The domain shift problem induced by variable working conditions severely constrains the cross-domain generalization capability of data-driven fault diagnosis models. Existing methods lack collaborative modeling of the multi-scale time-frequency characteristics of vibration signals at the feature extraction level. They also neglect the constraint guidance of fault physical mechanisms on the feature alignment process at the domain adaptation level. To address these deficiencies, this paper proposes a physics-guided cross-domain adaptation framework-a Hierarchical Hybrid Transformer network with Contrastive Learning (PgHHT-CL). The framework comprises three key designs. At the feature encoding level, a hierarchical hybrid Transformer encoder is constructed. It achieves collaborative extraction of transient impulse components and periodic modulation components in vibration signals through gated interactive fusion of local convolutional branches and global self-attention branches across multiple abstraction levels. At the domain adaptation level, a physics-guided cross-domain contrastive learning strategy leverages the order-invariance relationship between fault characteristic frequencies and rotational frequency from bearing dynamics prior knowledge to constrain the construction of cross-domain positive and negative sample pairs. The feature alignment process is thereby required to satisfy physical consistency beyond statistical distribution matching. At the training optimization level, a joint optimization objective integrates classification loss, cross-domain contrastive loss, and physical consistency loss, with a progressive weight adjustment strategy to ensure stable convergence of multi-task learning. Extensive cross-condition transfer experiments on two public bearing datasets from Case Western Reserve University and Paderborn University show that PgHHT-CL achieves average diagnostic accuracies of 94.94 ± 0.32% and 90.26 ± 0.50%, respectively, attaining the highest mean accuracy across all 18 transfer tasks among the representative state-of-the-art baselines selected for comparison. The framework also exhibits notable robustness under large domain shift and strong noise conditions. Ablation experiments and feature visualization analyses further validate the effectiveness and physical interpretability of the physics-guided strategy and hierarchical hybrid architecture.
Radiation-induced pulmonary fibrosis (RIPF) is a common complication in patients with thoracic malignancies undergoing radiotherapy, characterized by poor prognosis and limited therapeutic options. In recent years, the study of RIPF has attracted more attention. However, this area lacks a bibliometric analysis. This study uses bibliometric analysis to examine evolving trends and core themes in RIPF research from 2015 to 2025, while forecasting future research directions. This paper conducted a search in the Web of Science and Scopus databases for publications on RIPF from 2015 to 2025. Bibliometric and visualization analyses were carried out using VOSviewer, CiteSpace, and the "bibliometrix" package in R, with particular attention to research output by countries/regions, institutions, authors, journals, and keywords. A total of 542 articles were identified in this study, with a steady increase observed in annual publications. China was the most productive country, and the United States was the core of international cooperation; the University of Maryland was the institution with the most publications and citations; the International Journal of Radiation Oncology Biology Physics published the most papers. Keyword analysis indicates a shift from experimental exploration toward clinical optimization. Recently, epithelial-mesenchymal transition (EMT) has emerged as a prominent focus of research. Research on the prevention and treatment of RIPF holds significant clinical relevance and promising prospects. Future studies are expected to identify key regulatory nodes, refine intervention pathways, and facilitate the efficient translation of mechanistic insights into therapeutic strategies.
System discovery is an important part of the power systems asset management process. In this paper, we introduce an end-to-end approach for robust system discovery for a class of electrical dynamical systems with polynomial dynamics. To that end, we provide a theoretical analysis of the problem setting and the solution approach using a particular Scientific Machine Learning method called Physics-Informed Machine Learning. We introduce model architecture and training and validation methods for deterministic as well as probabilistic approaches to predict the solution to pertinent inverse problems and propose a sampling method to make the predictions robust to data sparsity. With empirical evidence drawn from a case study of thermal modeling of electrical induction machines, we establish the merits of the proposed method and discuss the implications of this research on possible future directions. In particular, we benchmark our proposed end-to-end method with multiple deterministic and probabilistic approaches and show that it outperforms all but one baseline in terms of performance in a range of 6% to 78% reduction of validation error. The drop in performance (increase in validation error) in our end-to-end probabilistic approach compared to a Bayesian approach is compensated by a large reduction (86%) in the computation time, making our method more balanced in terms of performance and cost. The experimental results establish that our end-to-end approach outperforms the baseline methods by demonstrating consistent balancing among performance and computation cost.
We introduce the Cognitive Near-Singularity (CNS) as a falsifiable phase transition in reasoning systems: the regime in which updates are globally contracting, closed under composition, and invariant to benign reparameterizations, so that heterogeneous reasoning processes converge to a common fixed point up to normal form. The CNS is situated within Human-Centric Functional Modeling (HCFM), which represents systems as navigable graphs of functional states, and the Functional Model of Intelligence (FMI), which applies HCFM to cognition. We contribute (i) a possibility theorem showing that CNS follows from standard contraction-closure conditions on a suitably instrumented conceptual space, (ii) a topological detection framework based on connectivity invariants of the conceptual graph, and (iii) a witness-based protocol that any lab can run to evaluate whether a given corpus or process is consistent with being in the basin of attraction of the CNS operator. Part I reviews the HCFM and FMI foundations, formalizing the conceptual space as a directed graph whose compositional closure makes it a monoid, and introducing the hierarchy of cognitive orders (zeroth, first, second) that motivates the CNS prediction. Part II formalizes a conceptual space (X, d) with a group of invariances G, a composition ⊗, and an update operator T:X→X that is globally Lipschitz with constant L < 1, G-invariant, and closed under ⊗. The possibility theorem uses Banach's fixed-point lemma and perturbation stability to show existence, uniqueness, and basin properties of the fixed point x ⋆. Part III introduces topological detection criteria: the zeroth Betti number β0 of the conceptual graph, a coherence ratio ρ(t), and proxy-graph observables that provide lower bounds on fragmentation. Part IV specifies preregistered witnesses: empirical measurements on trajectories (contractivity C, public loss L pub, drift Ḋ), invariance pass rates under paraphrase/unit transforms, morphism-level (procedure) contraction, and closure/composition witnesses via commuting diagrams. We provide thresholds, negative controls, and ablations. Three CNS Discriminator conditions (D1-D3) distinguish compositional self-enrichment from ordinary unification. Part V applies the witnesses to a bounded author corpus comprising interlinked second-order domains (e.g., physics2, mathematics2, economics2, and medicine2). All seven witnesses and all three discriminators pass under preregistered gates. A domain-general stress test evaluates seven independently selected alternative corpora (free energy principle, category theory, Bayesian probability, and diagrammatic reasoning); all seven fail, with the dominant failure mode being shallow composition (hub-and-spoke topology). All seven fail, with the dominant failure mode being shallow composition (hub-and-spoke topology).
Accurate identification of space groups from powder X-ray diffraction (pXRD) is essential for understanding crystal structures and accelerating materials discovery. However, this task remains highly challenging due to inherent peak overlap, experimental noise, and the complexity of the 230-class classification problem. To address the critical issues of class imbalance and data scarcity, we first design a general physics-informed data augmentation pipeline. We then propose a dual-channel fusion uncertainty-aware network (DFUN) for automated space group classification. The DFUN architecture integrates two complementary feature representations: convolutional features extracted directly from raw diffraction profiles and domain-specific peak descriptors. These distinct representations are adaptively fused through a gating mechanism. Furthermore, to mitigate the inherent long-tailed distribution of crystallographic data, we employ a hybrid loss function that combines Focal Loss with Label Smoothing. Finally, we incorporate Monte Carlo Dropout to provide predictive uncertainty estimation, thereby enabling not only accurate classification but also a crucial assessment of the model's reliability. Evaluated on large-scale simulated data and two public data sets (opXRD and RRUFF), DFUN outperforms the evaluated baseline methods across the reported metrics. The framework also provides uncertainty-aware predictions, establishing DFUN as a robust and interpretable solution for high-throughput automated crystallographic analysis from powder diffraction.
Spin-mediated promotion is a newly discovered electronic promotion mechanism for magnetic metal-catalyst surfaces. A promoter like Ba locally quenches the spin density of the surface atoms at the active site, which stabilizes nearby adsorbates. As this effect is geometrically constrained to atoms neighboring the promoter, and since adsorbates are stabilized to different degrees by this effect, this can break scaling relations, and allows for the design of more efficient catalysts. In this review, we give a detailed explanation of the spin-mediated promotion mechanism. We then illustrate the effect for three different reactions: ammonia synthesis, ammonia decomposition, and CO methanation. We conclude by discussing how spin-mediated promotion can be utilized for other reactions and classes of catalysts, and how it can guide new catalyst development.
This work explores high-dose MeV beam irradiation as a dopant-free, post-synthetic route to tune defect-related properties in 2-3 nm colloidal CeO2 nanoparticles. Oleate/oleylamine-stabilised nanoceria were reproducibly prepared via degassing-controlled thermal decomposition in dibenzyl ether. After that, the CeO2 nanoparticles were irradiated with a 16.5 MeV beam for 10, 40, and 80 min with nominal absorbed doses up to 171 ± 51 MGy while retaining crystalline fluorite cores. XPS and TEM-EELS analyses indicate the presence of irradiation-induced Ce3+/oxygen vacancy states, although spectral limitations prevent robust quantitative ranking of Ce3+. Surface-sensitive readouts show a non-monotonic response: the apparent optical bandgap narrows at the intermediate dose and partially recovers at the highest dose, accompanied by corresponding changes in the Urbach tail. In contrast, room-temperature magnetisation is substantially enhanced relative to pristine nanoceria and changes only weakly between the two highest-dose conditions. These observations suggest that defect centres persist within the nanoparticle volume even when the near-surface microstructure changes.
The urgent need to mitigate accelerating CO2 emissions has driven intense interest in photocatalytic CO2 reduction (CO2RR), a process that mimics natural photosynthesis to generate carbon-neutral, value-added chemicals. While efficiency has improved, the selective production of high-value C2+ products rather than C1 compounds remains a critical challenge to economic viability. Single-atom catalysts offer promise for steering selectivity, yet how atomic-scale spatial distribution dictates reaction pathways remains poorly understood. Here, we demonstrate a programmed spatial distribution approach to induce synergistic cooperativity between neighboring Cu motifs within a UiO-67 matrix. By precisely modulating site distribution, we reveal a spatial threshold at which the framework transitions from isolated sites favoring C1 products to correlated single-atom pairs (CSAPs) that facilitate C-C bond formation. Temperature-resolved electron paramagnetic resonance spectroscopy provides compelling evidence for the distribution-dependent proximity, capturing a unique magnetic feature that emerges as torsional linker motions are suppressed. This structural configuration utilizes the inherent rotational flexibility of the linkers to dynamically optimize interatomic distances, effectively stabilizing [OC-CO]* dimer intermediates and steering the reaction toward C2 products.
Harvesting multiexcitons generated by singlet fission (SF) holds promise for advancing optoelectronic devices and photochemistry. Conventional approaches have previously focused on interfacial exciton or charge transfer after dephasing the triplet-pair [T1T1] to low-energy free triplets. However, multiexciton-driven processes that directly leverage the unique characteristic multireference wave function of the [T1T1] state and its high chemical potential are underexplored, opening new opportunities for advancing photochemistry. Here, we report a functional multicomponent system with covalently integrated electron-rich moieties to direct multiexciton charge transfer directly from the [T1T1] state to a charge-separated diradical (CS) state, a previously unreported transformation. We elucidate the design rules of second generation [G2] SF chromophores using spectroscopic studies, including the role of the local dielectric environment in modulating the fate of the triplet pair from conventional triplet pair dephasing to multiexciton charge separation. These findings provide fundamental insights into multiexciton dynamics and lay the foundation for unconventional multiexciton-driven energy conversion systems.
Multistability-the presence of multiple stable states under identical conditions-is a hallmark of nonlinear complexity, and in optics, a key enabler for multilevel optical memory. Yet, realizing optical multistability in a compact footprint useful for on-chip applications remains challenging, because optical nonlinearities are intrinsically weak and large free spectral range increases the multistability threshold. Here we achieve multistability by engineering a pair of spectrally close, ultrahigh-Q resonances in a photonic crystal microcavity. Leveraging structural perturbations that deliberately introduce non-Hermitian coupling through a shared radiation channel, we drive the resonances towards an exceptional point with nearly degenerate wavelengths and almost-equal quality factors approaching 106. This configuration produces a pronounced tristability from thermo-optical nonlinearity within a 20-μm-diameter circular footprint, evidenced by hysteresis loops with 240-μW input power. Using this concept, we then demonstrate a proof-of-concept optical random-access memory that operates via controlled switching among the multistable states.
In order to provide an additional tool for clinical prognosis evaluation, this research attempts to build a nomogram for predicting the survival of patients with advanced (stage Ⅲ/Ⅳ) pancreatic cancer and to preliminary evaluate its predictive impact. Data from 336 patients diagnosed with stage III/IV pancreatic cancer (2018-2025) across two Chinese hospitals were analyzed. Multivariate Cox regression identified independent predictors in the training set, which were used to construct a nomogram estimating 6-, 12-, and 24-month overall survival. The model underwent internal and external validation via ROC curves, calibration plots, and decision curve analysis. Multivariate Cox regression analysis of the training set revealed that serum albumin (P = 0.001), liver metastasis (P = 0.023), ALT≥40U/L (P = 0.010), and CA199 level (P = 0.037) were independent predictors of overall survival. Based on this, a nomogram model was constructed in the training cohort, with a C-index of 0.741. In the internal validation, the AUC values for predicting 6, 12, and 24-month survival rates were 0.806, 0.753, and 0.628, respectively, and in the external validation, they were 0.922, 0.662, and 0.650, respectively. The calibration curve showed that the predicted probabilities were in good agreement with the actual observed results. The discrimination and calibration of this model in internal verification are acceptable, but its incremental value for clinical decision-making is limited, and large-scale multi-center studies are required to further verify its generalizability.
Tinnitus is a common auditory symptom - sound perceived without an external source. Chronic tinnitus affects about 65 million adults in the EU, often impairing quality of life through distress, sleep problems, anxiety, and depression. Yet, management remains inconsistent across Europe due to patient heterogeneity and lack of standardised care. Health literacy is increasingly recognised as key to empowering patients in self-management and reducing burden. The Erasmus+ project TinWise addresses this by creating a gamified health literacy platform for tinnitus patients and educating healthcare professionals on digital self-help strategies. Building on Tin-TRAC, which developed an open-access e-learning platform, TinWise integrates gamification to enhance motivation, engagement, and knowledge retention. The project applies the OPHELIA framework to optimise literacy strategies and follows the ASPIRE learning construct for co-creating content. TinWise will deliver interactive, co-created digital games to promote self-help literacy, an AI-powered chatbot for real-time guidance, and a patient-linking service to enhance community support. It also aims to train healthcare professionals using reusable learning objects, supporting the integration of digital tools into tinnitus care. Through modern technology and inclusive design, TinWise supports European priorities in digital education, patient empowerment, and healthcare innovation, ultimately improving tinnitus care and outcomes across Europe.
Silicon-rhodamine (SiR) dyes are among the most important fluorophores for super-resolution imaging owing to their far-red emission, high photostability, and tunable lactone-zwitterion equilibrium. However, their broader application in targeted probe development has been limited by the challenging synthesis of 5,6-carboxylated SiR derivatives, which are essential intermediates for bioconjugation. Here, we report a practical CO2-mediated strategy for the synthesis of 5,6-carboxylated SiRs from brominated SiR precursors via lithium-halogen exchange and direct carboxylation. Using n-BuLi and readily available CO2, this method delivers carboxylated SiR derivatives in 60-93% yields while avoiding the use of t-BuLi, toxic CO, and expensive palladium catalysts. In addition, the crude carboxylation mixtures can be directly subjected to amide coupling without chromatographic purification, enabling one-pot access to HaloTag-targeted SiR probes. The resulting probes were successfully applied to long-term live-cell super-resolution imaging, allowing visualization of filopodial dynamics and mitochondrial remodeling. This work establishes a concise and efficient route to functionalized SiR dyes and facilitates the rapid development of targeted SiR probes.
Novel phosphate glasses augmented with different amounts of the erbium (Er2O3) oxide were created in this work using the melt-quench process. The amorphous nature was verified by X-ray diffraction (XRD) investigation. The density for the resultant glass sample is increased when P2O5 is substituted with Er2O3. The structure of current glasses was investigated using Fourier transform infrared (FTIR) spectroscopy. Increased local ordering and the creation of Er-linked cross-bridges (Er-O-P interactions), which lower NBO concentration, are two structural changes brought about by Er2O3 doping up to 0.5 mol%. The dielectric properties were assessed throughout a wide frequency spectrum. Two distinct parts show the frequency dependence of the dielectric constant, ε': a falling portion during small frequencies and a plateau portion over large frequencies. It is clear that (ε') declines at 0.25 as well as 0.5 mol% Er2O3 and continuously increases at higher concentrations. Additionally, (σac) exhibits a similar trend, declining at Er2O3 values of 0.25 and 0.5 mol% and gradually increasing at higher concentrations. The computability of glass through cross linked at low Er doping is the main reason for reduction in ε', and σac. The Er-0.5 specimen with a minimum (ε') and ac conductivity is the ideal option for packing material because to its maximal propagation velocity. Phy-X/PSD software was used to calculate the mean free path (GMFP), equivalent atomic number (GZeq), and fast neutron removal cross-sections (GFNRCS). Furthermore, build up factors (GBF) were calculated for photon energies from 0.015 to 15 MeV and penetration depths from 0.5 to 40 mfp by using the G-P fitting technique. Er-1.0 sample has provided greater gamma-ray shielding than other samples, according to the results. Additionally, these findings highlight the potential of these glasses for radiation shielding in medical and industrial applications.
Phase-change materials have received attention as candidates for next-generation memory storage due to the robustness of multiple solid phases with different electronic and optical properties under ambient conditions. The phase change material Ge15Sb85, the eutectic composition of Ge-Sb, also exhibits a Peierls-like distortion which opens a pseudogap in the electronic density of states that can be exploited for materials design. It is known that this distortion diminishes on heating, and it has been speculated that the competition between distorted and nondistorted states may give rise to an amorphous-amorphous phase transition. To explore these possibilities, we developed a machine-learned interatomic potential for Ge-Sb mixtures that is transferable across densities and compositions using the atomic cluster expansion (ACE) model. Applying this potential to the Ge15Sb85 system, we reproduce experimentally measured structural changes and confirm the presence of a Peierls-like distortion that is suppressed at high temperatures and high pressures. We define a scalar structural order parameter to quantify the strength of the distortion and classify the dependence of this parameter on the pressure, temperature, and stoichiometry. We find that the Peierls-like distortion depends on thermodynamic conditions and is most prominent at low temperature and low density. However, energy minimization of equilibrium configurations reveals that density is the predominant driver of the underlying motif governing the local structure, with temperature affecting solely the sharpness of structural features. We demonstrate that the variation in both density and distortion strength under compression is smooth and continuous, leading us to conclude that structural changes occur via a gradual crossover as opposed to a discrete phase transition.
The boson peak is a universal vibrational anomaly of amorphous materials, yet its microscopic origin has remained unclear for decades. Using simulations of ordinary, hyperuniform and unstressed glasses in two and three dimensions, we show that the boson peak originates from the strong resonant coupling-arising from frequency matching-between phonons and intrinsic string-sliding vibrational modes. We identify two classes of excitations with distinct roles: quadrupolar quasi-localized modes (which dominate low-frequency non-affine responses) and string-sliding vibrational modes (which resonate with phonons at terahertz frequencies to generate the boson-peak excess). The boson peak persists even in glasses without quasi-localized modes or associated elastic heterogeneity, whereas phonon anomalies follow directly from this resonance mechanism. Together, these findings establish string-phonon resonance-rather than quasi-localized modes or elastic heterogeneity-as the central microscopic mechanism of the boson peak and provide a unified mode-based framework for understanding and tailoring the vibrational and mechanical properties of amorphous solids.
Herein, we report the construction of a novel N-doped δ-Al2O3 nanoparticle (NAO)-based gelatin support using a sol-gel/auto-combustion method. XRD analysis proved the NAO NPs' tetragonal structure, which confirmed the delta-phase (δ) formation of Al2O3 NPs. SEM micrographs of NAO NPs showed irregular shapes with rocky surfaces and grain sizes ranging from 34.9 to 66.6 nm. The direct band gap energy of the fabricated NAO-3 NPs was approximately 5.305 eV, indicating a promising response to electrocatalytic activity. NAO-3 NPs demonstrated effective electrocatalytic degradation of both carmine and eosin yellow dyes. The fabricated NAO-3 NPs catalyst achieved degradation efficiencies of ∼96.3% (0.28112 min-1) and 97.5% (0.19828 min-1) within 10 min and 12 min, respectively, for carmine and eosin yellow dyes, while mixed dyes were degraded by ∼98.60%. Trapping analysis revealed that the primary species that initiated the electrocatalytic degradation of carmine dye was the O2˙- radical. After five cycles of electrocatalytic degradation, the electrocatalytic performance of NAO-3 NPs decreased slightly to 90.5%, demonstrating that NAO NPs possess excellent stability and recyclability throughout the electrocatalytic reaction process for the degradation of organic pollutants.
Isotropic zero thermal expansion (ZTE) materials are essential for applications requiring extreme dimensional stability, yet their operation is typically limited to narrow temperature windows below 400 K. Here we report the incorporation of flexible interstitial groups via fractionally occupied atoms into a closed-framework sodalite structure (Cd4Al6O12SO4, CASO). This material exhibits isotropic ZTE, with a thermal expansion coefficient of 0.21(23) × 10-6 K-1 from 11 K to 893 K. The high-temperature ZTE behaviour originates from the preserved transverse vibrations that drive negative thermal expansion-arising from the enhanced vibrations of positionally disordered ligand atoms-which effectively counterbalance the intrinsic positive thermal expansion. Moreover, CASO maintains structural integrity up to 1,100 K, features a solar-blind ultraviolet transparency window down to 275 nm and exhibits thermally induced optical fluctuations at least twice as low as those of conventional optical materials. This work provides both a high-performance crystal for extreme thermal environments and a strategy for designing wide-temperature-range ZTE materials.
Particle radiotherapy offers significant dose sparing but is more susceptible to dose perturbations caused by physical uncertainties. This study aimed to assess the impact of dosimetric uncertainties on tumor control probability (TCP) and normal tissue complication probability (NTCP) for locally advanced lung cancer (LA-LC) among intensity-modulated proton radiotherapy (IMPT), intensity-modulated carbon-ion radiotherapy (IMCT), and intensity-modulated photon radiotherapy (IMRT). Ten LA-LC patients were enrolled in this retrospective study with three radiation modalities of IMPT, IMCT and IMRT for treatment planning. The nominal IMPT/IMCT plans were recalculated according to the four major uncertainty factors respectively, including the type of calculation engine, range uncertainty, setup uncertainty and intra-fractional respiratory movement uncertainty. TCP values were assessed by the model for curative intent. Radiation-induced esophageal injury (RIEI) and radiation-induced lung injury (RILI) were studied as the NTCP endpoints. NTCP and the difference of NTCP between the particle radiotherapy (PT) and IMRT (∆NTCP) values were evaluated through the 6 Lyman-Kutcher-Burman models (4 models for RIEI and 2 for RILI). Under the same prescription doses and similar dose distribution to the targets, deviations of the mean TCP values were less than 0.7% in IMPT, IMCT and IMRT plans under all the uncertainty scenarios. The deviations of the mean values of the ∆NTCP evaluation were -3.3-2.9% for the four models for RIEI and -0.8-1.9% for the two models for RILI under different uncertainty scenarios. The mean values of ∆NTCPL1 (the ∆NTCP values assessed through the first RILI-NTCP model) was -6.0%±6.1%/-6.9%±5.7% in the nominal IMPT/IMCT plans, while of ∆NTCPL2 (the ∆NTCP values assessed through the second RILI-NTCP model) was -12.0%±10.9%/-12.8%±10.1%. For non-robustly optimized IMPT and IMCT plans, the stability of TCP and reduction of NTCP of RILI, especially for larger tumor volumes, maintained in IMPT and IMCT after considering the calculation engine, range uncertainty, setup uncertainty and intra-fractional respiratory motions respectively with the application of several planning strategies. Proper TCP, NTCP and ∆NTCP evaluation may support the individual model-based selection for PT to maximize the clinical benefit for LA-LC.
Breast cancer in human patients often occur as multifocal lesions and the mechanisms through which primary tumors in proximity interact with each other is not well understood. Here we study an in vitro model of bifocal breast tumors by embedding tumor spheroids of MDA-MB-231 cells in 3D extracellular matrices (ECM) made of type I collagen at different concentrations. Combining quantitative experiment, mathematical modeling and numerical simulation, we show that collective traction force from the spheroids creates dipolar deformation in the ECM. As a result in the inter-spheroid region we see increased ECM alignment and decreased pore size. The effect is particularly pronounced for soft ECM, and leads to the spatial gradient of ECM microstructure. Guided by mechanical cues, cancer cells disseminating from spheroids exhibit strong polarization, but reduced speed and persistence in the inter-spheroid space. As a result, expansion rate of bifocal spheroids decreases over time, exhibiting self-limiting dynamics. Our results suggest that reciprocal interactions between cancer cells and ECM could mechanically connect multifocal lesions, altering the invasion dynamics of breast cancer in the tissue space.