arXiv subjects

Peter Bentley

Publications and source records attributed to Peter Bentley.

3 recordsLinked to original sources

arXiv2026

Hat guessing with proper colorings

We initiate the study of the hat guessing number of a graph where the adversary is only allowed to provide a proper coloring of the graph. This is the largest number $q$ for which there is a guessing strategy on each vertex that only depends on its neighborhood, such that for every proper coloring of the graph with $q$ colors at least one vertex guesses its color correctly. In this variation, we prove that the hat guessing number of the complete graphs on $n$ vertices is $2n - 1$, which is roughly twice the classical hat guessing number of the complete graph. Our winning strategy is related to finding perfect matchings between the middle layers of the boolean poset of dimension $2n - 1$. We prove that the hat guessing number of all trees on $n \geq 3$ vertices is equal to $4$. We derive general upper bounds in terms of the number of vertices, chromatic number, and maximum degree, and obtain improved bounds for book graphs. Using our results and an ILP formulation of the problem, we determine the exact hat guessing number for all graphs on at most $4$ vertices, give bounds on graphs on $5$ vertices, and suggest some open problems.

math.CO↗

arXiv2019

Normalisation of Weights and Firing Rates in Spiking Neural Networks with Spike-Timing-Dependent Plasticity

Maintaining the ability to fire sparsely is crucial for information encoding in neural networks. Additionally, spiking homeostasis is vital for spiking neural networks with changing numbers of weights and neurons. We discuss a range of network stabilisation approaches, inspired by homeostatic synaptic plasticity mechanisms reported in the brain. These include weight scaling, and weight change as a function of the network's spiking activity. We tested normalisation of the sum of weights for all neurons, and by neuron type. We examined how this approach affects firing rate and performance on clustering of time-series data in the form of moving geometric shapes. We found that neuron type-specific normalisation is a promising approach for preventing weight drift in spiking neural networks, thus enabling longer training cycles. It can be adapted for networks with architectural plasticity.

cs.NE↗

arXiv2008

Danger Theory: The Link between AIS and IDS?

We present ideas about creating a next generation Intrusion Detection System based on the latest immunological theories. The central challenge with computer security is determining the difference between normal and potentially harmful activity. For half a century, developers have protected their systems by coding rules that identify and block specific events. However, the nature of current and future threats in conjunction with ever larger IT systems urgently requires the development of automated and adaptive defensive tools. A promising solution is emerging in the form of Artificial Immune Systems. The Human Immune System can detect and defend against harmful and previously unseen invaders, so can we not build a similar Intrusion Detection System for our computers.

cs.NE↗