Constant Delay Model Research Articles

Irreversible investment with random delay and partial prepayment

Classical irreversible investment problem admits an optimal strategy of threshold type. But there is no consensus on how the investor should adjust the threshold, if there is an implementation delay. By formulating a general problem with random delay and partial prepayment, we find that the effect of delay can be opposite for different prepayment rates. Besides, although the constant delay model is commonly used, we argue that it is a reasonable approximation only if the discount rate is small.

Propagation graph estimation from individuals\u2019 time series of observed states

Various things propagate through the medium of individuals. Some individuals follow the others and take the states similar to their states a small number of time steps later. In this paper, we study the problem of estimating the state propagation order of individuals from the real-valued state sequences of all the individuals.We propose a method of constructing a state propagation graph from individuals’ time series of observed states. The propagation order estimated by our proposed method is demonstrated to be significantly more accurate than that by a baseline method (optimal constant delay model) for our synthetic datasets, and also to be consistent with visually recognizable propagation orders for the dataset of Japanese stock price time series and biological cell firing state sequences.

Bifurcation and Stability Analyses on Stick-Slip Vibrations of Deep Hole Drilling with State-Dependent Delay

To avoid stick-slip vibration, one of the most important forms of self-excited vibrations in deep hole drilling, this paper studies the stability and bifurcation characteristics of a drilling system based on a two-degree-of-freedom discrete model. It is a state-dependent delay model that could describe the non-linear dynamic characteristic of drilling systems more accurately, compared with the traditional constant delay models. In this paper, linear stability analyses of both the state-dependent delay model and the traditional constant delay model are carried out. Hopf bifurcation analyses are then performed by the method of multiple scales. The results show that the state-dependent delay model can provide more precise stability boundaries and more desirable supercritical Hopf bifurcation properties compared to the constant delay model. The control parameters (rotational velocity and feed velocity) will affect these results. It is noted that the method is reliable for deep hole drilling stability prediction and can provide a reference for dynamic optimization design.

Chemotactic response with a constant delay-time mechanism in Ciona spermatozoa revealed by a high time resolution analysis of flagellar motility.

ABSTRACTDuring their chemotactic swimming toward eggs, sperm cells detect their species-specific chemoattractant and sense concentration gradients by unknown mechanisms. After sensing the attractant, sperm cells commonly demonstrate a series of responses involving different swimming patterns by changing flagellar beats, gradually approaching a swimming path toward the eggs, which is the source of chemoattractants. Shiba et al. observed a rapid increase in intracellular Ca2+ concentrations in Ciona spermatozoa after sensing chemoattractants; however, the biochemical processes occurring inside the sperm cells are unclear. In the present study, we focused on the timing and sensing mechanism of chemical signal detection in Ciona. One of the most crucial problems to be solved is defining the initial epoch of chemotactic responses. We adopted a high rate of video recording (600 Hz) for detailed analysis of sperm motion and a novel method for detecting subtle signs of beat forms and moving paths of sperm heads. From these analyses, we estimated a virtual sensing point of the attractant before initiation of motility responses and found that the time delay from sensing to motility responses was almost constant. To evaluate the efficiency of this constant delay model, we performed computer simulation of chemotactic behaviors of Ciona spermatozoa.

Modeling of Random Delays in Networked Control Systems

In networked control systems (NCSs), the presence of communication networks in control loops causes many imperfections such as random delays, packet losses, multipacket transmission, and packet disordering. In fact, random delays are usually the most important problems and challenges in NCSs because, to some extent, other problems are often caused by random delays. In order to compensate for random delays which may lead to performance degradation and instability of NCSs, it is necessary to establish the mathematical model of random delays before compensation. In this paper, four major delay models are surveyed including constant delay model, mutually independent stochastic delay model, Markov chain model, and hidden Markov model. In each delay model, some promising compensation methods of delays are also addressed.

Scheduling and Resource Binding Algorithm Considering Timing Variation

The timing closure problem (e.g., meeting timing/clock period constraint) is one of the most important problems in the design automation. However, the rapid increase of the impact of the process variation on circuit timing makes the problem much more complicated and unpredictable to tackle in synthesis. This paper addresses a new problem of high-level synthesis (HLS) that effectively takes into account the timing variation. Conventional HLS may simply avoid the timing variation problem by considering the worst case or constant delay model of hardware resources, which are certainly not viable solutions. To overcome the impact of timing variation in HLS, this paper addresses the following two problems: 1) how can the statistical static timing analysis (SSTA) used in logic synthesis be modified and effectively applied to the delay and yield computation in HLS? and 2) how can scheduling and resource binding tasks effectively solve the HLS problem with the objective of minimizing latency under yield constraint? Through an extensive experimentation, we confirm that the proposed variation-aware HLS algorithm is able to reduce the latency by 19.7% under 90% performance yield constraint, compared with the result by conventional timing variation-unaware HLS .

Simultaneous area and delay minimum K-LUT mapping for K-exact networks

We address the technology mapping problem for lookup table FPGAs. The area minimization problem, for mapping K-bounded networks, consisting of nodes with at most K inputs, using K-input lookup tables, is known to be NP-complete for K ⩾ 5. The complexity was unknown for K = 2, 3, and 4. The corresponding delay minimization problem (under the constant delay model) was solved in polynomial time by the flow-map algorithm, for arbitrary values of K. We study the class of K-bounded networks, where all nodes have exactly K inputs. We call such networks K-exact. We give a characterization of mapping solutions for such networks. This leads to a polynomial time algorithm for computing the simultaneous area and delay minimum mapping for such networks using K-input lookup tables. We also show that the flow-map algorithm computes the same mapping solution as our algorithm. We then show that for K = 2 the mapping solution for a 2-bounded network, minimizing the area and delay simultaneously, can be easily obtained from that of a 2-exact network derived from it by eliminating single input nodes. Thus the area minimization problem for 2-input lookup tables can be solved in polynomial time, resolving an open problem.