arXiv subjects

Maximilian Schäfer

Publications and source records attributed to Maximilian Schäfer.

At least 19 recordsLinked to original sources

arXiv2026

Source Distance and Source Strength Estimation in Turbulent Flow: Exploiting Molecule Degradation Diversity

Locating an odor source and estimating its strength are central problems in nature and engineering. For example, an insect may decide whether a food source is worth traveling to based on its distance and how many molecules it emits. Similarly, a drone or sensor network may need to locate a pipe leak and quantify how much chemical is released. Such tasks are highly challenging due to complex turbulent propagation dynamics. While source distance and strength estimation have been extensively investigated for sources releasing a single molecule type, in both turbulent and non-turbulent flow, many odor sources release multiple molecule types. We investigate whether considering multiple molecule types can aid source distance and strength estimation in challenging turbulent flow. We exploit that different molecule types in a mixture degrade at different rates in the atmosphere. Consequently, the relative abundance of the molecule types observed at a receiver provides information about the source distance that a single molecule type does not. Since this relative abundance is independent of the source strength, it resolves the distance-strength ambiguity inherent in the observed signal intensity and thus also improves strength estimation. Building on this, we propose heuristic low-complexity and learning-based schemes that combine the relative abundance of different molecule types with established features such as mean concentration and whiff duration. All schemes are validated via simulations of turbulent molecule propagation. The low-complexity schemes can achieve estimation quality competitive with learning-based schemes that rely only on a single molecule type, while the proposed learning-based schemes outperform their single-type counterparts. Molecule mixtures can therefore support goal-oriented tasks such as source distance and strength estimation even in challenging turbulent flow.

cs.ET↗

arXiv2026

Analytical Modeling of Open- and Closed-Loop Dispersive Molecular Communication Channels with Pulsatile Flow

Molecular communication (MC) is a communication paradigm in which information is conveyed through the release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside the human body, where the cardiovascular system (CVS) may serve as the physical propagation environment and molecular transport is governed by diffusion and blood flow. Although blood flow is inherently pulsatile, most analytical MC channel models assume steady flow. In this paper, we develop a time-variant analytical model for dispersive MC channels with pulsatile flow. We derive the straight-duct response as a Normal distribution with time-variant mean and variance, capturing the combined effects of diffusion and pulsatile flow, and extend it to closed-loop channels through a wrapped-Normal representation. The model is validated against three-dimensional (3D) particle-based simulations (PBSs) for synthetic and physiologically motivated velocity waveforms. We further derive a closed-form first-order approximation for the first-arrival peak time and introduce the nondimensional indicator $S_{\mathrm{Rx}}$ for assessing the applicability of the reduced one-dimensional (1D) model. Our results show that pulsatility has the strongest influence when molecular transport is predominantly advective and the temporal flow variations are not averaged out, whereas stronger diffusion and faster pulsations reduce its impact on the received signal. Moreover, a PBS-based parameter sweep supports $S_{\mathrm{Rx}} \ge 2$ as a practical criterion for the applicability of the proposed analytical model. Finally, relating the analytical assumptions to representative blood-vessel classes shows that model applicability depends not only on the transport conditions but also on physiological properties such as vessel rigidity, geometric uniformity, and blood rheology.

cs.ET↗

arXiv2026

Simulation and Analysis of Solute Transport in Multi-Lymphangion Lymphatic Vessels

The lymphatic system (LS), a body-wide network of vessels and lymphoid organs governing fluid homeostasis and immune surveillance, has so far not been investigated as a domain for diagnostic and therapeutic molecular communications (MC) applications, despite several properties that make it a promising, complementary alternative to the cardiovascular system. These favorable properties include slower flow, simpler and less dense molecular fluid composition, and direct anatomical access to lymph nodes. Realizing this potential, however, requires a quantitative understanding of how solutes propagate through the LS, a problem that, unlike lymph flow itself, remains largely unaddressed in the literature. As a first step towards narrowing this gap, we develop a particle-based simulation (PBS) framework of solute transport through a three-dimensional chain of valve-separated, concatenated vessel segments, called lymphangions. We simulate the spatiotemporal evolution of solute concentration and qualitatively validate the resulting transport dynamics against existing in vivo measurements of fluorescent tracer propagation in multi-lymphangion lymphatic vessels. Our simulations show that the valve-gated nature of solute transport in lymphatic vessels leads to bursty solute concentrations over time, a characteristic that can also be observed in vivo. Additionally, we find that, within one pumping period, peak timing is dictated by the valves' synchronizing effect rather than the particle release time, while diffusivity and receiver placement determine peak sharpness. Overall, the proposed PBS framework provides a first quantitative basis for solute transport modeling in the LS and several concrete application scenarios for MC in this underexplored domain. Supplementary video material illustrating the PBS is publicly available on Zenodo [DOI: 10.5281/zenodo.21888066].

q-bio.TO↗

arXiv2026

Equilibrium stability as a driver of cooperation among Q-learners

Algorithmic collusion among pricing algorithms has raised concerns about sustained supra-competitive prices and their implications for social welfare. Existing work has largely focused on the probability that reinforcement-learning algorithms converge to cooperative strategies, typically under the assumption that exploration vanishes over time. Motivated by the observation that algorithms deployed in practice are likely to continue exploring in order to remain adaptive to changing environments, we study learning dynamics under constant exploration. In this setting, the relevant question is no longer whether an algorithm converges to a particular strategy profile, but rather what fraction of time the algorithms spend playing cooperative strategies. Even in the benchmark case of the repeated Prisoner's Dilemma with one-period memory, this yields high-dimensional stochastic learning dynamics, for which a complete analytic treatment is intractable. We show that cooperative strategies can be dominant in this time-averaged sense and derive a boundary predicting when such dominance arises, based on the expected dynamics of the Q-learning process. Extensive simulations show that this boundary is a strong predictor for non-defection-dominated behaviour under epsilon-greedy Q-learning.

cs.MA↗

arXiv2026

Analytical Modeling of Dispersive Closed-loop MC Channels with Pulsatile Flow

Molecular communication (MC) is a communication paradigm in which information is conveyed through the controlled release, propagation, and reception of molecules. Many envisioned healthcare applications of MC are expected to operate inside the human body. In this environment, the cardiovascular system ( CVS) acts as the physical channel, which forms a closed-loop network where particle transport is mainly governed by the combined effects of diffusion and flow. Despite the fact that physiological flows in many parts of the human body are inherently pulsatile due to the cardiac cycle, most existing models for dispersive closed-loop MC channels assume a constant flow velocity. In this paper, we present a time-variant one-dimensional (1D ) channel model for dispersive closed-loop MC systems with pulsatile flow. We derive an analytical expression for the channel impulse response (CIR ), which follows a wrapped Normal distribution with time-variant mean and variance. The obtained model reveals the cyclostationary nature of the channel and quantifies the influence of pulsation on the temporal concentration profile compared to steady-flow systems. Finally, the model is validated by three-dimensional ( 3D ) particle-based simulations (PBS s), showing excellent agreement and enabling an efficient analytical characterization of the channel.

cs.ET↗

arXiv2026

Multipath Channel Metrics and Detection in Vascular Molecular Communication: A Wireless-Inspired Perspective

Motivated by classical communications engineering, early works in molecular communication (MC) largely adopted established modeling and signal processing concepts from wireless electromagnetic communication systems. In the context of the human cardiovascular system (CVS), MC channel models evolved from simple unbounded and single-duct environments mimicking individual blood vessels to complex vessel network (VN) topologies, generally at the expense of analytical tractability. Up until now, this has largely prohibited rigorous communication-theoretic analysis of large-scale VNs. In this work, we leverage a recently established closed-form analytical channel model for VNs, named mixture of inverse Gaussians for hemodynamic transport (MIGHT), to conduct the first systematic communication-theoretic study of MC in complex, large-scale VNs. Based on MIGHT, we derive a Poisson channel noise model and unveil structural analogies between multipath wireless communications (MWC) and advective-diffusive MC in VNs. In particular, we establish classical MWC metrics, namely the root mean squared (RMS) delay spread, the mean excess delay, and the coherence bandwidth, for MC in VNs and derive closed-form expressions for the channel frequency response and power delay profile (PDP). Building on this characterization, we propose a VN-adapted, coherent decision-feedback (DF) detector and show how the derived multipath metrics can inform the choice of critical system parameters like the symbol duration, the sampling time, and the memory length. Additionally, we evaluate the detector's performance in different VNs exhibiting inter-symbol interference (ISI). Together, these contributions open the door to a systematic, MWC-inspired MC system design for large-scale VNs.

cs.IT↗

arXiv2026

Autoencoder-based Optimization of Multi-user Molecule Mixture Communication Systems

In this paper, we introduce an autoencoder (AE)-based scheme for end-to-end optimization of a multi-user molecule mixture communication system. In the proposed scheme, each transmitter leverages an encoder network that maps the user symbol to a molecule mixture. The mixtures then propagate through the channel to the receiver, which samples the channel using a non-linear, cross-reactive sensor array. A decoder network then estimates the symbol transmitted by each user based on the sensor observations. The proposed scheme achieves, for a given signal-to-noise ratio, lower symbol error rates than a baseline scheme from the literature in a single-user setting with full channel state information. We additionally demonstrate that the proposed AE-based scheme allows reliable communication when the channel is unknown or changing. Finally, we show that for multiple access the system can account for different user priorities. In summary, the proposed AE-based scheme enables end-to-end system optimization in complex scenarios unsuitable for analytical treatment and thereby brings molecular communication systems closer to real-world deployment.

cs.IT↗

arXiv2026

Matched Filter-Based Molecule Source Localization in Advection-Diffusion-Driven Pipe Networks with Known Topology

Synthetic molecular communication (MC) has emerged as a powerful framework for modeling, analyzing, and designing communication systems where information is encoded into properties of molecules. Among the envisioned applications of MC is the localization of molecule sources in pipe networks (PNs) like the human cardiovascular system (CVS), sewage networks (SNs), and industrial plants. While existing algorithms mostly focus on simplified scenarios, in this paper, we propose the first framework for source localization in complex PNs with known topology, by leveraging the mixture of inverse Gaussians for hemodynamic transport (MIGHT) model as a closed-form representation for advection-diffusion-driven MC in PNs. We propose a matched filter (MF)-based approach to identify molecule sources under realistic conditions such as unknown release times, random numbers of released molecules, sensor noise, and limited sensor sampling rate. We apply the algorithm to localize a source of viral markers in a real-world SN and show that the proposed scheme outperforms randomly guessing sources even at low signal-to-noise ratios (SNRs) at the sensor and achieves error-free localization under favorable conditions, i.e., high SNRs and sampling rates. Furthermore, by identifying clusters of frequently confused sources, reliable cluster-level localization is possible at substantially lower SNRs and sampling rates.

eess.SY↗

arXiv2026

Mixture of Inverse Gaussians for Hemodynamic Transport (MIGHT) in Multiple-Input Multiple-Output Vascular Networks

Synthetic molecular communication (MC) in the cardiovascular system is a key enabler for many envisioned medical applications inside the human body, such as targeted drug delivery, early disease detection, and continuous health monitoring. The design of synthetic MC systems for such applications requires suitable models for the signaling molecule propagation through complex vessel networks (VNs). Existing theoretical models offer limited analytical tractability and lack closed-form solutions, making the analysis of realistic large-scale VNs either infeasible or not insightful. To overcome these limitations, in this paper, we propose a novel closed-form physical model, termed mixture of inverse Gaussians for hemodynamic transport (MIGHT), for the advection-diffusion-driven transport of signaling molecules through complex VNs. The model represents the received molecule flux as a weighted sum of inverse Gaussian distributions, parameterized by the physical properties of the underlying VN. We show that MIGHT is capable of accurately representing the transport dynamics of signaling molecules in large-scale VNs ranging from simple single-input single-output (SISO) to complex multiple-input multiple-output (MIMO) network topologies. The accuracy of the proposed model is validated by comparison to the results from an existing convolution-based model and numerical finite-element simulations, with all finite-element simulation data available on Zenodo. Furthermore, we investigate three applications of the model, namely the reduction of SISO-VNs to obtain simplified representations preserving the essential transport dynamics, the identification and analysis of network regions that are most important for molecule transport in MIMO-VNs comprising multiple transmitters and multiple receivers, and the estimation of representative SISO-VNs that can reproduce the received signal of an unknown SISO-VN.

q-bio.QM↗

arXiv2025

Modulation Schemes for Functionalized Vesicle-based MC Transmitters

Molecular communication (MC) enables information exchange through the transmission of signaling molecules (SMs) and holds promise for many innovative applications. However, most existing works in MC rely on simplified transmitter (TX) models that do not account for the physical and biochemical limitations of realistic biological hardware and environments. This work extends previous efforts toward developing models for practical MC systems by proposing a more realistic TX model that incorporates the delay in SM release and TX noise introduced by biological components. Building on this more realistic, functionalized vesicle-based TX model, we propose two novel modulation schemes specifically designed for this TX to mitigate TX-induced memory effects that arise from delayed and imperfectly controllable SM release. The proposed modulation schemes enable low-complexity receiver designs by mitigating memory effects directly at the TX. Numerical evaluations demonstrate that the proposed schemes improve communication reliability under realistic biochemical constraints, offering an important step toward physically realizable MC systems.

cs.ET↗

arXiv2025

Closed-Loop Long-Term Experimental Molecular Communication System

We present a fluid-based experimental molecular communication (MC) testbed which uses media modulation. Motivated by the natural human cardiovascular system, the testbed operates in a closed-loop tube system. The proposed system is designed to be biocompatible, resource-efficient, and controllable from outside the tube. As signaling molecule, the testbed employs the green fluorescent protein variant "Dreiklang" (GFPD). GFPDs can be reversibly switched via light of different wavelengths between a bright fluorescent state and a less fluorescent state. GFPDs in solution are filled into the testbed prior to the start of information transmission and remain there for an entire experiment. For information transmission, an optical transmitter (TX) and an optical eraser (EX), which are located outside the tube, are used to write and erase the information encoded in the state of the GFPDs, respectively. At the receiver (RX), the state of the GFPDs is read out by fluorescence detection. In our testbed, due to the closed-loop setup, we observe new forms of inter-symbol interferences (ISI), which do not occur in short experiments and open-loop systems. For the testbed, we developed a communication scheme, which includes blind transmission start detection, symbol-by-symbol synchronization, and adaptive threshold detection. We comprehensively analyze our MC experiments using different performance metrics. Moreover, we experimentally demonstrate the error-free transmission of 5370 bit at a data rate of 36 $\textrm{bit}\, \textrm{min}^{\boldsymbol{-1}}$ using 8-ary modulation and the error-free binary transmission of around 90000 bit at a data rate of 12 $\textrm{bit}\, \textrm{min}^{\boldsymbol{-1}}$. For the latter experiment, data was transmitted for a period of 125 hours. All signals recorded and parts of the evaluation code are publicly available on Zenodo and Github, respectively.

cs.ET↗

arXiv2025

Neural Network based Distance Estimation for Branched Molecular Communication Systems

Molecular Communications (MC) is an emerging research paradigm that utilizes molecules to transmit information, with promising applications in biomedicine such as targeted drug delivery or tumor detection. It is also envisioned as a key enabler of the Internet of BioNanoThings (IoBNT). In this paper, we propose algorithms based on Recurrent Neural Networks (RNN) for the estimation of communication channel parameters in MC systems. We focus on a simple branched topology, simulating the molecule movement with a macroscopic MC simulator. The Deep Learning architectures proposed for distance estimation demonstrate strong performance within these branched environments, highlighting their potential for future MC applications.

eess.SP↗

arXiv2025

Inferring the Chemotaxis Distortion Function from Cellular Decision Strategies

Cellular intelligence enables cells to process environmental signals and make context-dependent decisions, as exemplified by chemotaxis, where cells navigate chemical gradients despite noisy signaling pathways. To investigate how cells deal with uncertainty, we apply an information-theoretic framework based on rate distortion theory (RDT). The Blahut-Arimoto algorithm (BAA) computes optimal decision strategies that minimize mutual information while satisfying distortion constraints, balancing sensing accuracy with distortion constraint equivalent to resource cost. We propose the inverse Blahut-Arimoto algorithm (IBAA) to compute the distortion function, which quantifies the system's decision-making criteria for realizing a decision strategy to map input signals to outputs. This general framework extends beyond chemotaxis to biological and engineered systems requiring efficient information processing under uncertainty. We validate the proposed IBAA by accurately estimating theoretical distortion functions in a cellular apoptosis scenario. Additionally, using the local excitation global inhibition (LEGI) model to simulate chemotactic responses, we compute the distortion functions from the cell's perspective. Our finding reveals a state-dependent decision criteria by the cell.

cs.IT↗

arXiv2025

Closed-Loop Molecular Communication with Local and Global Degradation: Modeling and ISI Analysis

This paper presents a novel physics-based model for signal propagation in closed-loop molecular communication (MC) systems, which are particularly relevant for many envisioned biomedical applications, such as health monitoring or drug delivery within the closed-loop human cardiovascular system (CVS). Compared to open-loop systems, which are mostly considered in MC, closed-loop systems exhibit different characteristic effects influencing signaling molecule (SM) propagation. One key phenomenon are the periodic SM arrivals at the receiver (RX), leading to various types of inter-symbol interference (ISI) inherent to closed-loop system. To capture these characteristic effects, we propose an analytical model for the SM propagation inside closed-loop systems. The model accounts for arbitrary spatio-temporal SM release patterns at the transmitter (TX), and incorporates several environmental effects such as fluid flow, SM diffusion, and SM degradation. Moreover, to capture a wide range of practically relevant degradation and clearance mechanisms, the model includes both local removal (e.g., due to SM absorption into organs) and global removal (e.g., due to chemical degradation) of SMs. The accuracy of the proposed model is validated with three-dimensional (3-D) particle-based simulations (PBSs). Moreover, we utilize the proposed model to develop a rigorous characterization of the various types of ISI encountered in closed-loop MC systems.

eess.SY↗

arXiv2025

Practical Transmitters for Molecular Communication: Functionalized Nanodevices Employing Cooperative Transmembrane Transport Proteins

This paper introduces a novel optically controllable molecular communication (MC) transmitter (TX) design based on vesicular nanodevices (NDs). The NDs are functionalized for the controlled release of signaling molecules (SMs) via transmembrane proteins. The proposed design contributes to overcoming the current barrier between MC theory and practical implementation, as all components of the system are chemically realizable. The NDs possess an optical-to-chemical conversion capability, therefore, the proposed NDs can be employed as externally controllable TXs in various MC systems. The proposed ND design comprises two cooperating modules, namely an energizing module and a release module, and, depending on the specific choices for the modules, allows for the release of different types of SMs. After introducing the general system model for the proposed realistic TX design, we provide a detailed mathematical analysis of a specific TX realization. In particular, we derive both an exact and a closed-form approximate analytical solution for the concentration of the released SMs and validate our results by comparison with a numerical solution. Moreover, we model the impact of a buffering medium, which is typically present in liquid environments, e.g., in experimental settings or in in-body applications. This allows the evaluation of the feasibility of our proposed TX design in practical chemical implementations. We consider various forms of parameter randomness occurring during vesicle synthesis, i.e., deviations which are unavoidable during experiments. We show that considering random distributions of the parameter values, such as the ND size, the number of incorporated proteins on the vesicle surface, and the vesicle membrane permeability, is crucial for an adequate kinetic analysis of the system.

cs.ET↗

arXiv2025

The CAM Model: An in vivo Testbed for Molecular Communication Systems

Molecular communication (MC) research increasingly focuses on biomedical applications like health monitoring and drug delivery, demanding testing in realistic living environments. Elevating MC research requires developing advanced in vivo testbeds. We introduce the chorioallantoic membrane (CAM) model as the first versatile 3D in vivo MC platform. The CAM, a highly vascularized membrane in fertilized chicken eggs, is established in bioengineering, cancer research, and drug development. Its biological realism, reproducibility, and versatility make it ideal for next-generation MC testbeds, bridging proof-of-concept systems and practical applications. We comprehensively characterize the CAM model's properties and MC system relevance. Through experimental studies, we investigate fluorescent molecule distribution in the CAM's closed-loop vascular system. We derive an analytical model using the wrapped normal distribution to describe particle propagation in dispersive closed-loop systems dominated by diffusion and flow. Parametric models are developed to approximate particle dynamics in the CAM, with parameters estimated via nonlinear least squares curve fitting. A dataset of 69 regions from 25 eggs validates our models. We analyze parameter relationships and biological plausibility. Finally, we develop a parametric model for long-term particle behavior and liver accumulation in chick embryos.

eess.SY↗

arXiv2024

The Chorioallantoic Membrane Model: A 3D in vivo Testbed for Design and Analysis of MC Systems

Molecular Communications (MC) research is increasingly focused on applications within the human body, such as health monitoring and drug delivery. These applications require testing in realistic and living environments. Thus, advancing experimental MC research to the next level requires the development of in vivo experimental testbeds. In this paper, we introduce the Chorioallantoic Membrane ( CAM ) model as a versatile 3D in vivo MC testbed. The CAM is a highly vascularized membrane formed in fertilized chicken eggs and has gained significance in various research fields, including bioengineering, cancer research, and drug development. Its versatility, reproducibility, and realistic biological properties make the CAM model perfectly suited for next-generation MC testbeds, facilitating the transition from proof-of-concept systems to practical applications. We provide a comprehensive introduction to the CAM model, its properties, and its applications in practical research. Additionally, we present a characterization of the CAM model as an MC system. As a preliminary experimental study, we investigate the distribution of fluorescent molecules in the closed-loop vascular system of the CAM model. We also derive an approximate analytical model for the propagation of molecules in closed-loop systems, and show that the proposed model is able to approximate molecule propagation in the CAM model.

cs.ET↗

arXiv2024

Closing the Implementation Gap in MC: Fully Chemical Synchronization and Detection for Cellular Receivers

In the context of the Internet of Bio-Nano Things (IoBNT), nano-devices are envisioned to perform complex tasks collaboratively, i.e., by communicating with each other. One candidate for the implementation of such devices are engineered cells due to their inherent biocompatibility. However, because each engineered cell has only little computational capabilities, transmitter and receiver (RX) functionalities can afford only limited complexity. In this paper, we propose a simple, yet modular, architecture for a cellular RX that is capable of processing a stream of observed symbols using chemical reaction networks. Furthermore, we propose two specific detector implementations for the RX. The first detector is based on a machine learning model that is trained offline, i.e., before the cellular RX is deployed. The second detector utilizes pilot symbol-based training and is therefore able to continuously adapt to changing channel conditions online, i.e., after deployment. To coordinate the different chemical processing steps involved in symbol detection, the proposed cellular RX leverages an internal chemical timer. Furthermore, the RX is synchronized with the transmitter via external, i.e., extracellular, signals. Finally, the proposed architecture is validated using theoretical analysis and stochastic simulations. The presented results confirm the feasibility of both proposed implementations and reveal that the proposed online learning-based RX is able to perform reliable detection even in initially unknown or slowly changing channels. By its modular design and exclusively chemical implementation, the proposed RX contributes towards the realization of versatile and biocompatible nano-scale communication networks for IoBNT applications narrowing the existing implementation gap in cellular molecular communication (MC).

cs.ET↗