Papers

Tissues are active composites in which multicellular collectives and extracellular matrices mechanically reorganize one another. We develop a three-dimensional micromechanical model that couples deformable, rearranging cell clusters to a disordered network of semiflexible fibers through a dynamic, force-generating interface. Cell clusters are represented as solid-like or fluid-like vertex-model spheroids and coupled to the matrix by passive or contractile linkers renewed as the cluster boundary reorganizes. Matched intact, voided, and passive-linker controls separate cavity formation, interfacial tethering, and active loading. At small strain, passive tethering provides modest reinforcement, whereas active contraction prestresses and strongly stiffens the matrix. Solid-like clusters preserve coherent force transmission and exhibit an excess modulus scaling approximately as $|\sigma|^{1.4}$ across changes in activity, cluster size, and cluster number. Fluid-like clusters undergo greater interfacial renewal, producing weaker and nonmonotonic coupling between prestress and stiffness. Increasing cluster number produces collective stiffening when prestressed regions become connected through sufficiently persistent interfaces. At large strain, both solid-like and fluid-like systems approach the corresponding voided-network response as the residual fiber backbone becomes mechanically dominant. Thus, cell-generated prestress controls macroscopic stiffness only together with the organization and persistence of its transmission across the cell-matrix interface.

Motile microorganisms often navigate crowded and structurally complex environments, where surrounding obstacles can strongly influence locomotion. The bloodstream form of the flagellate parasite Trypanosoma brucei circulates in blood, a dense suspension of red blood cells (RBCs), yet the physical mechanisms governing its locomotion under such conditions remain poorly understood because direct experimental observations are challenging. Here, we combine numerical simulations with in vitro experiments to investigate trypanosome motility in concentrated RBC suspensions and in suspensions of spherical colloidal particles. Simulations reveal that the parasite swimming speed increases by up to $50\%$ at RBC volume fractions comparable to those in blood. To identify the origin of this enhancement, we perform controlled studies in colloidal suspensions with particles of different sizes. We find that suspended particles substantially increase the anisotropy between the perpendicular and parallel friction coefficients acting on the beating flagellum, thereby enhancing propulsion. This effect is most pronounced when the suspended particles are comparable to or smaller than the characteristic wavelength of the flagellar beat. Experiments with microparticle suspensions confirm an increase in trypanosome propulsion with increasing particle concentration, in qualitative agreement with the simulations. Our results uncover a general physical mechanism by which concentrated particle suspensions can enhance flagellar-beat-driven locomotion and suggest that the densely crowded, particulate environment of blood may facilitate trypanosome propulsion. These findings provide new insight into trypanosome motility in the bloodstream and may apply broadly to other flagellated microswimmers in complex suspensions.

This chapter reconstructs the Hopfield network as a physical theory of memory rather than merely an early neural-network algorithm. It begins with the problem as it stood before 1982-threshold logic, Hebbian association, correlation memories, and recurrent binary networks-and isolates what Hopfield's synthesis added: a dynamical definition of content-addressable memory, a symmetric recurrent architecture with a Lyapunov function, a Hebbian embedding of patterns in its couplings, and a physical account of basins, robustness, and graceful degradation. The binary and graded-response energy functions are derived in full, together with the signal-crosstalk decomposition governing pattern stability, the mean-field theory of retrieval at extensive load, and the zero-temperature retrieval spinodal at (alpha 0.138) established by Amit, Gutfreund, and Sompolinsky. The energy-based program is then followed through analog optimization networks, polynomial dense associative memories, exponential interactions, and modern continuous Hopfield updates, including the precise conditions under which the update becomes scaled dot-product attention. Throughout, capacity claims are tied to their disorder ensemble, scaling limit, and success criterion, showing why numerically different storage limits need not conflict. A closing assessment distinguishes established results from surviving principles, assumption-bound limitations, and open problems, treating the Hopfield network as an effective theory whose symmetry, locality, and point-neuron assumptions delimit its biological reach. Fixed-seed numerical experiments expose the mechanisms discussed but do not substitute for analytical results.

This chapter reconstructs the McCulloch-Pitts program as a physics of neural computation rather than the familiar cartoon of a binary neuron. The 1943 logical calculus is developed in both directions: given a net, characterize the propositions realized by its activity; given an admissible logical expression, construct a net that realizes it. We recover the original distinction between thresholded excitatory summation and absolute inhibitory veto-one the weighted-threshold form cannot preserve for arbitrarily large excitatory inputs-and read unit-time delay as the physical realization of logical depth. Recurrence is treated exactly: an autonomous, deterministic network of finitely many binary units has a finite state space, so every trajectory eventually enters a periodic orbit-a fact about finite-state dynamics, not unbounded Turing computation. A single threshold element realizes only linearly separable Boolean functions, whereas finite feedforward networks of them synthesize any Boolean function on a finite domain. We then follows McCulloch and Pitts beyond threshold logic. The 1945 heterarchy paper turns cyclic preference into an obstruction to representation by a scalar utility. The 1947 work on universals asks how a physical network can identify inputs related by nuisance transformations, developed here via group averaging and feedback canonicalization. The 1959 frog-retina study makes the adequate-stimulus question experimental, revealing parallel invariant operations before the brain proper. Spike-triggered analysis shows how a nonlinearly driven neuron can have a vanishing first-order average while second-order statistics recover its hidden selectivity: methodological failure can masquerade as physiological absence. Modern mathematical tools are used without projecting their notation onto the historical papers, and limitations of the idealization are stated explicitly.

We introduce a mesoscopic physics-based framework that transforms conventional transmission optical micrographs into quantitative maps of tissue structural heterogeneity using the Inverse Participation Ratio (IPR). For the first time, to our knowledge, IPR-based light-localization analysis is applied to cancer tissue imaging to quantify nano- to submicron-scale structural alterations through spatial fluctuations in tissue mass density or refractive index. Unlike conventional morphology-based assessment, this physics-driven approach provides objective structural biomarkers from label-free or routinely stained tissue images. The method establishes a scalable, reproducible platform for quantitative computational pathology and enhanced cancer diagnosis by integrating mesoscopic optical physics with standard optical microscopy.

In this study, we aim to theoretically investigate antipolar cell-cell adhesion, in which adhesion sites are located on the opposite side of the leading edge of migrating cells, as a candidate for irregularly polarized adhesion that induces disorder in collective cell migration. We employ the cellular Potts model to simulate the effects of antipolar adhesion on collective migration driven by cell motility. Antipolar adhesion induces a collective motility disorder, which exhibits a disordered configuration in the motility direction, even when collective motion occurs in the absence of adhesion. Consequently, antipolar adhesion inhibits collective migration. The effect is in contrast to that of polar adhesion, which accelerates the directional intercellular order of cell motility. At a specific motility strength, a depinning transition emerges from a collective motility disorder to a collective motion. The collective motility disorder can be physically explained by the cooperative effect between antipolar adhesion and motility persistence within the mean-field approximation.

Asymmetric cell division – in which a mother cell divides into two daughter cells of unequal size – is a fundamental problem in biology. It is believed that the asymmetry originates from the prior polarization of the mother cell. Here we show that division asymmetry can occur spontaneously even in unpolarized mother cells. Specifically, curvature-dependent active stresses in the cell cortex can lead to this symmetry breaking without any molecular polarity cue if the mother cell is confined within a restricted space. Either reducing the cell size or tightening mechanical confinement triggers the same spontaneous symmetry-breaking instability, in which the contractile ring slips off the equator to yield daughters of unequal volume. In the presence of a polarity cue, this instability cooperates with the cue to program the division asymmetry. The model prediction is compared with the imaging data of C. elegans embryogenesis, in which successive cell divisions in a confined eggshell lead to smaller and smaller cell sizes. The measured division asymmetry indeed increases as the cells shrink, and is further amplified when the embryo is mechanically compressed, both in agreement with the model prediction.

Sensory adaptation provides a concrete setting in which low-order system identification can fail qualitatively. We show that one fixed higher-order adaptive system composed entirely of real first-order relaxation modes can be reduced to opposite sides of the second-order pole boundary: low-frequency moment matching gives $\rho_{\rm moment}=4.50$, whereas finite-window fitting gives $\rho_{\rm window}=3.31$, and the inferred pole class changes further with sampling protocol. Thus the real-versus-complex classification of a reduced model is not itself reduction invariant. We then use the general two-state spectrum to connect stochastic identifiability to adaptation: for nontrivial coupling and one-state observation, cross diffusion drops out of the scalar spectrum when the hidden state has no self-relaxation. In the adaptive model, this condition is precisely the integral-memory limit that produces exact adaptation, while leaky memory restores spectral sensitivity. For the exact-adaptation model, the Gaussian path-space irreversibility nevertheless depends on the hidden cross-diffusion channel. Hence $\{H,S_x\}$ does not determine the irreversibility rate. Independently, for a specified all-even reduced two-state drift with $\rho<4$, the drift-only lower bound is $\sigma \ge \tau_x^{-1}(4/\rho-1)$. Published E.~coli and C.~elegans responses provide biological examples of these limits. The distinction established here between transfer-function invariants, reduction-dependent properties, and hidden-state quantities provides a concrete framework for evaluating the limitations of low-dimensional models of adaptive biological dynamics.

Geometric eigenmodes provide a compact and biologically grounded representation of large-scale neural activity. Previous work demonstrated that they can mitigate the underdetermined nature of electroencephalographic (EEG) and magnetoencephalographic (MEG) source localisation, an ill-posed inverse problem in which neural activity is reconstructed from non-invasive recordings. Beyond their spatial structure, neural field theory predicts the temporal evolution of eigenmodes through analytically derived transfer functions. Motivated by this framework, the present work investigates whether these transfer functions can be used to introduce temporal constraints into EEG source imaging. The approach is evaluated using simulated seizure dynamics generated by coupled Epileptor neural mass models. Transfer functions derived directly from neural field theory were found to be generally ineffective as temporal constraints for source localisation, primarily because they neglect cross-eigenmode coupling. Incorporating empirically estimated coupling terms substantially improves localisation performance, particularly in noisy conditions. Although estimating these eigenmode coupling interactions from experimental data remains challenging, the findings motivate dynamical source imaging approaches that combine spatial eigenmode structure with empirically informed cross-modal dynamics.

At the water-land interface, amphibious fishes encounter wet flowable substrates made of granular solid-water mixtures, which can stay solid or flow like a fluid. As these substrates become wetter or drier, their yield strength (at which solid-fluid transition occurs) and cohesion (how sticky they are) both change, challenging locomotion. Despite substantial understanding of tetrapod locomotion on flowable substrates (mostly dry sand), we know little about how amphibious fishes cope with wet flowable substrates of various wetness. Here, we studied mudskippers on clay mud of controlled, variable wetness over the range where solid-fluid transition occurs. As mud became wetter, its strength decreased by 100-fold, leading the animal to sink deeper, with larger areas of body and fins contacting mud. By contrast, mud stuck most easily at intermediate wetness. The increased sinkage and contact and stickiness change caused more mud to stick to and pull against the animal on wetter mud. We also tested dry mud, which stuck to animal fins as its mucus dried. Despite these challenges, the mudskipper predominately used a conserved crutching gait on all except the wettest mud tested, with a modest performance reduction. When normal crutching became less effective, the animal assisted it with tail thrusting, by bending and straightening it to push downward and backward to generate additional thrust and lift, or even thrusting the tail to jump. These observations suggest that mudskipper's crutching motor program is well adapted to its native muddy substrates but inflexible, with most novelty in tail use.

Animals and robots encounter mud at the water-land interface. Like sand, mud can stay solid or flow like a fluid. Unlike sand, the yield strength of mud at which solid-fluid transitions occur depends on not only the amount of solid relative to fluid (water in mud, air in dry sand), but also how much coarse grains and fine clay are within the solid. Despite understanding of locomotion on/within dry sand dominated by coarse grains with repulsive normal forces and friction, little is known for mud dominated by fine clay with strong cohesion. Here, we developed methods to prepare uniform mud of controlled, variable yield strength and characterize and track its drift from water evaporation. Compared to other flowable substrates, mud strength measured by upward force during penetration is weaker and can vary more, and mud sticks more during extraction to pull downward, making it more challenging for locomotion.

Noninvasive live-cell imaging in deep human tissues is crucial for exploring the cellular biological and pathogenic processes, but remains a significant unmet challenge. Diffusion magnetic resonance imaging (dMRI) promises to narrow this gap by noninvasively providing cellular-level microstructural information. Within a single crowded voxel containing millions of living cells, the intricate cellular-level microstructures create numerous microcompartments, each characterized by a specific diffusivity. However, conventional dMRI methods relying on voxel-averaged macroscopic parameters, merely reflect aggregate microstructural properties and fail to quantify this distribution of microcompartment-specific diffusivity within a voxel, thereby obscuring microstructural details. Here, we propose an intravoxel diffusivity probability distribution (IDPD) model to resolve a wealth of essential microstructural information via quantifying microcompartment-specific diffusivity distribution, thereby enabling direct cellular-level characterization. This exceptional capability is realized through a multi-tiered analytical workflow spanning targeted single-voxel or region of interest (ROI) analysis to global visualization using dynamic videos and statistic parametric maps. Ultimately, the IDPD model enables noninvasive cellular-level microstructure imaging, offering a promising avenue to evaluate living cell functions in vivo.

Canonical neural circuit motifs are usually described functionally: divisive normalization rescales population activity by a pooled signal, and winner-take-all competition selects one pattern through recurrent excitation and shared inhibition. We represent them, and their compositions, algebraically as finite transformation systems and analyze the transition monoids generated by their input-conditioned updates, distinguishing structure already present in a generator from structure that appears only through composition, and, on a joint state space, structure inherited from one factor from structure that lives on a joint configuration. Individually aperiodic updates can generate non-aperiodic monoids. In the WTA, every frozen-drive generator collapses to fixed points, yet short input sequences create local cycles of winner-dependent inhibitory gating: globally dissipative dynamics with a reversible action. The strongest result arises in WTA-to-DN composition. The composed monoid then contains a genuinely composite local cycle in which normalization state and the winner's gating state change together, although every primitive generator is aperiodic. Holonomy analysis certifies this as a group component of the Krohn-Rhodes cascade rather than an incidental cycle, and finds most group-carrying image sets on joint configurations, whereas the uncoupled product has none. An exhaustive interface sweep shows that the composite cycle is a property of the coupling rather than of a chosen map. If motifs are building blocks of neural computation, composing them is a form of programming: one chooses primitives and interfaces so that the generated algebra has the intended repertoire. The transition monoid is that repertoire - what a primitive presents to any later construction. Recurrent circuits are compositional transformation systems; their algebra constrains what they can be programmed to compute.

Medical AI is moving beyond recognition towards clinical dialogue and longitudinal prediction. Yet a central question remains: how would a patient's state change under intervention? Statistical models learn future observations, whereas mechanistic models describe selected processes. Neither provides a common framework for representing patient state, coupling scales or revising failed assumptions. We propose Life Operators: task-bounded mappings that define three scientific roles. Perception operators infer task-relevant biological states from multimodal observations, Evolution operators propagate these states under natural or intervention-conditioned dynamics, and Generation operators map them to measurable signals. Each role may be realised by equations, statistical models, neural networks or hybrids. Bridge operators connect components with different variables, scales and time steps. Selected operators and bridges form task-specific Operator Graphs containing the smallest set of states and mechanisms sufficient for a declared claim. This modular structure also makes scientific revision localisable. An AI co-scientist may propose changes to states, operators, bridges or graph structure, while independent evidence determines which variants are retained, restricted or retired. Over time, validated components could accumulate into broader multiscale models of the human body and provide a computational foundation for medical artificial superintelligence.

This study presents a theoretical investigation of generalized solute dispersion in magnetohydrodynamic multiphase tube flow with porous layers. A two-fluid analytical model is developed for applications in biofluid and environmental fluid dynamics. The model comprises a micropolar (non-Newtonian) fluid core representing the rotational behaviour of red blood cells and a Newtonian plasma periphery embedded with Brinkman and Darcy porous structures, corresponding to the glycocalyx and endothelial layers with distinct permeability characteristics. A transverse magnetic field is incorporated to investigate how magnetic-field-induced modifications of the carrier flow influence solute localisation, with potential relevance to magnetic nanoparticle-mediated drug delivery. Using the generalised dispersion framework of Sankarasubramanian & Gill, analytical solutions are derived to investigate how the coupled axial velocity field and associated microrotational dynamics influence solute transport. The analytical predictions are independently validated through Brownian dynamics simulations, demonstrating excellent agreement for the temporal evolution of the zeroth and first transport moments. The results reveal the previously unexplored influence of microrotational dynamics on solute concentration, convection coefficients and effective dispersion, providing new insights into the coupled roles of translational and rotational fluid motion in biofluid transport. This work bridges an important gap in the literature and establishes a generalized theoretical framework linking magnetic fields, micropolar fluids and porous arterial structures for biofluid transport, targeted drug delivery and clinical engineering applications.

During many biological processes, cell aggregates spread on substrates in a process of active wetting. The existing models of tissue spreading, however, do not explicitly capture the state of partial wetting, in which the cell aggregate reaches a non-zero contact angle. Here, modeling cell aggregates as active polar liquid droplets, we predict a transition between partial and complete wetting. This transition emerges from the competition between tissue surface tension and active traction forces, which is captured in an active Young-Dupré equation. The active wetting transition is discontinuous, and it features a region of parameters in which both partial and complete wetting are possible. Unlike in passive wetting, the transition depends on dynamical parameters such as the tissue viscosity and substrate friction. Finally, adding contractile intercellular active stresses leads to higher contact angles and even full dewetting. Overall, our work predicts an active wetting transition for tissues and it captures the partial wetting states often seen in experiments.

Collective behaviour in living systems is usually modelled as the outcome of a direct social drive: agents are rewarded, or hard-wired, to align with or approach their neighbours. Here we show that aggregation can instead emerge from an indirect objective. We let reinforcement learning foragers, initially performing a random walk, optimize their dynamics from a purely individual reward for finding replenishable targets, while perceiving only their conspecifics and never the targets themselves. As the visual range grows, the agents undergo a sharp crossover from an environment-tuned individual search to a scale-agnostic collective one, and this crossover coincides with the onset of spatial aggregation. Thus a collective phase arises as a by-product of optimal foraging, without any direct reward for grouping. A minimal analytical first-passage model reproduces the transition as a crossover between the two search strategies. Our results identify indirect, resource-driven reward as a generic route to emergent collective phenomena.

We numerically investigate the dynamics of a deformable closed ring filled with active particles. The ring is modeled as a flexible boundary made up of passive beads interacting with a harmonic spring force. The interior of the ring is filled with active Brownian particles (ABPs), and their activity is controlled through the rotational diffusion coefficient. We explore how, by systematically varying the activity of ABPs, packing fraction, and size of the ring, we can control the shape deformation and dynamics of the ring. At low packing fractions, low rotational diffusion coefficients, and smaller ring sizes, the ring exhibits highly irregular and strongly deformed shapes due to the uneven spatial arrangement of active particles along the boundary. Increasing the packing fraction, rotational diffusion coefficient, or ring size promotes a more even distribution of active particles within the ring, thereby suppressing shape deformations and fluctuations, driving the ring toward a more circular shape. We further analyze the mean-squared displacement (MSD) of the ring's center of mass and observe a crossover from ballistic to diffusive dynamics, which can be tuned by varying the system parameters. Our results demonstrate that, despite its internal complexity and deformability, the ring exhibits emergent behavior analogous to that of a single effective active particle. This study provides insight into the collective effects of confined active matter and the resulting macroscopic dynamics of deformable systems.

The organization of RNA genomes within viral capsids is primarily controlled by electrostatic interactions between the negatively charged genome and positively charged N-terminal domains of coat proteins. In theoretical approaches, these interactions are commonly captured by mean-field models that smooth capsid charge over the inner surface and treat ionic screening as a continuum. However, charges are localized at discrete N-terminal binding sites and ionic screening arises from correlated ion distributions. Here we use molecular dynamics simulations with explicit ions, explicit water, and full Coulomb electrostatics to simulate a linear polyelectrolyte confined within a model capsid bearing discrete N-terminal-like charge sites. We first validate our approach by simulating a polyelectrolyte in bulk solution and demonstrating that persistence length decreases with increasing salt, matching experimental measurements for single-stranded RNA. When confined within a capsid, radial density profiles shift systematically inward from the capsid wall with increasing salt concentration, in agreement with mean-field predictions. By independently varying charge magnitude, binding-site density, and N-terminal protrusion length, we show that total electrostatic coupling governs global organization while geometric details modulate local genome-wall contact and angular genome organization near N-terminals (within the T=3 architecture, linear genome topology, and monovalent salt range studied here). Across all simulations, equilibration times increase sevenfold with salt, revealing kinetic effects inaccessible to equilibrium theory. These results validate continuum approximations for radial organization while revealing deviations arising from discrete molecular details and establishing a framework for future investigations of genome secondary structure, capsid geometry, and assembly kinetics.

How do organisms navigate when the signals guiding them are noisy? Variance adaptation, the rescaling of sensitivity to noise, is common in sensory systems, but its role in navigation is unexplored. We introduce a minimal active Brownian particle whose run-and-tumble policy follows from an optimality principle. Variance adaptation emerges as part of this policy. Adaptation keeps chemotactic drift finite as noise grows, while a non-adaptive particle's collapses exponentially. Adaptation also carries a cost, degrading performance in quiet environments and requiring a tuned adaptation sensitivity.

Recent research grounded in experiments has connected neural ring models of vision to how animals navigate a complex landscape of attractive targets. In this paper we investigate the mathematical and biological implications of a three-stage model where animals pre-process visual stimuli to identify a discrete set of targets, process this input to select the dominant targets, and then post-process this information to navigate the landscape. Incorporating finite target sizes and a neural density allows consistent target acquisition and pursuit reflecting what is seen in nature. Mathematically, we show this model corresponds to an energy minimization problem, simplifying both its analysis and numerical implementation. Biologically, we argue that the model is physiologically motivated, reproduces experimental observations, and presents a fairly direct pathway to decoding neural geometry via empirical data. Our results also demonstrate an analysis pipeline for future model extensions and suggest specific avenues for experimental research to test and parameterize our quantitative framework.

The maximum energy dissipation principle is employed to nonlinear chemical thermodynamics in terms of distance variable (generalized displacement) from the global equilibrium, applying the optimal control interpretation to develop a variational formulation. The cost-like functional was chosen to support the suggestion that such a formulation corresponds to the maximum energy dissipation principle. Using this approach, the variational framework was proposed for a nonlinear chemical thermodynamics, including general cooperative kinetics model. The formulation is in good agreement with standard linear non-equilibrium chemical thermodynamics.

Academic libraries hold ebook collections so large that no reader can inspect more than a negligible fraction of the catalogue. Assessment of those collections rests almost entirely on usage telemetry. A title that generates no recorded interaction is treated as a title nobody wanted. That inference is unavailable on the present evidence. We separate two constructs the literature conflates: retrievability, the probability that a system returns an item to a query that already specifies it, and encounterability, the probability that an item enters a reader's attention without prior title-level intent. Following a stated protocol over work published from 2018 onward, we find three things. Large zero-use populations are robustly documented. Usage depends heavily on the measuring instrument. And no standard library metric records an item impression. The consequence is an identification problem. Recorded non-use mixes non-exposure, unnoticed exposure, rejection, and off-channel use, and no study located under our protocol decomposes it. Recommender-system research already names this problem: there, feedback is missing not at random. We close with four measurement directions that would narrow the gap without closing it.

Epidemic models often pool air travel, commuting, and other mobility layers into a single weighted network. Pooling keeps the total imported infections into a region but discards the transport mode and route that delivered them, the information a mode-specific intervention needs. We make this precise for directed multilayer flows with heavy-tailed variation. Pooling acts as an asymmetric filter. The magnitude of an extreme importation, its radial tail index, is an exact invariant of sampling and nonnegative aggregation, whereas its composition across layers and routes, the angular part, is reweighted by layer-specific sampling and can be irrecoverably merged. We give a necessary and sufficient condition for recovering route composition, attach a surveillance decision cost to the loss, and show that the first established route need not be the busiest. A controlled metapopulation study calibrates the cost, and two contrasting reconstructions show where it bites. In US pandemic influenza, air adds fitted information beyond commuting, and a layer-resolved ranking targets more air-import burden than a pooled one. In the early Italian COVID-19 wave, commuting improves onset reconstruction while air attribution stays unresolved. Pooling can therefore support total-importation surveillance but cannot in general identify the mode or route behind an importation.

Kinetic proofreading buys accuracy with energy. Where the energy is spent, we show, caps how much accuracy it can buy. Drive layer $j$ of a $K$-checkpoint cascade and the error never falls below $\eeq^{K-j+1}$, where $\eeq$ is the error the same network reaches at equilibrium. The exponent is one plus the first Betti number of the downstream subgraph, which counts its independent cycles. Driving the first layer can recruit all $K$ checkpoints, whereas driving the final layer restricts the best possible scaling to $\eeq^2$, independently of network depth. We also derive the exact dependence on driving strength and show that the error either decreases monotonically or has a unique global minimum, beyond which stronger driving worsens accuracy. Drive placement therefore imposes a topological limit on nonequilibrium error correction.

Motility-induced phase separation (MIPS) describes a central clustering phenomenon in active matter systems where particles spontaneously separate into dense and dilute phases even in the absence of interparticle attractive forces. Recent theoretical and experimental efforts have taken the first steps to extend active matter concepts to the quantum level. However, whether a genuine quantum analog of MIPS exists and how quantum coherence would compete or cooperate with the dissipative self-propulsion has remained open so far. Here, we provide evidence that quantum MIPS can occur in a model of active hard-core bosons in one dimension. Our model yields superlinear number fluctuations characteristic of MIPS, leading to microphase separation with large but finite cluster size. Adding nearest-neighbor repulsive interactions, we find numerical evidence for restoring genuine phase separation with a divergent correlation length. Crucially, the clustered steady states maintain a long-distance quantum coherence, revealing a genuinely quantum feature with no classical counterpart. These results provide a foundation for exploring quantum MIPS and suggest that the coherence-activity interplay can generate new types of nonequilibrium quantum states.

The nonlinear differential equation, which describes changes of membrane's density in the process of propagation of active potential along a nerve, has been studied. Depending on values of dispersion terms of that equation, forms and possible existence of exact periodic and solitary solutions were considered.

Contractile cells and external loads reorganize the fibrous extracellular matrix, aligning and compacting fibers over distances far exceeding a cell's size, strongly affecting bioprocesses such as wound healing, angiogenesis and tumor invasion. We develop a continuum micromechanical theory that links, at every material point, the load-induced orientational order to the mechanical response that the reoriented network then exhibits. The network is described statistically, by the probability density of fiber orientations, and deforms affinely, so that a single-fiber stress-strain law is carried into the network stress, with the deformation set self-consistently by mechanical equilibrium. Critical to realistic biological relevant conditions, this theory allows both geometrical and material nonlinearities. Applied to a two-dimensional network under uniaxial stretch, the theory collapses onto a single anisotropy parameter that governs the orientation distribution, the nematic order, the Poisson ratio, and the densification of fibers. Our theory reveals that induced order and densification are highly positively correlated, and in the case of uniaxial stretch they collapse onto a nearly universal curve, independent of the single-fiber stiffness behavior. For a contracting cell, we find that buckling controls how far nematic orientational order and densification propagate. We find an algebraic decay of deformations with distance and solve for the dependence of the power-law exponent on the buckled-reduced stiffness of a single fiber. We validate our theory by comparison with non-affine discrete fiber-network simulations.

We used simulations of short single stranded DNA (ssDNA) homopolymers, based on the sequence dependent Three Interaction Site (TIS) model, to calculate the persistence length ($l_p$) in polyvalent cations. The TIS model accounts for stacking interactions and electrostatic interactions are treated using the Coulomb potential. We find that $l_p$ for $\mathrm{dT_{30}}$ (T is thymine) and $\mathrm{dA_{30}}$ (A is adenine) is quantitatively fit using $l_p = l_p^0 + \lambda \kappa^{-1}$ ($l_p^0$ is the bare persistence length, $\lambda$ is a dimensionless constant, and $\kappa$ is the inverse Debye length) in the divalent cations $\mathrm{Mg^{2+}}$ and $\mathrm{Ca^{2+}}$. The dependence of $l_p$ on $\kappa$ is surprising because it was derived for long flexible polyelectrolytes in which the charges interact via the Debye-Hückel potential. The $l_p^0$ values are 0.4 nm and 1.1 nm for polyT and polyA, respectively. Strikingly, $l_p$ is almost independent of the tetravalent spermine concentration. There is no clear theoretical explanation although simulations suggest that the number of spermine molecules that bind to the ssDNA saturates at a small value. A qualitative picture, based on the restrictions of access to the phosphate groups due to volume exclusion of the anisotropic structure of $\mathrm{Spm^{4+}}$, rationalizes the simulation results. The predicted dependence of $l_p$ in spermine awaits experimental test.

Evolution in changing environments requires both reliable expression of the currently favored phenotype, as quantified by penetrance, and the capacity to reach alternative phenotypes through mutation. Previous studies suggest that high penetrance may restrict such mutational access. However, because these studies focus on evolved genotypes and local mutational neighborhoods, they cannot determine whether this local constraint limits mutational adaptability under environmental change. Such adaptability depends on a genotype's position relative to high-fitness regions for other environments. Addressing this question requires reconstructing the full probability distribution over phenotypes for every genotype and the resulting environment-specific fitness landscapes across genotype space. Such reconstruction is generally infeasible because genotype and phenotype spaces grow combinatorially. Here, an abstract model of stochastic genotype-phenotype mapping, inspired by interacting spins in statistical physics, permits exhaustive reconstruction of the map. We find that high-penetrance genotypes tend to occupy the interior of environment-specific high-fitness regions and are mutationally robust, whereas lower-penetrance genotypes tend to lie near their boundaries and have greater mutational access to high-fitness regions for alternative environments. This global geometry generates a trade-off between penetrance and mutational adaptability. In evolutionary simulations, stronger phenotypic noise in a fixed environment increases the selective advantage of reliable expression, thereby favoring high penetrance and mutational robustness. Frequent environmental change instead favors mutational accessibility at the expense of penetrance. Thus, penetrance and adaptability are opposing consequences of the same global geometry, with environmental conditions determining their evolutionary balance.