arXiv subjects

Claudius Gros

Publications and source records attributed to Claudius Gros.

At least 37 records · Page 2Linked to original sources

arXiv2021

Nonlinear Dendritic Coincidence Detection for Supervised Learning

Cortical pyramidal neurons have a complex dendritic anatomy, whose function is an active research field. In particular, the segregation between its soma and the apical dendritic tree is believed to play an active role in processing feed-forward sensory information and top-down or feedback signals. In this work, we use a simple two-compartment model accounting for the nonlinear interactions between basal and apical input streams and show that standard unsupervised Hebbian learning rules in the basal compartment allow the neuron to align the feed-forward basal input with the top-down target signal received by the apical compartment. We show that this learning process, termed coincidence detection, is robust against strong distractions in the basal input space and demonstrate its effectiveness in a linear classification task.

q-bio.NC↗

arXiv2021

A devil's advocate view on 'self-organized' brain criticality

Stationarity of the constituents of the body and of its functionalities is a basic requirement for life, being equivalent to survival in first place. Assuming that the resting state activity of the brain serves essential functionalities, stationarity entails that the dynamics of the brain needs to be regulated on a time-averaged basis. The combination of recurrent and driving external inputs must therefore lead to a non-trivial stationary neural activity, a condition which is fulfilled for afferent signals of varying strengths only close to criticality. In this view, the benefits of working vicinity of a second-order phase transition, such as signal enhancements, are not the underlying evolutionary drivers, but side effects of the requirement to keep the brain functional in first place. It is hence more appropriate to use the term 'self-regulated' in this context, instead of 'self-organized'.

q-bio.NC↗

arXiv2021

Incentives for accelerating the production of Covid-19 vaccines in the presence of adjustment costs

Delays in the availability of vaccines are costly as the pandemic continues. However, in the presence of adjustment costs firms have an incentive to increase production capacity only gradually. The existing contracts specify only a fixed quantity to be supplied over a certain period and thus provide no incentive for an accelerated buildup in capacity. A high price does not change this. The optimal contract would specify a decreasing price schedule over time which can replicate the social optimum.

econ.TH↗

arXiv2021

Investment vs. reward in a competitive knapsack problem

Natural selection drives species to develop brains, with sizes that increase with the complexity of the tasks to be tackled. Our goal is to investigate the balance between the metabolic costs of larger brains compared to the advantage they provide in solving general and combinatorial problems. Defining advantage as the performance relative to competitors, a two-player game based on the knapsack problem is used. Within this framework, two opponents compete over shared resources, with the goal of collecting more resources than the opponent. Neural nets of varying sizes are trained using a variant of the AlphaGo Zero algorithm. A surprisingly simple relation, $N_A/(N_A+N_B)$, is found for the relative win rate of a net with $N_A$ neurons against one with $N_B$. Success increases linearly with investments in additional resources when the networks sizes are very different, i.e. when $N_A \ll N_B$, with returns diminishing when both networks become comparable in size.

cs.AI↗

arXiv2021

Local homeostatic regulation of the spectral radius of echo-state networks

Recurrent cortical networks provide reservoirs of states that are thought to play a crucial role for sequential information processing in the brain. However, classical reservoir computing requires manual adjustments of global network parameters, particularly of the spectral radius of the recurrent synaptic weight matrix. It is hence not clear if the spectral radius is accessible to biological neural networks. Using random matrix theory, we show that the spectral radius is related to local properties of the neuronal dynamics whenever the overall dynamical state is only weakly correlated. This result allows us to introduce two local homeostatic synaptic scaling mechanisms, termed flow control and variance control, that implicitly drive the spectral radius towards the desired value under working conditions. We demonstrate the effectiveness of the two adaptation mechanisms under different external input protocols and the network performance after adaptation by training the network to perform a time-delayed XOR operation on binary sequences. As our main result, we found that flow control reliably regulates the spectral radius for different types of input statistics. Precise tuning is however negatively affected when interneural correlations are substantial. Furthermore, we found a consistent task performance over a wide range of input strengths/variances. Variance control did however not yield the desired spectral radii with the same precision, being less consistent across different input strengths. Given the effectiveness and remarkably simple mathematical form of flow control, we conclude that self-consistent local control of the spectral radius via an implicit adaptation scheme is an interesting and biological plausible alternative to conventional methods using setpoint homeostatic feedback controls of neural firing.

q-bio.NC↗

arXiv2021

Collective strategy condensation: When envy splits societies

Human societies are characterized, besides others, by three constituent features. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option with others. (C) People care how they are doing relatively to others. The latter trait, the propensity to compare one's own success with that of others, expresses itself as envy. It is shown that the combination of (A)-(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper class agents do not condense, following individualist pure strategies. Model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.

physics.soc-ph↗

arXiv2021

Containment efficiency and control strategies for the Corona pandemic costs

The rapid spread of the Coronavirus (COVID-19) confronts policy makers with the problem of measuring the effectiveness of containment strategies, balancing public health considerations with the economic costs of social distancing measures. We introduce a modified epidemic model that we name the controlled-SIR model, in which the disease reproduction rate evolves dynamically in response to political and societal reactions. An analytic solution is presented. The model reproduces official COVID-19 cases counts of a large number of regions and countries that surpassed the first peak of the outbreak. A single unbiased feedback parameter is extracted from field data and used to formulate an index that measures the efficiency of containment strategies (the CEI index). CEI values for a range of countries are given. For two variants of the controlled-SIR model, detailed estimates of the total medical and socio-economic costs are evaluated over the entire course of the epidemic. Costs comprise medical care cost, the economic cost of social distancing, as well as the economic value of lives saved. Under plausible parameters, strict measures fare better than a hands-off policy. Strategies based on current case numbers lead to substantially higher total costs than strategies based on the overall history of the epidemic.

physics.soc-ph↗

arXiv2020

Self induced class stratification in competitive societies of agents: Nash stability in the presence of envy

Envy, the inclination to compare rewards, can be expected to unfold when inequalities in terms of payoff differences are generated in competitive societies. It is shown that increasing levels of envy lead inevitably to a self-induced separation into a lower and an upper class. Class stratification is Nash stable and strict, with members of the same class receiving identical rewards. Upper class agents play exclusively pure strategies, all lower class agents the same mixed strategy. The fraction of upper class agents decreases progressively with larger levels of envy, until a single upper class agent is left. Numerical simulations and a complete analytic treatment of a basic reference model, the shopping trouble model, are presented. The properties of the class-stratified society are universal and only indirectly controllable through the underlying utility function, which implies that class stratified societies are intrinsically resistant to political control. Implications for human societies are discussed. It is pointed out that the repercussions of envy are amplified when societies become increasingly competitive.

physics.soc-ph↗

arXiv2019

Absorbing phase transitions in a non-conserving sandpile model

We introduce and study a non-conserving sandpile model, the autonomously adapting sandpile (AAS) model, for which a site topples whenever it has two or more grains, distributing three or two grains randomly on its neighboring sites, respectively with probability $p$ and $(1-p)$. The toppling process is independent of the actual number of grains $z_i$ of the toppling site, as long as $z_i\ge2$. For a periodic lattice the model evolves into an inactive state for small $p$, with the number of active sites becoming stationary for larger values of $p$. In one and two dimensions we find that the absorbing phase transition occurs for $p_c\!\approx\!0.717$ and $p_c\!\approx\!0.275$. The symmetry of bipartite lattices allows states in which all active sites are located alternatingly on one of the two sublattices, A and B, respectively for even and odd times. We show that the AB-sublattice symmetry is spontaneously broken for the AAS model, an observation that holds also for the Manna model. One finds that a metastable AB-symmetry conserving state is transiently observable and that it has the potential to influence the width of the scaling regime, in particular in two dimensions. The AAS model mimics the behavior of integrate-and-fire neurons which propagate activity independently of the input received, as long as the threshold is crossed. Abstracting from regular lattices, one can identify sites with neurons and consider quenched networks of neurons connected to a fixed number $G$ of other neurons, with $G$ being drawn from a suitable distribution. The neuronal activity is then propagated to $G$ other neurons. The AAS model is hence well suited for theoretical studies of nearly critical brain dynamics. We also point out that the waiting-time distribution allows an avalanche-free experimental access to criticality.

cond-mat.dis-nn↗

arXiv2019

A generic framework for task selection driven by synthetic emotions

Given a certain complexity level, humanized agents may select from a wide range of possible tasks, with each activity corresponding to a transient goal. In general there will be no overarching credit assignment scheme allowing to compare available options with respect to expected utilities. For this situation we propose a task selection framework that is based on time allocation via emotional stationarity (TAES). Emotions are argued to correspond to abstract criteria, such as satisfaction, challenge and boredom, along which activities that have been carried out can be evaluated. The resulting timeline of experienced emotions is then compared with the `character' of the agent, which is defined in terms of a preferred distribution of emotional states. The long-term goal of the agent, to align experience with character, is achieved by optimizing the frequency for selecting the individual tasks. Upon optimization, the statistics of emotion experience becomes stationary.

cs.AI↗

arXiv2019

Five decades of US, UK, German and Dutch music charts show that cultural processes are accelerating

Analyzing the timeline of US, UK, German and Dutch music charts, we find that the evolution of album lifetimes and of the size of weekly rank changes provide evidence for an acceleration of cultural processes. For most of the past five decades number one albums needed more than a month to climb to the top, nowadays an album is in contrast top ranked either from the start, or not at all. Over the last three decades, the number of top-listed albums increased as a consequence from roughly a dozen per year to about 40. The distribution of album lifetimes evolved during the last decades from a log-normal distribution to a powerlaw, a profound change. Presenting an information-theoretical approach to human activities, we suggest that the fading relevance of personal time horizons may be causing this phenomenon. Furthermore we find that sales and airplay based charts differ statistically and that the inclusion of streaming affects chart diversity adversely. We point out in addition that opinion dynamics may accelerate not only in cultural domains, as found here, but also in other settings, in particular in politics, where it could have far reaching consequences.

physics.soc-ph↗

arXiv2019

Embodied robots driven by self-organized environmental feedback

Which kind of complex behavior may arise from self-organizing principles? We investigate this question for the case of snake-like robots composed of passively coupled segments, with every segment containing two wheels actuated separately by a single neuron. The robot is self organized both on the level of the individual wheels and with respect to inter-wheel coordination, which arises exclusively from the mechanical coupling of the individual wheels and segments. For the individual wheel, the generating principle proposed results in locomotive states that correspond to self-organized limit cycles of the sensorimotor loop. Our robot interacts with the environment by monitoring the state of its actuators, that is via propriosensation. External sensors are absent. In a structured environment the robot shows complex emergent behavior that includes pushing movable blocks around, reversing direction when hitting a wall and turning when climbing a slope. On flat grounds the robot wiggles in a snake-like manner, when moving at higher velocities. We also investigate the emergence of motor primitives, viz the route to locomotion, which is characterized by a series of local and global bifurcations in terms of dynamical system theory.

q-bio.NC↗

arXiv2019

When the goal is to generate a series of activities: A self-organized simulated robot arm

Behavior is characterized by sequences of goal-oriented conducts, such as food uptake, socializing and resting. Classically, one would define for each task a corresponding satisfaction level, with the agent engaging, at a given time, in the activity having the lowest satisfaction level. Alternatively, one may consider that the agent follows the overarching objective to generate sequences of distinct activities. To achieve a balanced distribution of activities would then be the primary goal, and not to master a specific task. In this setting, the agent would show two types of behaviors, task-oriented, and task-searching phases, with the latter interseeding the former. We study the emergence of autonomous task switching for the case of a simulated robot arm. Grasping one of several moving objects corresponds in this setting to a specific activity. Overall, the arm should follow a given object temporarily and then move away, in order to search for a new target and reengage. We show that this behavior can be generated robustly when modeling the arm as an adaptive dynamical system. The dissipation function is in this approach time dependent. The arm is in a dissipative state when searching for a nearby object, dissipating energy on approach. Once close, the dissipation function starts to increase, with the eventual sign change implying that the arm will take up energy and wander off. The resulting explorative state ends when the dissipation function becomes again negative and the arm selects a new target. We believe that our approach may be generalized to generate self-organized sequences of activities in general.

nlin.AO↗

arXiv2019

Chaos in time delay systems, an educational review

The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with it various kinds of chaotic phases. Which are then the possible types of time delays, induced chaotic states, and methods suitable to characterize the resulting dynamics? This review presents an overview of the field that includes an in-depth discussion of the most important results, of the standard numerical approaches and of several novel tests for identifying chaos. Special emphasis is placed on a structured representation that is straightforward to follow. Several educational examples are included in addition as entry points to the rapidly developing field of time delay systems.

nlin.CD↗

arXiv2019

Why planetary and exoplanetary protection differ: The case of long duration Genesis missions to habitable but sterile M-dwarf oxygen planets

Time is arguably the key limiting factor for interstellar exploration. At high speeds, flyby missions to nearby stars by laser propelled wafersats taking 50-100 years would be feasible. Directed energy launch systems could accelerate on the other side also crafts weighing several tons to cruising speeds of the order of 1000\,km/s (c/300). At these speeds, superconducting magnetic sails would be able to decelerate the craft by transferring kinetic energy to the protons of the interstellar medium. A tantalizing perspective, which would allow interstellar probes to stop whenever time is not a limiting factor. Prime candidates are in this respect Genesis probes, that is missions aiming to offer terrestrial life new evolutionary pathways on potentially habitable but hitherto barren exoplanets. Genesis missions raise important ethical issues, in particular with regard to planetary protection. Here we argue that exoplanetary and planetary protection differ qualitatively as a result of the vastly different cruising times for payload delivering probes, which are of the order of millennia for interstellar probes, but only of years for solar system bodies. Furthermore we point out that our galaxy may harbor a large number of habitable exoplanets, M-dwarf planets, which could be sterile due to the presence of massive primordial oxygen atmospheres. We believe that the prospect terrestrial life has in our galaxy would shift on a fundamental level in case that the existence of this type of habitable but sterile oxygen planets will be corroborated by future research. It may also explain why our sun is not a M dwarf, the most common star type, but a medium-sized G-class star.

physics.pop-ph↗

arXiv2018

Kick control: using the attracting states arising within the sensorimotor loop of self-organized robots as motor primitives

Self-organized robots may develop attracting states within the sensorimotor loop, that is within the phase space of neural activity, body, and environmental variables. Fixpoints, limit cycles, and chaotic attractors correspond in this setting to a non-moving robot, to directed, and to irregular locomotion respectively. Short higher-order control commands may hence be used to kick the system from one self-organized attractor robustly into the basin of attraction of a different attractor, a concept termed here as kick control. The individual sensorimotor states serve in this context as highly compliant motor primitives. We study different implementations of kick control for the case of simulated and real-world wheeled robots, for which the dynamics of the distinct wheels is generated independently by local feedback loops. The feedback loops are mediated by rate-encoding neurons disposing exclusively of propriosensoric inputs in terms of projections of the actual rotational angle of the wheel. The changes of the neural activity are then transmitted into a rotational motion by a simulated transmission rod akin to the transmission rods used for steam locomotives. We find that the self-organized attractor landscape may be morphed both by higher-level control signals, in the spirit of kick control, and by interacting with the environment. Bumping against a wall destroys the limit cycle corresponding to forward motion, with the consequence that the dynamical variables are then attracted in phase space by the limit cycle corresponding to backward moving. The robot, which does not dispose of any distance or contact sensors, hence reverses direction autonomously.

nlin.AO↗

arXiv2018

Universal scaling relation for magnetic sails: momentum braking in the limit of dilute interstellar media

The recent progress in laser propulsion research has advanced substantially the prospects to realize interstellar spaceflight within a few decades. Here we examine passive deceleration via momentum braking from ionized interstellar media. The very large area to mass relations needed as a consequence of the low interstellar densities, of the order of 0.1 particles per $\mathrm{cm}^{3}$, or lower, are potentially realizable with magnetic sails generated by superconducting coils. Integrating the equations of motion for interstellar protons hitting a Biot Savart loop we evaluate the effective reflection area $A(v)$ in terms of the velocity $v$ of the craft. We find that the numerical data is fitted over two orders of magnitude by the scaling relation $A(v)\ =\ 0.081A_R\log^3(I/(βI_c))$, where $A_R=πR^2$ is the bare sail area, $I$ the current and $β=v/c$. The critical current $I_c$ is $1.55\cdot10^6$ Ampere. The resulting universal deceleration profile can be evaluated analytically and mission parameters optimized for a minimal craft mass. For the case of a sample high speed transit to Proxima Centauri we find that magnetic momentum braking would involve daunting mass requirements of the order of $10^3$ tons. A low speed mission to the Trappist-1 system could be realized on the other side already with a 1.5 ton spacecraft, which would be furthermore compatible with the specifications of currently envisioned directed energy launch systems. The extended cruising times of the order of $10^4$ years imply however that a mission to the Trappist-1 system would be viable only for mission concepts for which time constrains are not relevant.

physics.space-ph↗

arXiv2018

Attractor metadynamics in terms of target points in slow-fast systems: adiabatic vs. symmetry protected flow in a recurrent neural network

In dynamical systems with distinct time scales the time evolution in phase space may be influenced strongly by the fixed points of the fast subsystem. Orbits then typically follow these points, performing in addition rapid transitions between distinct branches on the time scale of the fast variables. As the branches guide the dynamics of a system along the manifold of former fixed points, they are considered transiently attracting states and the intermittent transitions between branchescorrespond to state switching within transient-state dynamics. A full characterization of the set of former fixed points, the critical manifold, tends to be difficult in high-dimensional dynamical systems such as large neural networks. Here we point out that an easily computable subset of the critical manifold, the set of target points, can be used as a reference for the investigation of high-dimensional slow-fast systems. The set of target points corresponds in this context to the adiabatic projection of a given orbit to the critical manifold. Applying our framework to a simple recurrent neural network, we find that the scaling relation of the Euclidean distance between the trajectory and its target points with the control parameter of the slow time scale allows to distinguish an adiabatic regime from a state that is effectively independent from target points.

cond-mat.dis-nn↗