Transcranial ultrasound stimulation (TUS) is an emerging non-invasive neuromodulation technique, offering a potential alternative to pharmacological treatments for psychiatric and neurological disorders. While functional analysis has been instrumental in characterizing the TUS effects, understanding its indirect influence across the network remains challenging. Here, we developed a whole-brain model to represent functional changes as measured by fMRI, enabling us to investigate how TUS-induced effects propagate throughout the brain with increasing stimulus intensity. We implemented two mechanisms: one based on anatomical distance and another on broadcasting dynamics, to explore plasticity-driven changes in specific brain regions. Finally, we highlighted the role of higher-order functional interactions in localizing spatial effects of off-line TUS at two target areas-the right thalamus and inferior frontal cortex-revealing distinct patterns of functional reorganization. This work lays the foundation for mechanistic insights and predictive models of TUS, advancing its potential clinical applications.

A key feature of information theory is its universality, as it can be applied to study a broad variety of complex systems. However, many information-theoretic measures can vary significantly even across systems with similar properties, making normalisation techniques essential for allowing meaningful comparisons across datasets. Inspired by the framework of Partial Information Decomposition (PID), here we introduce Null Models for Information Theory (NuMIT), a null model-based non-linear normalisation procedure which improves upon standard entropy-based normalisation approaches and overcomes their limitations. We provide practical implementations of the technique for systems with different statistics, and showcase the method on synthetic models and on human neuroimaging data. Our results demonstrate that NuMIT provides a robust and reliable tool to characterise complex systems of interest, allowing cross-dataset comparisons and providing a meaningful significance test for PID analyses.

Cognitive processes usually take place at a macroscopic scale in systems characterised by emergent properties, which make the whole ‘more than the sum of its parts.’ While recent proposals have provided quantitative, information-theoretic metrics to detect emergence in time series data, it is often highly non-trivial to identify the relevant macroscopic variables a priori. In this paper we leverage recent advances in representation learning and differentiable information estimators to put forward a data-driven method to find emergent variables. The proposed method successfully detects emergent variables and recovers the ground-truth emergence values in a synthetic dataset. Furthermore, we show the method can be extended to learn multiple independent features, extracting a diverse set of emergent quantities. We finally show that a modified method scales to real experimental data from primate brain activity, paving the ground for future analyses uncovering the emergent structure of cognitive representations in biological and artificial intelligence systems.

Striking progress has been made in understanding cognition by analyzing how the brain is engaged in different modes of information processing. For instance, so-called synergistic information (information encoded by a set of neurons but not by any subset) plays a key role in areas of the human brain linked with complex cognition. However, two questions remain unanswered: (a) how and why a cognitive system can become highly synergistic; and (b) how informational states map onto artificial neural networks in various learning modes. Here we employ an information-decomposition framework to investigate neural networks performing cognitive tasks. Our results show that synergy increases as networks learn multiple diverse tasks, and that in tasks requiring integration of multiple sources, performance critically relies on synergistic neurons. Overall, our results suggest that synergy is used to combine information from multiple modalities-and more generally for flexible and efficient learning. These findings reveal new ways of investigating how and why learning systems employ specific information-processing strategies, and support the principle that the capacity for general-purpose learning critically relies on the system's information dynamics.

A topic of growing interest in computational neuroscience is the discovery of fundamental principles underlying global dynamics and the self-organization of the brain. In particular, the notion that the brain operates near criticality has gained considerable support, and recent work has shown that the dynamics of different brain states may be modeled by pairwise maximum entropy Ising models at various distances from a phase transition, i.e., from criticality. Here we aim to characterize two brain states (psychedelics-induced and placebo) as captured by functional magnetic resonance imaging (fMRI), with features derived from the Ising spin model formalism (system temperature, critical point, susceptibility) and from algorithmic complexity. We hypothesized, along the lines of the entropic brain hypothesis, that psychedelics drive brain dynamics into a more disordered state at a higher Ising temperature and increased complexity. We analyze resting state blood-oxygen-level-dependent (BOLD) fMRI data collected in an earlier study from fifteen subjects in a control condition (placebo) and during ingestion of lysergic acid diethylamide (LSD). Working with the automated anatomical labeling (AAL) brain parcellation, we first create "archetype" Ising models representative of the entire dataset (global) and of the data in each condition. Remarkably, we find that such archetypes exhibit a strong correlation with an average structural connectome template obtained from dMRI (r = 0.6). We compare the archetypes from the two conditions and find that the Ising connectivity in the LSD condition is lower than in the placebo one, especially in homotopic links (interhemispheric connectivity), reflecting a significant decrease of homotopic functional connectivity in the LSD condition. The global archetype is then personalized for each individual and condition by adjusting the system temperature. The resulting temperatures are all near but above the critical point of the model in the paramagnetic (disordered) phase. The individualized Ising temperatures are higher in the LSD condition than in the placebo condition (p = 9 × 10-5). Next, we estimate the Lempel-Ziv-Welch (LZW) complexity of the binarized BOLD data and the synthetic data generated with the individualized model using the Metropolis algorithm for each participant and condition. The LZW complexity computed from experimental data reveals a weak statistical relationship with condition (p = 0.04 one-tailed Wilcoxon test) and none with Ising temperature (r(13) = 0.13, p = 0.65), presumably because of the limited length of the BOLD time series. Similarly, we explore complexity using the block decomposition method (BDM), a more advanced method for estimating algorithmic complexity. The BDM complexity of the experimental data displays a significant correlation with Ising temperature (r(13) = 0.56, p = 0.03) and a weak but significant correlation with condition (p = 0.04, one-tailed Wilcoxon test). This study suggests that the effects of LSD increase the complexity of brain dynamics by loosening interhemispheric connectivity-especially homotopic links. In agreement with earlier work using the Ising formalism with BOLD data, we find the brain state in the placebo condition is already above the critical point, with LSD resulting in a shift further away from criticality into a more disordered state.

The human brain generates a rich repertoire of spatio-temporal activity patterns, which support a wide variety of motor and cognitive functions. These patterns of activity change with age in a multi-factorial manner. One of these factors is the variations in the brain's connectomics that occurs along the lifespan. However, the precise relationship between high-order functional interactions and connnectomics, as well as their variations with age are largely unknown, in part due to the absence of mechanistic models that can efficiently map brain connnectomics to functional connectivity in aging. To investigate this issue, we have built a neurobiologically-realistic whole-brain computational model using both anatomical and functional MRI data from 161 participants ranging from 10 to 80 years old. We show that the differences in high-order functional interactions between age groups can be largely explained by variations in the connectome. Based on this finding, we propose a simple neurodegeneration model that is representative of normal physiological aging. As such, when applied to connectomes of young participant it reproduces the age-variations that occur in the high-order structure of the functional data. Overall, these results begin to disentangle the mechanisms by which structural changes in the connectome lead to functional differences in the ageing brain. Our model can also serve as a starting point for modeling more complex forms of pathological ageing or cognitive deficits.

Learning and compression are driven by the common aim of identifying and exploiting statistical regularities in data, which opens the door for fertile collaboration between these areas. A promising group of compression techniques for learning scenarios is normalised maximum likelihood (NML) coding, which provides strong guarantees for compression of small datasets — in contrast with more popular estimators whose guarantees hold only in the asymptotic limit. Here we consider a NMLbased decision strategy for supervised classification problems, and show that it attains heuristic PAC learning when applied to a wide variety of models. Furthermore, we show that the misclassification rate of our method is upper bounded by the maximal leakage, a recently proposed metric to quantify the potential of data leakage in privacy-sensitive scenarios.

The broad concept of emergence is instrumental in various of the most challenging open scientific questions-yet, few quantitative theories of what constitutes emergent phenomena have been proposed. This article introduces a formal theory of causal emergence in multivariate systems, which studies the relationship between the dynamics of parts of a system and macroscopic features of interest. Our theory provides a quantitative definition of downward causation, and introduces a complementary modality of emergent behaviour-which we refer to as causal decoupling. Moreover, the theory allows practical criteria that can be efficiently calculated in large systems, making our framework applicable in a range of scenarios of practical interest. We illustrate our findings in a number of case studies, including Conway's Game of Life, Reynolds' flocking model, and neural activity as measured by electrocorticography.

Perfect data privacy seems to be in fundamental opposition to the economical and scientific opportunities related to extensive data exchange. This paper defies this intuition by developing the principle of synergistic disclosure, in which collective properties of datasets are revealed without compromising the privacy of individual data samples. We study the properties of optimal strategies/mappings on finite as well as asymptotically large datasets, and discuss its fundamental limits defined as the synergistic disclosure capacity. Furthermore, we present explicit analytical expressions for the synergistic disclosure capacity of large datasets in various scenarios, and present cases in which our approach can disclose most of the information of interest. We finally discuss suboptimal schemes to provide sample privacy guarantees to large datasets at a reduced computational cost.

The growing use of aerial user equipments (UEs) in various applications requires ubiquitous and reliable connectivity for safe control and data exchange between these devices and ground stations. Key questions that need to be addressed when planning the deployment of aerial UEs are whether the cellular network is a suitable candidate for enabling such connectivity and how the inclusion of aerial UEs might impact the overall network efficiency. This paper provides an in-depth analysis of user and network-level performance of a cellular network that serves both unmanned aerial vehicles (UAVs) and ground users in the downlink. Our results show that the favorable propagation conditions that UAVs enjoy due to their height often backfire on them, as the increased load-dependent co-channel interference received from neighboring ground base stations (BSs) is not compensated by the improved signal strength. When compared with a ground user in an urban area, our analysis shows that a UAV flying at 100 m can experience a throughput decrease of a factor 10 and a coverage drop from 76% to 30%. Motivated by these findings, we develop UAV and network-based solutions to enable an adequate integration of UAVs into cellular networks. In particular, we show that an optimal tilting of the UAV antenna can increase the coverage from 23% to 89% and throughput from 3.5 to 5.8 b/s/Hz, outperforming ground UEs. Furthermore, our findings reveal that depending on the UAV altitude and its antenna configuration, the aerial user performance can scale with respect to the network density better than that of a ground user. Finally, our results show that network densification and the use of microcells limit the UAV performance. Although UAV usage has the potential to increase the area spectral efficiency (ASE) of cellular networks with a moderate number of cells, they might hamper the development of future ultradense networks.

This paper studies the feasibility of supporting drone operations using existent cellular infrastructure. We propose an analytical framework that includes the effects of base station (BS) height and antenna radiation pattern, drone antenna directivity and various propagation environments. With this framework, we derive an exact expression for the coverage probability of ground and drone users through a practical cell association strategy. Our results show that a carefully designed network can control the radiated interference that is received by the drones, and therefore guarantees a satisfactory quality of service. Moreover, as the network density grows the increasing level of interference can be partially managed by lowering the drone flying altitude. However, even at optimal conditions the drone coverage performance converges to zero considerably fast, suggesting that ultra-dense networks might be poor candidates for serving aerial users.

Aerial base stations are a promising technology to increase the capabilities of existing communication networks. However, existing analytical frameworks do not sufficiently characterize the impact of ground interferers on aerial base stations. In order to address this issue, we model the effect of interference coming from coexisting ground networks on the aerial link, which could be the uplink of an aerial cell served by a drone base station. By considering a Poisson field of ground interferers, we characterize aggregate interference experienced by the drone. This result includes the effect of drone antenna pattern, the height-dependent shadowing, and various types of environment. We show that benefits a drone obtains from a better line-of-sight (LoS) at high altitudes is counteracted by a high vulnerability to the interference coming from ground. However, by deriving link coverage probability and transmission rate we show that a drone base station is still a promising technology if the overall system is properly dimensioned according to given density and transmission power of interferers. Particularly, our results illustrate how benefits of such network is maximized by defining the optimal drone altitude and signal-to-interference (SIR) requirement.

The use of unmanned aerial vehicles (UAVs) serving as aerial base stations is expected to become predominant in the next decade. However, in order, for this technology, to unfold its full potential, it is necessary to develop a fundamental understanding of the distinctive features of air-to-ground (A2G) links. As a contribution in this direction, this paper proposes a generic framework for the analysis and optimization of the A2G systems. In contrast to the existing literature, this framework incorporates both height-dependent path loss exponent and small-scale fading, and unifies a widely used ground-to-ground channel model with that of A2G for the analysis of large-scale wireless networks. We derive analytical expressions for the optimal UAV height that minimizes the outage probability of an arbitrary A2G link. Moreover, our framework allows us to derive a height-dependent closed-form expression for the outage probability of an A2G cooperative communication network. Our results suggest that the optimal location of the UAVs with respect to the ground nodes does not change by the inclusion of ground relays. This enables interesting insights about the deployment of future A2G networks, as the system reliability could be adjusted dynamically by adding relaying nodes without requiring changes in the position of the corresponding UAVs. Finally, to optimize the network for multiple destinations, we derive an optimum altitude of the UAV for maximum coverage region by guaranteeing a minimum outage performance over the region.

The growing demand for wireless connectivity has turned bandwidth into a scarce resource that has to be carefully managed and fairly distributed to users. However, the variability of the wireless channel can severely degrade the service received by each user. The Double Relay Communication Protocol (DRCP) [1] is a transmission scheme that addresses these problems by exploiting spatial diversity to enhance the fairness of the system without requiring any additional infrastructure (i.e relay nodes or a backhaul connection). Although DRCP has originally been proposed to work without channel state information at the transmitter (CSIT), in this paper we study how the performance of DRCP can be further improved through power control when CSIT is available. Our approach provides the highest fairness and the largest minimum spectral efficiency for most conditions compared to other studied baseline approaches.

The use of drone base stations to provide wireless connectivity for ground terminals is becoming a promising part of future technologies. The design of such aerial networks is however different compared to cellular 2D networks, as antennas from the drones are looking down, and the channel model becomes height-dependent. In this paper, we study the effect of antenna patterns and height-dependent shadowing. We consider a random network topology to capture the effect of dynamic changes of the flying base stations. First we characterize the aggregate interference imposed by the co-channel neighboring drones. Then we derive the link coverage probability between a ground user and its associated drone base station. The result is used to obtain the optimum system parameters in terms of drones antenna beamwidth, density and altitude. We also derive the average LoS probability of the associated drone and show that it is a good approximation and simplification of the coverage probability in low altitudes up to 500 m according to the required signal-to-interference-plus-noise ratio (SINR).

The densification of wireless networks that contend for a shared medium, demands improved MAC solutions that can reduce the energy cost of packet collisions. In this paper we analyze a novel in-band full duplex collision and interference detection scheme for dense networks, studying the energy savings that it can bring with respect to the performance of half duplex communications. Under a high external interference scenario, results show that the proposed full duplex scheme is more energy-efficient than half duplex transmissions for any network density. When the interference is low, the full duplex scheme provides energy gains when the number of contending devices is above a critical value. Expressions for calculating this critical number of devices are provided, showing that it is smaller when the likelihood of collisions increases. In the studied cases, results show the energy savings grow exponentially with the density of the network.

Aerial communication platforms have been recently recognized as an effective solution to provide wireless access to terrestrial users, which promise to increase reliability and throughput thanks to their superior coverage capabilities. In this paper, we explore the impact of the height of an Unmanned Aerial Vehicle (UAV) on the area over which it can provide wireless service. We investigate the problem by characterizing the coverage area for a target outage probability, showing that for the case of Rician fading there exist a unique optimum height that maximizes the coverage area. The optimum UAV height guarantees a beneficial trade-off between path loss and fading, which vary as function of distance and the elevation angle with respect to the ground terminals. Moreover, a closed-form approximated solution is provided, which is valid for any functional dependency between the elevation angle and the Rician factor.

The ability to efficiently assess and track the utility of each sensor signal is crucial to reduce the energy consumption in a wireless sensor network (WSN), e.g., by putting the sensors with low utility to sleep. Methods to track the sensor signal utility have been described for several multichannel signal estimation methods. For linear minimum mean squared error (LMMSE) estimation, the utility of a sensor signal is defined as the predicted increase in the minimum mean squared error when the sensor would be shut down. However, rather than making such a binary decision, more flexible energy-saving methods could be considered where a sensor changes internal parameters such as, e.g., the number of bits per sample, which results in noise injection in the transmitted sensor signal. We propose a generalization of the original definition of sensor signal utility to include this effect, and we show that it can be efficiently computed and tracked at hardly any computational cost compared to the already available LMMSE estimator. In addition, we illustrate how it can be used to assign a number of bits to each sensor with a greedy approach. Simulation results show that a greedy assignment based on the proposed generalized utility leads to improved results compared to the original utility measure.

Retransmissions due to decoding errors have a big impact on the energy budget of low-power wireless communication devices, which can be reduced by using hybrid automatic repeat request (HARQ) techniques. Nevertheless, this reduction comes at the cost of extra energy consumption introduced by the added computational load. No complete analysis of the tradeoff between retransmissions reduction and baseband consumption of low-power communications over fading channels has been reported so far. In this paper, we study the energy efficiency achievable by HARQ schemes when the code rate of the error-correcting code is optimized. For this purpose, we develop an energy consumption model that focuses on simple HARQ (S-HARQ) and Chase combining (HARQ-CC) transmissions, which are studied under fast-fading and block-fading scenarios with Nakagami-m fading. The retransmission statistics are analyzed, and expressions for the expected number of transmission trials are derived. Using this framework, it is shown that transmission schemes with high diversity gain are the most efficient choice for long range transmissions, which in our case correspond to HARQ-CC and codes with low code rate. On the other hand, schemes with good multiplexing capabilities are optimal for short link distances, which in our analysis correspond to S-HARQ and high code rates. It is also shown that HARQ-CC can effectively extend the transmission range of a low-power communication device.

Saving energy is vital in real-world underwater acoustic networks, since a lot of energy is spent to transmit acoustic waves and battery replacement is highly undesirable. In this paper, we study how the energy consumption of underwater acoustic communications can be reduced in order to extend the lifetime of underwater sensor nodes. We analyze the effect of selecting the best frequency within a given operating range for various link distances. We also consider the use of error correcting codes, and optimize the code rate and the signal to noise ratio for each link distance and frequency. Our results show that energy consumption can be greatly reduced by optimizing code rate. In particular, it is shown that uncoded transmissions can be more energy efficient for a considerable range of link distances than fixed rate convolutional codes which are popular in commercial devices. Results also show that the optimal number of average retransmissions is very small (less than one) for all studied link distances. This is an encouraging result, as acoustic communication channels impose much longer delays than RF channels and therefore schemes which require several retransmissions impose unfeasible delay constrains.

Although multiple-input multiple-output (MIMO) techniques provide attractive tools for reducing the energy consumption of wireless communications, many of them require transmitter-side channel state information (TCSI). While the effect of the TCSI on the MIMO channel capacity is well known, its impact on the achievable energy-efficiency is still not well determined. In this paper, we address this issue by studying the energy consumption of the singular value decomposition (SVD), beamforming, zero forcing and generalized Alamouti MIMO schemes. Although TCSI provides important savings in long-range communications, our results suggest that it is not critical when transmitting over short link distances. Results also show that large antenna arrays using schemes with a large diversity gain are energy-optimal for transmitting data over long transmission distances, while small arrays using schemes with a large multiplexing gain are more energy-efficient for performing short-range communications.

In this paper we analyze the energy efficiency of multi-hop communication in wireless sensor networks when packet transmissions between adjacent nodes employ Hybrid ARQ (HARQ) with Chase combining (CC) technique under Rayleigh block-fading channels. The energy analysis can be constrained by either a target outage probability or end-to-end delay. Closed form expressions for the end-to-end outage probability and energy consumption are derived. Results show how to determine the optimal number of retransmissions of the HARQ-CC scheme for a given number of relays between the source and destination nodes, in order to achieve the target constraints. The impact of the path loss environment conditions on the overall energy consumption is also investigated. Finally, we analyze the energy consumption assuming a visual sensor network application with multiple cameras and different outage and delay constraints.

Error correcting coding is a well-known technique for reducing the required signal-to-noise ratio (SNR) needed to attain a given bit error-rate. Nevertheless, this reduction comes at the cost of extra energy consumption introduced by the baseband processing required for encoding and decoding the data. No complete analysis of the trade-off between coding gain and baseband consumption of communications over wireless channels has been reported so far. In this paper, we study the energy-consumption of BCH codes with various code rates over AWGN and Rayleigh fading channels. Our results show that codes with low code rate are optimal for performing long-range communications, while is better to use less coding redundancy when the transmission distance is short. Our results also show that the transmission range of a low-power communication device can be increased up to 25% for AWGN channels and up to 300% for Rayleigh fading channels by using an optimized BCH code.

Coordination of base stations is a promising technique for reducing inter‐cell interference in next‐generation cellular systems. For the downlink of such systems, the authors study the degradation of zero‐forcing precoded transmissions caused by imperfect channel estimation and channel variation over time. They derive exact expressions for the mean power of the desired signal received by an arbitrary user and of the interference caused by the mismatched precoder. By using these expressions, they show that for attaining a given signal‐to‐interference power ratio (SIR) these systems are limited by a maximum feedback delay of updated channel state information. Finally, they present a procedure to calculate the maximum tolerable feedback delay and to determine the separation between the non‐precoded pilot symbols for guaranteeing a desired SIR.

The multiple‐input multiple‐output singular value decomposition (MIMO SVD) modulation is an efficient way of sending data through a multi‐antenna communications link in which the transmitter has knowledge of the channel state. Despite its importance, no simple formula for its symbol error rate (SER) has been found, and hence no intuitive characterisation of the quality of this technique for data transmission is available at the present. In this study, the authors present a method for approximating the statistics of each eigenchannel of MIMO SVD using the Nakagami‐ m fading model. Using the proposed method, it is seen that the SER of the entire MIMO SVD link can be approximated by the average of the SER of Nakagami‐ m channels. The expression found is simple and yet accurate. This leads to characterise the eigenchannels of N × N MIMO channels with N larger than 14, showing that the smallest eigenchannel distributes as a Rayleigh channel, the next four eigenchannels closely distributes as Nakagami‐ m channels with m = 4, 9, 25 and 36, and the N − 5 remaining eigenchannels have statistics similar to an additive white Gaussian noise (AWGN) channel within 1 dB signal‐to‐noise ratio. It is also shown that 75% of the total mean power gain of the MIMO SVD channel goes to the top third of all the eigenchannels.

Multiple-input multiple-output (MIMO) techniques can be used for reducing the energy consumption of wireless communications. Although some research has been reported on this topic, the rules by which the MIMO physical layer parameters should be chosen in order to achieve energy efficiency have not yet been formally established. In this paper, we analyze the case of MIMO singular value decomposition (SVD) technique. We present a model for the mean energy consumption of a MIMO SVD system per data bit transferred without error. We find that, for a given number of eigenchannels used with equal power allocation, exists a single optimal radiation power level at which the mean energy consumption is minimized. We also find that beamforming (only the best eigenchannel is used) is optimal in the energy consumption sense for long transmission distances, while the optimal number of eigenchannels to be used grows as transmission distance shortens. Using all the eigenchannels is optimal only for very short transmission distances.

It is commonly assumed that the energy consumption of wireless communications is minimized when low-order modulations such as BPSK are used. Nevertheless, the literature provides some evidence that low-order modulations are suboptimal for short transmission distances. A thorough analysis on how the modulation scheme and transmission power must be chosen as a function of distance in order to achieve energy-efficient communications over fading channels has not been reported yet. In this paper we provide this analysis by presenting a model that determines the energy consumed per payload bit transferred without error over correlated or uncorrelated random channels. We find that each modulation scheme has a single optimal signal- to-noise ratio (SNR) at which the energy consumption is minimized. We also find that if all modulations are operated at their optimal SNR, BPSK and QPSK are the optimal choices for long transmission distances, but as the transmission distance shortens the optimal modulation size grows to 16-QAM and even to 64- QAM. This result leads to showing that for short-range communications the lifetime of a typical low-power transceiver can be increased by up to 600% by selecting the optimal constellation rather than BPSK.

It is commonly assumed that the energy consumption of wireless communications is minimized when low-order modulations such as BPSK are used. Nevertheless, the literature provides some evidence that low-order modulations are suboptimal for short transmission distances. No complete analysis on how the modulation size and transmission power must be chosen in order to achieve energy-efficient communications over fading channels has been reported so far. In this paper we provide this analysis by presenting a model that determines the energy consumed per payload bit transferred without error over fading channels of various statistics. We find that each modulation scheme has a single optimal signal-to-noise ratio (SNR) at which the energy consumption is minimized. The optimal SNR and the minimal energy consumption are larger for channels with less favorable error statistics. We also find that, if each modulations is operated at its optimal SNR, BPSK and QPSK are the optimal choices for long transmission distances, but as the transmission distance shortens the optimal modulation size grows to 16-QAM and even to 64-QAM. This result leads to showing that for short-range communications the lifetime of a typical low-power transceiver can be up to 500% longer by selecting the optimal constellation instead of BPSK.