Consistent Recovery of Sensory Stimuli Encoded with MIMO Neural Circuits

We consider the problem of reconstructing finite energy stimuli encoded with a population of spiking leaky integrate-and-fire neurons. The reconstructed signal satisfies a consistency condition: when passed through the same neuron, it triggers the same spike train as the original stimulus. The recovered stimulus has to also minimize a quadratic smoothness optimality criterion. We formulate the reconstruction as a spline interpolation problem for scalar as well as vector valued stimuli and show that the recovery has a unique solution. We provide explicit reconstruction algorithms for stimuli encoded with single as well as a population of integrate-and-fire neurons. We demonstrate how our reconstruction algorithms can be applied to stimuli encoded with ON-OFF neural circuits with feedback. Finally, we extend the formalism to multi-input multi-output neural circuits and demonstrate that vector-valued finite energy signals can be efficiently encoded by a neural population provided that its size is beyond a threshold value. Examples are given that demonstrate the potential applications of our methodology to systems neuroscience and neuromorphic engineering

Load Balancing Algorithms for Jacksonian Networks with Acknowledgement Delays

Load balancing algorithms for Jacksonian networks are derived. The state of the network is represented by the total number of packets for which the source has not yet received an acknowledgement, The networks studied are subject to the state independent routing and, state dependent and state independent flow control. The objective is to maximize the throughput of the network so that the end-to-end expected packet time delay does not exceed an upper bound. The optimal flow control is shown to be a window type, while the routing policy balances the traffic inside the network. Several load balancing algorithms are evaluated

Decentralized Network Flow Control

In this paper, the problem of finding the decentralized flow control of a BCMP network is investigated. The packets of each of the users correspond to different classes of customers. The servers in the network are exponential and serve packets with FIFO policy. Each network user operates with either a state-dependent arrival rate (i.e. an arrival rate which depends upon the number of the user\u27s packets that have not yet been acknowledged) or a state-dependent arrival rate (which the user chooses). The decentralized flow control problem is formulated udder two optimization criteria. Under the first optimization criterion, the decentralized flow control corresponding to each of the network users maximizes the throughput of the network, under the constraint that the expected time delay of the packets in the network does not exceed a preassigned upper bound. Under the second optimization criterion, the decentralized flow control corresponding to each of the network users maximizes the throughput of the network, under the constraint that the expected time delay of each particular class of packets does not exceed a preassigned (user dependent) upper bound. In this paper all the previous classes of problems are handled uniformly, using efficient nonlinear optimization techniques

Optimal Resource Allocation for Markovian Queueing Networks: The Complete Information Case

The problem of finding the optimal routing and flow control of a single-class Markovian network under a suitable optimization criterion is analyzed. It is proven that, if complete information about the state of the network is made available to the network controller, the optimal state dependent routing is essentially deterministic, and the optimal flow control is of a generalized window type. An iterative linear programming algorithm is given for the derivation of the optimal routing and flow control policy

The Effect of Delayed Feedback Information on Network Performance

The performance of a network subject to either state dependent or state independent flow control is investigated. In the state dependent case, the flow control policy is a function of the total number of packets for which the controller has not yet received an acknowledgement. In this case it is shown that the optimal flow control is a sliding window mechanism. The effect of the delayed feedback on the network performance as well as the size of the window are studied. The state independent optimal rate is also derived. The performance of the state dependent and state independent flow control policies are compared. Conditions for employing one of the two types of flow control policies for superior end-to-end network performance are discussed. All the results obtained are demonstrated using simple examples

Neurokernel: An Open Source Platform for Emulating the Fruit Fly Brain

We have developed an open software platform called Neurokernel for collaborative development of comprehensive models of the brain of the fruit fly Drosophila melanogaster and their execution and testing on multiple Graphics Processing Units (GPUs). Neurokernel provides a programming model that capitalizes upon the structural organization of the fly brain into a fixed number of functional modules to distinguish between these modules’ local information processing capabilities and the connectivity patterns that link them. By defining mandatory communication interfaces that specify how data is transmitted between models of each of these modules regardless of their internal design, Neurokernel explicitly enables multiple researchers to collaboratively model the fruit fly’s entire brain by integration of their independently developed models of its constituent processing units. We demonstrate the power of Neurokernel’s model integration by combining independently developed models of the retina and lamina neuropils in the fly’s visual system and by demonstrating their neuroinformation processing capability. We also illustrate Neurokernel’s ability to take advantage of direct GPU-to-GPU data transfers with benchmarks that demonstrate scaling of Neurokernel’s communication performance both over the number of interface ports exposed by an emulation’s constituent modules and the total number of modules comprised by an emulation

Asynchronous Algorithms for Optimal Flow Control of BCMP Networks

The decentralized flow control problem for an open multiclass BCMP network is studied. The power based optimization criterion is employed for the derivation of the optimal flow control for each of the network\u27s users. It is shown that that optimal arrival rates correspond to the unique Nash equilibrium point of a noncooperative game problem. Asynchronous algorithms are presented for the computation of the Nash equilibrium point of the network. Among them, the nonlinear Gauss-Seidel algorithms is distinguished for its robustness and speed of convergence

A Motion Detection Algorithm Using Local Phase Information

Previous research demonstrated that global phase alone can be used to faithfully represent visual scenes. Here we provide a reconstruction algorithm by using only local phase information. We also demonstrate that local phase alone can be effectively used to detect local motion. The local phase-based motion detector is akin to models employed to detect motion in biological vision, for example, the Reichardt detector. The local phase-based motion detection algorithm introduced here consists of two building blocks. The first building block measures/evaluates the temporal change of the local phase. The temporal derivative of the local phase is shown to exhibit the structure of a second order Volterra kernel with two normalized inputs. We provide an efficient, FFT-based algorithm for implementing the change of the local phase. The second processing building block implements the detector; it compares the maximum of the Radon transform of the local phase derivative with a chosen threshold. We demonstrate examples of applying the local phase-based motion detection algorithm on several video sequences. We also show how the locally detected motion can be used for segmenting moving objects in video scenes and compare our local phase-based algorithm to segmentation achieved with a widely used optic flow algorithm