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There has recently been an explosion of interest in how "higher-order" structures emerge in complex systems. This "emergent" organization has been found in a variety of natural and artificial systems, although at present the field lacks a unified understanding of what the consequences of higher-order synergies and redundancies are for systems. Typical research treat the presence (or absence) of synergistic information as a dependent variable and report changes in the level of synergy in response to some change in the system. Here, we attempt to flip the script: rather than treating higher-order information as a dependent variable, we use evolutionary optimization to evolve boolean networks with significant higher-order redundancies, synergies, or statistical complexity. We then analyse these evolved populations of networks using established tools for characterizing discrete dynamics: the number of attractors, average transient length, and Derrida coefficient. We also assess the capacity of the systems to integrate information. We find that high-synergy systems are unstable and chaotic, but with a high capacity to integrate information. In contrast, evolved redundant systems are extremely stable, but have negligible capacity to integrate information. Finally, the complex systems that balance integration and segregation (known as Tononi-Sporns-Edelman complexity) show features of both chaosticity and stability, with a greater capacity to integrate information than the redundant systems while being more stable than the random and synergistic systems. We conclude that there may be a fundamental trade-off between the robustness of a systems dynamics and its capacity to integrate information (which inherently requires flexibility and sensitivity), and that certain kinds of complexity naturally balance this trade-off.

The computational demands of modern AI have spurred interest in optical neural networks (ONNs) which offer the potential benefits of increased speed and lower power consumption. However, current ONNs face various challenges,most significantly a limited calculation precision (typically around 4 bits) and the requirement for high-resolution signal format converters (digital-to-analogue conversions (DACs) and analogue-to-digital conversions (ADCs)). These challenges are inherent to their analog computing nature and pose significant obstacles in practical implementation. Here, we propose a digital-analog hybrid optical computing architecture for ONNs, which utilizes digital optical inputs in the form of binary words. By introducing the logic levels and decisions based on thresholding, the calculation precision can be significantly enhanced. The DACs for input data can be removed and the resolution of the ADCs can be greatly reduced. This can increase the operating speed at a high calculation precision and facilitate the compatibility with microelectronics. To validate our approach, we have fabricated a proof-of-concept photonic chip and built up a hybrid optical processor (HOP) system for neural network applications. We have demonstrated an unprecedented 16-bit calculation precision for high-definition image processing, with a pixel error rate (PER) as low as $1.8\times10^{-3}$ at an signal-to-noise ratio (SNR) of 18.2 dB. We have also implemented a convolutional neural network for handwritten digit recognition that shows the same accuracy as the one achieved by a desktop computer. The concept of the digital-analog hybrid optical computing architecture offers a methodology that could potentially be applied to various ONN implementations and may intrigue new research into efficient and accurate domain-specific optical computing architectures for neural networks.

Since the start of the operational use of ensemble prediction systems, ensemble-based probabilistic forecasting has become the most advanced approach in weather prediction. However, despite the persistent development of the last three decades, ensemble forecasts still often suffer from the lack of calibration and might exhibit systematic bias, which calls for some form of statistical post-processing. Nowadays, one can choose from a large variety of post-processing approaches, where parametric methods provide full predictive distributions of the investigated weather quantity. Parameter estimation in these models is based on training data consisting of past forecast-observation pairs, thus post-processed forecasts are usually available only at those locations where training data are accessible. We propose a general clustering-based interpolation technique of extending calibrated predictive distributions from observation stations to any location in the ensemble domain where there are ensemble forecasts at hand. Focusing on the ensemble model output statistics (EMOS) post-processing technique, in a case study based on wind speed ensemble forecasts of the European Centre for Medium-Range Weather Forecasts, we demonstrate the predictive performance of various versions of the suggested method and show its superiority over the regionally estimated and interpolated EMOS models and the raw ensemble forecasts as well.

This simulation study evaluates the effectiveness of multiple imputation (MI) techniques for multilevel data. It compares the performance of traditional Multiple Imputation by Chained Equations (MICE) with tree-based methods such as Chained Random Forests with Predictive Mean Matching and Extreme Gradient Boosting. Adapted versions that include dummy variables for cluster membership are also included for the tree-based methods. Methods are evaluated for coefficient estimation bias, statistical power, and type I error rates on simulated hierarchical data with different cluster sizes (25 and 50) and levels of missingness (10\% and 50\%). Coefficients are estimated using random intercept and random slope models. The results show that while MICE is preferred for accurate rejection rates, Extreme Gradient Boosting is advantageous for reducing bias. Furthermore, the study finds that bias levels are similar across different cluster sizes, but rejection rates tend to be less favorable with fewer clusters (lower power, higher type I error). In addition, the inclusion of cluster dummies in tree-based methods improves estimation for Level 1 variables, but is less effective for Level 2 variables. When data become too complex and MICE is too slow, extreme gradient boosting is a good alternative for hierarchical data. Keywords: Multiple imputation; multi-level data; MICE; missRanger; mixgb

Open sets are central to mathematics, especially analysis and topology, in ways few notions are. In most, if not all, computational approaches to mathematics, open sets are only studied indirectly via their 'codes' or 'representations'. In this paper, we study how hard it is to compute, given an arbitrary open set of reals, the most common representation, i.e. a countable set of open intervals. We work in Kleene's higher-order computability theory, which was historically based on the S1-S9 schemes and which now has an intuitive lambda calculus formulation due to the authors. We establish many computational equivalences between on one hand the 'structure' functional that converts open sets to the aforementioned representation, and on the other hand functionals arising from mainstream mathematics, like basic properties of semi-continuous functions, the Urysohn lemma, and the Tietze extension theorem. We also compare these functionals to known operations on regulated and bounded variation functions, and the Lebesgue measure restricted to closed sets. We obtain a number of natural computational equivalences for the latter involving theorems from mainstream mathematics.

While Product of Exponentials (POE) formula has been gaining increasing popularity in modeling the kinematics of a serial-link robot, the Denavit-Hartenberg (D-H) notation is still the most widely used due to its intuitive and concise geometric interpretation of the robot. This paper has developed an analytical solution to automatically convert a POE model into a D-H model for a robot with revolute, prismatic, and helical joints, which are the complete set of three basic one degree of freedom lower pair joints for constructing a serial-link robot. The conversion algorithm developed can be used in applications such as calibration where it is necessary to convert the D-H model to the POE model for identification and then back to the D-H model for compensation. The equivalence of the two models proved in this paper also benefits the analysis of the identifiability of the kinematic parameters. It is found that the maximum number of identifiable parameters in a general POE model is 5h+4r +2t +n+6 where h, r, t, and n stand for the number of helical, revolute, prismatic, and general joints, respectively. It is also suggested that the identifiability of the base frame and the tool frame in the D-H model is restricted rather than the arbitrary six parameters as assumed previously.

Remotely sensed data are dominated by mixed Land Use and Land Cover (LULC) types. Spectral unmixing (SU) is a key technique that disentangles mixed pixels into constituent LULC types and their abundance fractions. While existing studies on Deep Learning (DL) for SU typically focus on single time-step hyperspectral (HS) or multispectral (MS) data, our work pioneers SU using MODIS MS time series, addressing missing data with end-to-end DL models. Our approach enhances a Long-Short Term Memory (LSTM)-based model by incorporating geographic, topographic (geo-topographic), and climatic ancillary information. Notably, our method eliminates the need for explicit endmember extraction, instead learning the input-output relationship between mixed spectra and LULC abundances through supervised learning. Experimental results demonstrate that integrating spectral-temporal input data with geo-topographic and climatic information significantly improves the estimation of LULC abundances in mixed pixels. To facilitate this study, we curated a novel labeled dataset for Andalusia (Spain) with monthly MODIS multispectral time series at 460m resolution for 2013. Named Andalusia MultiSpectral MultiTemporal Unmixing (Andalusia-MSMTU), this dataset provides pixel-level annotations of LULC abundances along with ancillary information. The dataset (//zenodo.org/records/7752348) and code (//github.com/jrodriguezortega/MSMTU) are available to the public.

Bayesian sampling is an important task in statistics and machine learning. Over the past decade, many ensemble-type sampling methods have been proposed. In contrast to the classical Markov chain Monte Carlo methods, these new methods deploy a large number of interactive samples, and the communication between these samples is crucial in speeding up the convergence. To justify the validity of these sampling strategies, the concept of interacting particles naturally calls for the mean-field theory. The theory establishes a correspondence between particle interactions encoded in a set of coupled ODEs/SDEs and a PDE that characterizes the evolution of the underlying distribution. This bridges numerical algorithms with the PDE theory used to show convergence in time. Many mathematical machineries are developed to provide the mean-field analysis, and we showcase two such examples: The coupling method and the compactness argument built upon the martingale strategy. The former has been deployed to show the convergence of ensemble Kalman sampler and ensemble Kalman inversion, and the latter will be shown to be immensely powerful in proving the validity of the Vlasov-Boltzmann simulator.

Languages have long been described according to their perceived rhythmic attributes. The associated typologies are of interest in psycholinguistics as they partly predict newborns' abilities to discriminate between languages and provide insights into how adult listeners process non-native languages. Despite the relative success of rhythm metrics in supporting the existence of linguistic rhythmic classes, quantitative studies have yet to capture the full complexity of temporal regularities associated with speech rhythm. We argue that deep learning offers a powerful pattern-recognition approach to advance the characterization of the acoustic bases of speech rhythm. To explore this hypothesis, we trained a medium-sized recurrent neural network on a language identification task over a large database of speech recordings in 21 languages. The network had access to the amplitude envelopes and a variable identifying the voiced segments, assuming that this signal would poorly convey phonetic information but preserve prosodic features. The network was able to identify the language of 10-second recordings in 40% of the cases, and the language was in the top-3 guesses in two-thirds of the cases. Visualization methods show that representations built from the network activations are consistent with speech rhythm typologies, although the resulting maps are more complex than two separated clusters between stress and syllable-timed languages. We further analyzed the model by identifying correlations between network activations and known speech rhythm metrics. The findings illustrate the potential of deep learning tools to advance our understanding of speech rhythm through the identification and exploration of linguistically relevant acoustic feature spaces.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.