An infinite-period phase transition versus nucleation in a stochastic model of collective oscillations

A lattice model of three-state stochastic phase-coupled oscillators has been shown by Wood et al (2006 Phys. Rev. Lett. 96 145701) to exhibit a phase transition at a critical value of the coupling parameter, leading to stable global oscillations. We show that, in the complete graph version of the model, upon further increase in the coupling, the average frequency of collective oscillations decreases until an infinite-period (IP) phase transition occurs, at which point collective oscillations cease. Above this second critical point, a macroscopic fraction of the oscillators spend most of the time in one of the three states, yielding a prototypical nonequilibrium example (without an equilibrium counterpart) in which discrete rotational (C_3) symmetry is spontaneously broken, in the absence of any absorbing state. Simulation results and nucleation arguments strongly suggest that the IP phase transition does not occur on finite-dimensional lattices with short-range interactions.Comment: 15 pages, 8 figure

István Deák (1926–2023) : in memoriam

Published online: 25 May 2023This is a tribute to István Deák, a prominent historian of Habsburg history. The tribute covers his early life in Budapest, the son of a middle-class family of Jewish origins who suffered as a Jew in 1944. Deák left Hungary in 1944, spent several years in France and Germany, and then came to the United States in 1956. Much of the commemoration covers his career as a professor of history at Columbia University and his very significant scholarly contributions

Collective oscillations of excitable elements: order parameters, bistability and the role of stochasticity

We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with stable collective oscillations exists even with non-deterministic refractory periods. Moreover, further increasing the coupling strength leads to a reentrant transition, where the synchronized phase loses stability. In an intermediate regime, we also observe bistability (and consequently hysteresis) between a synchronized phase and an active but incoherent phase without oscillations. The onset of the oscillations appears in the mean-field equations as a Neimark-Sacker bifurcation, the nature of which (i.e. super- or subcritical) is determined by the first Lyapunov coefficient. This allows us to determine the borders of the oscillating and of the bistable regions. The mean-field prediction thus obtained agrees quantitatively with simulations of complete graphs and, for random graphs, qualitatively predicts the overall structure of the phase diagram. The latter can be obtained from simulations by defining an order parameter q suited for detecting collective oscillations of excitable elements. We briefly review other commonly used order parameters and show (via data collapse) that q satisfies the expected finite size scaling relations.Comment: 19 pages, 7 figure

Swarmodroid 1.0: A Modular Bristle-Bot Platform for Robotic Active Matter Studies

Large swarms of extremely simple robots (i.e., capable just of basic motion activities, like propelling forward or self-rotating) are widely applied to study collective task performance based on self-organization or local algorithms instead of sophisticated programming and global swarm coordination. Moreover, they represent a versatile yet affordable platform for experimental studies in physics, particularly in active matter - non-equilibrium assemblies of particles converting their energy to a directed motion. However, a large set of robotics platforms is being used in different studies, while the universal design is still lacking. Despite such platforms possess advantages in certain application scenarios, their large number sufficiently limits further development of results in the field, as advancing some study requires to buy or manually produce the corresponding robots. To address this issue, we develop an open-source Swarmodroid 1.0 platform based on bristle-bots with reconfigurable 3D-printed bodies, external control of motion velocity, and basic capabilities of velocity profile programming. In addition, we introduce AMPy software package in Python featuring OpenCV-based extraction of robotic swarm kinematics accompanied by the evaluation of key physical quantities describing the collective dynamics. We perform a detailed analysis of individual Swarmodroids' motion characteristics and address their use cases with two examples: a cargo transport performed by self-rotating robots and a velocity-dependent jam formation in a bottleneck by self-propelling robots. Finally, we provide a comparison of existing centimeter-scale robotic platforms, a review of key quantities describing collective dynamics of many-particle systems, and a comprehensive outlook considering potential applications as well as further directions for fundamental studies and Swarmodroid 1.0 platform development.Comment: 18 pages, 7 figures, 1 table + Supplementary Information. Comments are welcom

Transcriptomic profiles conducive to immune-mediated tumor rejection in human breast cancer skin metastases treated with Imiquimod

Imiquimod is a topical toll-like-receptor-7 agonist currently used for treating basal cell carcinoma. Recently, imiquimod has demonstrated tumor regression in melanoma and breast cancer skin metastases. However, the molecular perturbations induced by imiquimod in breast cancer metastases have not been previously characterized. Here, we describe transcriptomic profiles associated with responsiveness to imiquimod in breast cancer skin metastases. Baseline and post-treatment tumor samples from patients treated with imiquimod in a clinical trial were profiled using Nanostring technology. Through an integrative analytic pipeline, we showed that tumors from patients who achieved a durable clinical response displayed a permissive microenvironment, substantiated by the upregulation of transcripts encoding for molecules involved in leukocyte adhesion and migration, cytotoxic functions, and antigen presentation. In responding patients, Imiquimod triggered a strong T-helper-1 (Th-1)/cytotoxic immune response, characterized by the coordinated upregulation of Th-1 chemokines, migration of Th-1 and cytotoxic T cells into the tumor, and activation of immune-effector functions, ultimately mediating tumor destruction. In conclusion, we have shown that topical imiquimod can induce a robust immune response in breast cancer metastases, and this response is more likely to occur in tumors with a pre-activated microenvironment. In this setting, imiquimod could be utilized in combination with other targeted immunotherapies to increase therapeutic efficacy

Advancing Precision Medicine: Algebraic Topology and Differential Geometry in Radiology and Computational Pathology

Precision medicine aims to provide personalized care based on individual patient characteristics, rather than guideline-directed therapies for groups of diseases or patient demographics. Images-both radiology- and pathology-derived-are a major source of information on presence, type, and status of disease. Exploring the mathematical relationship of pixels in medical imaging ("radiomics") and cellular-scale structures in digital pathology slides ("pathomics") offers powerful tools for extracting both qualitative and, increasingly, quantitative data. These analytical approaches, however, may be significantly enhanced by applying additional methods arising from fields of mathematics such as differential geometry and algebraic topology that remain underexplored in this context. Geometry's strength lies in its ability to provide precise local measurements, such as curvature, that can be crucial for identifying abnormalities at multiple spatial levels. These measurements can augment the quantitative features extracted in conventional radiomics, leading to more nuanced diagnostics. By contrast, topology serves as a robust shape descriptor, capturing essential features such as connected components and holes. The field of topological data analysis was initially founded to explore the shape of data, with functional network connectivity in the brain being a prominent example. Increasingly, its tools are now being used to explore organizational patterns of physical structures in medical images and digitized pathology slides. By leveraging tools from both differential geometry and algebraic topology, researchers and clinicians may be able to obtain a more comprehensive, multi-layered understanding of medical images and contribute to precision medicine's armamentarium

Impact of hormone receptor status and tumor subtypes of breast cancer in young BRCA carriers

Background: Hormone receptor expression is a known positive prognostic and predictive factor in breast cancer; however, limited evidence exists on its prognostic impact on prognosis of young patients harboring a pathogenic variant (PV) in the BRCA1 and/or BRCA2 genes. Patients and methods: This international, multicenter, retrospective cohort study included young patients (aged ≤40 years) diagnosed with invasive breast cancer and harboring germline PVs in BRCA genes. We investigated the impact of hormone receptor status on clinical behavior and outcomes of breast cancer. Outcomes of interest [disease-free survival (DFS), breast cancer-specific survival (BCSS), and overall survival (OS)] were first investigated according to hormone receptor expression (positive versus negative), and then according to breast cancer subtype [luminal A-like versus luminal B-like versus triple-negative versus human epidermal growth factor receptor 2 (HER2)-positive breast cancer]. Results: From 78 centers worldwide, 4709 BRCA carriers were included, of whom 2143 (45.5%) had hormone receptor-positive and 2566 (54.5%) hormone receptor-negative breast cancer. Median follow-up was 7.9 years. The rate of distant recurrences was higher in patients with hormone receptor-positive disease (13.1% versus 9.6%, P < 0.001), while the rate of second primary breast cancer was lower (9.1% versus 14.7%, P < 0.001) compared to patients with hormone receptor-negative disease. The 8-year DFS was 65.8% and 63.4% in patients with hormone receptor-positive and negative disease, respectively. The hazard ratio of hormone receptor-positive versus negative disease changed over time for DFS, BCSS, and OS (P < 0.05 for interaction of hormone receptor status and survival time). Patients with luminal A-like breast cancer had the worst long-term prognosis in terms of DFS compared to all the other subgroups (8-year DFS: 60.8% in luminal A-like versus 63.5% in triple-negative versus 65.5% in HER2-positive and 69.7% in luminal B-like subtype). Conclusions: In young BRCA carriers, differences in recurrence pattern and second primary breast cancer among hormone receptor-positive versus negative disease warrant consideration in counseling patients on treatment, follow-up, and risk-reducing surgery

Characteristics and clinical outcomes of breast cancer in young BRCA carriers according to tumor histology

Background: Young women with breast cancer (BC) have an increased chance of carrying germline BRCA pathogenic variants (PVs). Limited data exist on the prognostic impact of tumor histology (i.e. ductal versus lobular) in hereditary breast cancer. Methods: This multicenter retrospective cohort study included women aged ≤40 years with early-stage breast cancer diagnosed between January 2000 and December 2020 and known to carry germline PVs in BRCA1/2. Histology was locally assessed in each center. The Kaplan-Meier method and Cox regression analysis were used to assess disease-free survival and overall survival. Results: Of 4628 patients included from 78 centers worldwide, 3969 (86%) had pure ductal, 135 (3%) pure lobular, and 524 (11%) other histologies. Compared with ductal tumors, lobular tumors were more often grade 1/2 (57.7% versus 22.1%), stage III (29.6% versus 18.5%), and luminal A-like (42.2% versus 12.2%). Lobular tumors were more often associated with BRCA2 PVs (71.1% BRCA2), while ductal tumors were more often associated with BRCA1 PVs (65.7% BRCA1). Patients with lobular tumors more often had mastectomy (68.9% versus 58.3%), and less often received chemotherapy (83.7% versus 92.9%). With a median follow-up of 7.8 years, no significant differences were observed in disease-free survival (adjusted hazard ratio 1.01, 95% confidence interval 0.74-1.37) or overall survival (hazard ratio 0.96, 95% confidence interval 0.62-1.50) between patients with ductal versus lobular tumors. No significant survival differences were observed according to specific BRCA gene, breast cancer subtype, or body mass index. Conclusions: In this large global cohort of young BRCA carriers with breast cancer, the incidence of pure lobular histology was low and associated with higher disease stage at diagnosis, luminal-like disease and BRCA2 PVs. Histology did not appear to impact prognosis

Characterization of HER2-low breast cancer in young women with germline BRCA1/2 pathogenetic variants: Results of a large international retrospective cohort study

Background: Breast cancer (BC) in women aged ≤40 years carrying germline pathogenetic variants (PVs) in BRCA1/2 genes is infrequent but often associated with aggressive features. Human epidermal growth factor receptor 2 (HER2)-low-expressing BC has recently emerged as a novel therapeutic target but has not been characterized in this rare patient subset. Methods: Women aged ≤40 years with newly diagnosed early-stage HER2-negative BC (HER2-0 and HER2-low) and germline BRCA1/2 PVs from 78 health care centers worldwide were retrospectively included. Chi-square test and Student t-test were used to describe variable distribution between HER2-0 and HER2-low. Associations with HER2-low status were assessed with logistic regression. Kaplan–Meier method and Cox regression analysis were used to assess disease-free survival (DFS) and overall survival. Statistical significance was considered for p&nbsp;≤.05. Results: Of 3547 included patients, 32.3% had HER2-low BC, representing 46.3% of hormone receptor–positive and 21.3% of triple-negative (TN) tumors. HER2-low vs. HER2-0 BC were more often of grade 1/2 (p&nbsp;&lt;.001), hormone receptor–positive (p&nbsp;&lt;.001), and node-positive (p&nbsp;=.003). BRCA2 PVs were more often associated with HER2-low than BRCA1 PVs (p&nbsp;&lt;.001). HER2-low versus HER2-0 showed better DFS (hazard ratio [HR], 0.86; 95% CI, 0.76–0.97) in the overall population and more favorable DFS (HR, 0.78; 95% CI, 0.64–0.95) and overall survival (HR, 0.65; 95% CI, 0.46–0.93) in the TN subgroup. Luminal A–like tumors in HER2-low (p&nbsp;=.014) and TN and luminal A-like in HER2-0 (p&nbsp;=.019) showed the worst DFS. Conclusions: In young patients with HER2-negative BC and germline BRCA1/2 PVs, HER2-low disease was less frequent than expected and more frequently linked to BRCA2 PVs and associated with luminal-like disease. HER2-low status was associated with a modestly improved prognosis

Characteristics and clinical outcomes of breast cancer in young BRCA carriers according to tumor histology

Background: Young women with breast cancer (BC) have an increased chance of carrying germline BRCA pathogenic variants (PVs). Limited data exist on the prognostic impact of tumor histology (i.e. ductal versus lobular) in hereditary breast cancer. Methods: This multicenter retrospective cohort study included women aged ≤40 years with early-stage breast cancer diagnosed between January 2000 and December 2020 and known to carry germline PVs in BRCA1/2. Histology was locally assessed in each center. The Kaplan–Meier method and Cox regression analysis were used to assess disease-free survival and overall survival. Results: Of 4628 patients included from 78 centers worldwide, 3969 (86%) had pure ductal, 135 (3%) pure lobular, and 524 (11%) other histologies. Compared with ductal tumors, lobular tumors were more often grade 1/2 (57.7% versus 22.1%), stage III (29.6% versus 18.5%), and luminal A-like (42.2% versus 12.2%). Lobular tumors were more often associated with BRCA2 PVs (71.1% BRCA2), while ductal tumors were more often associated with BRCA1 PVs (65.7% BRCA1). Patients with lobular tumors more often had mastectomy (68.9% versus 58.3%), and less often received chemotherapy (83.7% versus 92.9%). With a median follow-up of 7.8 years, no significant differences were observed in disease-free survival (adjusted hazard ratio 1.01, 95% confidence interval 0.74-1.37) or overall survival (hazard ratio 0.96, 95% confidence interval 0.62-1.50) between patients with ductal versus lobular tumors. No significant survival differences were observed according to specific BRCA gene, breast cancer subtype, or body mass index. Conclusions: In this large global cohort of young BRCA carriers with breast cancer, the incidence of pure lobular histology was low and associated with higher disease stage at diagnosis, luminal-like disease and BRCA2 PVs. Histology did not appear to impact prognosis