The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. The network operates using a biologically-plausible alpha synaptic transfer function. Additionally, we use trainable synchronisation pulses that provide bias, add flexibility during training and exploit the decay part of the alpha function. We show that such networks can be successfully trained on noisy Boolean logic tasks and on the MNIST dataset encoded in time. We show that the spiking neural network outperforms comparable spiking models on MNIST and achieves similar quality to fully connected conventional networks with the same architecture. The spiking network spontaneously discovers two operating modes, mirroring the accuracy-speed trade-off observed in human decision-making: a highly accurate but slow regime, and a fast but slightly lower-accuracy regime. These results demonstrate the computational power of spiking networks with biological characteristics that encode information in the timing of individual neurons. By studying temporal coding in spiking networks, we aim to create building blocks towards energy-efficient, state-based and more complex biologically-inspired neural architectures.

Algorithms for listing the subgraphs satisfying a given property (e.g., being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an indicator F ⊆ 2 U of which subsets of U have the required property. For the problem of listing all sets in F maximal under inclusion, the ambitious goal is to cover a large class of set systems, preserving at the same time the efficiency of the enumeration. Among the existing algorithms, the best-known ones list the maximal subsets in time proportional to their number but may require exponential space. In this paper we improve the state of the art in two directions by introducing an algorithmic framework that, under standard suitable conditions, simultaneously (i) extends the class of problems that can be solved efficiently to strongly accessible set systems, and (ii) reduces the additional space usage from exponential in |U| to stateless, thus accounting for just O(q) space, where q ≤ |U| is the largest size of a maximal set in F.

An update on the JPEG XL standardization effort: JPEG XL is a practical approach focused on scalable web distribution and efficient compression of high-quality images. It will provide various benefits compared to existing image formats: significantly smaller size at equivalent subjective quality; fast, parallelizable decoding and encoding configurations; features such as progressive, lossless, animation, and reversible transcoding of existing JPEG; support for high-quality applications including wide gamut, higher resolution/bit depth/dynamic range, and visually lossless coding. Additionally, a royalty-free baseline is an important goal. The JPEG XL architecture is traditional block-transform coding with upgrades to each component. We describe these components and analyze decoded image quality.

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The Burrows-Wheeler Transform (BWT) is a reversible transformation on which are based several text compressors and many other tools used in Bioinformatics and Computational Biology. The BWT is not actually a compressor, but a transformation that performs a context-dependent permutation of the letters of the input text that often create runs of equal letters (clusters) longer than the ones in the original text, usually referred to as the â\u80\u9cclustering effectâ\u80\u9d of BWT. In particular, from a combinatorial point of view, great attention has been given to the case in which the BWT produces the fewest number of clusters (cf. [5,16,21,23],). In this paper we are concerned about the cases when the clustering effect of the BWT is not achieved. For this purpose we introduce a complexity measure that counts the number of equal-letter runs of a word. This measure highlights that there exist many words for which BWT gives an â\u80\u9cun-clustering effectâ\u80\u9d, that is BWT produce a great number of short clusters. More in general we show that the application of BWT to any word at worst doubles the number of equal-letter runs. Moreover, we prove that this bound is tight by exhibiting some families of words where such upper bound is always reached. We also prove that for binary words the case in which the BWT produces the maximal number of clusters is related to the very well known Artin's conjecture on primitive roots. The study of some combinatorial properties underlying this transformation could be useful for improving indexing and compression strategies

Given a connected graph G of m edges and n vertices, we consider the basic problem of listing all the choices of k vertex-disjoint st-paths, for any two input vertices s, t of G and a positive integer k. Our algorithm takes O(m) time per solution, using O(m) space and requiring O(F k (G)) setup time, where F k (G) = O(m min{k, n 2/3 log n, √ m log n}) is the cost of running a max-flow algorithm on G to compute a flow of size k. The proposed techniques are simple and apply to other related listing problems discussed in the paper.

Spiking neural networks with temporal coding schemes process information based on the relative timing of neuronal spikes. In supervised learning tasks, temporal coding allows learning through backpropagation with exact derivatives, and achieves accuracies on par with conventional artificial neural networks. Here we introduce spiking autoencoders with temporal coding and pulses, trained using backpropagation to store and reconstruct images with high fidelity from compact representations. We show that spiking autoencoders with a single layer are able to effectively represent and reconstruct images from the neuromorphically-encoded MNIST and FMNIST datasets. We explore the effect of different spike time target latencies, data noise levels and embedding sizes, as well as the classification performance from the embeddings. The spiking autoencoders achieve results similar to or better than conventional non-spiking autoencoders. We find that inhibition is essential in the functioning of the spiking autoencoders, particularly when the input needs to be memorised for a longer time before the expected output spike times. To reconstruct images with a high target latency, the network learns to accumulate negative evidence and to use the pulses as excitatory triggers for producing the output spikes at the required times. Our results highlight the potential of spiking autoencoders as building blocks for more complex biologically-inspired architectures. We also provide open-source code for the model.

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