 6.25 million connections per second. Digital’s first GIGAswitch system product uses 2-port FDDI line cards to construct a 22-port IEEE 802.1d FDDI bridge. The FDDI bridge implements distributed forwarding in hardware to yield forwarding rates in excess of 200,000 packets per second per port. The GIGAswitch system is highly available and provides robust operation in the presence of overload. The GIGAswitch system is a multiport packetswitching platform that combines distributed forwarding hardware and crossbar switching to attain very high network performance. When a packet is received, the receiving line card decides where to forward the packet autonomously. The ports on a GIGAswitch system are fully interconnected with a custom-designed, very large-scale integration (VLSI) crossbar that permits up to 36 simultaneous conversations. Data flows through 100 megabits per second (Mb/s) point-to-point connections, rather than through any shared media. Movement of unicast packets through the GIGAswitch system is accomplished completely by hardware. The GIGAswitch system can be used to eliminate network hierarchy and concomitant delay. It can aggregate traffic from local area networks (LANs) and be used to construct workstation farms. The use of LAN and wide area network (WAN) line cards makes the GIGAswitch system suitable for building, campus, and metropolitan interconnects. The GIGAswitch system provides robustness and availability features useful in high-availability applications like financial networks and enterprise backbones. In this paper, we present an overview of the switch architecture and discuss the principles influencing its design. We then describe the implementation of an FDDI bridge on the GIGAswitch syste

Endocannabinoid gene × gene interaction association to alcohol use disorder in two adolescent cohorts.

Genetic markers of the endocannabinoid system have been linked to a variety of addiction-related behaviors that extend beyond cannabis use. In the current study we investigate the relationship between endocannabinoid (eCB) genetic markers and alcohol use disorder (AUD) in European adolescents (14-18 years old) followed in the IMAGEN study ( = 2,051) and explore replication in a cohort of North American adolescents from Canadian Saguenay Youth Study (SYS) ( = 772). Case-control status is represented by a score of more than 7 on the Alcohol Use Disorder Identification Test (AUDIT). First a set-based test method was used to examine if a relationship between the eCB system and AUDIT case/control status exists at the gene level. Using only SNPs that are both independent and significantly associated to case-control status, we perform Fisher's exact test to determine SNP level odds ratios in relation to case-control status and then perform logistic regressions as analysis, while considering various covariates. Generalized multifactor dimensionality reduction (GMDR) was used to analyze the most robust SNP×SNP interaction of the five eCB genes with positive AUDIT screen. While no gene-sets were significantly associated to AUDIT scores after correction for multiple tests, in the case/control analysis, 7 SNPs were significantly associated with AUDIT scores of > 7 ( < 0.05; OR<1). Two SNPs remain significant after correction by false discovery rate (FDR): rs9343525 in (p =0.042, OR = 0.73) and rs507961 in (p = 0.043, OR = 0.78). Logistic regression showed that both rs9353525 () and rs507961 () remained significantly associated with positive AUDIT screens ( < 0.01; OR < 1) after correction for multiple covariables and interaction of covariable × SNP. This result was not replicated in the SYS cohort. The GMDR model revealed a significant three-SNP interaction ( = 0.006) involving rs484061 (), rs4963307 (), and rs7766029 () predicted case-control status, after correcting for multiple covariables in the IMAGEN sample. A binomial logistic regression of the combination of these three SNPs by phenotype in the SYS cohort showed a result in the same direction as seen in the IMAGEN cohort (BETA = 0.501, = 0.06). While preliminary, the present study suggests that the eCB system may play a role in the development of AUD in adolescents