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Title: Remember the Past and Forget Thresholds
One of the most popular existing models for task allocation in ant colonies is the so-called threshold-based task allocation model. Here, each ant has a fixed, and possibly distinct, threshold. Each task has a fixed demand which represents the number of ants required to perform the task.1Thestimulusanant receives for a task is defined as the demand of the task minus the number of ants currently working at the task. An ant joins a task if the stimulus of the task exceeds the ant’s threshold.A large body of results has studied this model for over four decades; however, most of the theoretical works focuses on the study of two tasks. Interestingly, no work in this line of research shows that the number of ants working at a task eventually converges towards the demand nor does any work bound the distance to the demands over time.In this work, we study precisely this convergence. Our results show that while the threshold-based model works fine in the case of two tasks (for certain distributions of thresholds); the threshold model no longer works for the case of more than two tasks. In fact, we show that there is no possible setting of thresholds that yields a satisfactory deficit (demand minus number of ants working on the task) for each task.This is in stark contrast to other theoretical results in the same setting [CDLN14] that rely on state-machines, i.e., some form of small memory together with probabilistic decisions. Note that, the classical threshold model assumes no states or memory (apart from the bare minimum number of states required to encode which task an ant is working on). The resulting task allocation is near-optimal and much better than what is possible using joining thresholds. This remains true even in a noisy environment [DLM+18]. While the deficit is not the only important metric, it is conceivably one of the most important metrics to guarantee the survival of a colony: for example if the number of workers assigned for foraging stays significantly below the demand, then starvation may occur. Moreover, our results do not imply that ants do not use thresholds; we merely argue that relying on thresholds yields a considerable worse performance.  more » « less
Award ID(s):
1810758
NSF-PAR ID:
10161888
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
7th Workshop on Biological Distributed Algorithms (BDA)
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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Using the offline decoder and postprocessor, the model performed at 36.23% sensitivity with 9.52 FAs per 24 hours. The trained model was then evaluated with the online modules. The current performance of the overall online system is 45.80% sensitivity with 28.14 FAs per 24 hours. Table 2 summarizes the performances of these systems. The performance of the online system deviates from the offline P1 model because the online postprocessor fails to combine the events as the seizure probability fluctuates during an event. The modules in the online system add a total of 11.1 seconds of delay for processing each second of the data, as shown in Figure 3. In practice, we also count the time for loading the model and starting the visualizer block. When we consider these facts, the system consumes 15 seconds to display the first hypothesis. The system detects seizure onsets with an average latency of 15 seconds. Implementing an automatic seizure detection model in real time is not trivial. We used a variety of techniques such as the file locking mechanism, multithreading, circular buffers, real-time event decoding, and signal-decision plotting to realize the system. A video demonstrating the system is available at: https://www.isip.piconepress.com/projects/nsf_pfi_tt/resources/videos/realtime_eeg_analysis/v2.5.1/video_2.5.1.mp4. The final conference submission will include a more detailed analysis of the online performance of each module. ACKNOWLEDGMENTS Research reported in this publication was most recently supported by the National Science Foundation Partnership for Innovation award number IIP-1827565 and the Pennsylvania Commonwealth Universal Research Enhancement Program (PA CURE). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the official views of any of these organizations. REFERENCES [1] A. Craik, Y. He, and J. L. 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