2362478
On the profile of the corona of two graphs
The concept of profile, together with bandwidth, originates from handling sparse matrices in solving linear systems of equations. Given a graph G, the profile minimization problem is to find a one-to-one mapping f : V(G) → {1,2 ..., |V(G)|} such that Σv ∈ v(G) maxx ∈ N [v] (f(v) - f(x)) is as small as possible, where N[v] = {v} ∪ {x: x is adjacent to v}. This paper studies the profile of the corona G ∧ H of two graphs G and H. In particular, bounds for the profile of the corona of two graphs are established. Also, exact values of the profiles of coronas G ∧ H are obtained when G has certain properties, including when G is a caterpillar, a complete graph or a cycle.
7685789
On Bandwidth for the Tensor Product of Paths and Cycles
The tensor product of graphs G1 and G2 is defined to be G = (V, E) where V = V(G1) × V(G2) and edge ((x1, y1), (x2, y2)) ϵ E whenever (x1, x2) ϵ E(G1) and (y1, y2) ϵ E(G2). We use G1(Tp)G2 to denote G. This paper establishes the bandwidth of the tensor product of a path with a path, a cycle with a path, and a cycle with a cycle. Optimal numberings to achieve each of these bandwidths are provided.
20059595
Probing Changes in Neural Interaction During Adaptation
A procedure is developed to probe the changes in the functional interactions among neurons in primary motor cortex of the monkey brain during adaptation. A monkey is trained to learn a new skill, moving its arm to reach a target under the influence of external perturbations. The spike trains of multiple neurons in the primary motor cortex are recorded simultaneously. We utilize the methodology of directed transfer function, derived from a class of linear stochastic models, to quantify the causal interactions between the neurons. We find that the coupling between the motor neurons tends to increase during the adaptation but return to the original level after the adaptation. Furthermore, there is evidence that adaptation tends to affect the topology of the neural network, despite the approximate conservation of the average coupling strength in the network before and after the adaptation.
2452257
Web server QoS models: applying scheduling rules from production planning
Most web servers, in practical use, use a queuing policy based on the Best Effort model, which employs the first-in-first-out (FIFO) scheduling rule to prioritize web requests in a single queue. This model does not provide Quality of Service (QoS). In the Differentiated Services (DiffServ) model, separate queues are introduced to differentiate QoS for separate web requests with different priorities. This paper presents web server QoS models that use a single queue, along with scheduling rules from production planning in the manufacturing domain, to differentiate QoS for classes of web service requests with different priorities. These scheduling rules are Weighted Shortest Processing Time (WSPT), Apparent Tardiness Cost (ATC), and Earliest Due Date. We conduct simulation experiments and compare the QoS performance of these scheduling rules with the FIFO scheme used in the basic Best Effort model with only one queue, and the basic DiffServ model with two separate queues. Simulation results demonstrate better QoS performance using WSPT and ATC, especially when requested services exceed the capacity of a web server.
2935951
Enhancing router QoS through job scheduling with weighted shortest processing time-adjusted
Most routers on the Internet employ a first-in-first-out (FIFO) scheduling rule to determine the order of serving data packets. This scheduling rule does not provide quality of service (QoS) with regards to the differentiation of services for data packets with different service priorities and the enhancement of routing performance. We develop a scheduling rule called Weighted Shortest Processing Time-Adjusted (WSPT-A), which is derived from WSPT (a scheduling rule for production planning in the manufacturing domain), to enhance router QoS. We implement a QoS router model based on WSPT-A and run simulations to measure and compare the routing performance of our model with that of router models based on the FIFO and WSPT scheduling rules. The simulation results show superior QoS performance when using the router model with WSPT-A.