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This letter illustrates the opinion of the molecular dynamics (MD) community on the need to adopt a new FAIR paradigm for the use of molecular simulations. It highlights the necessity of a collaborative effort to create, establish, and sustain a database that allows findability, accessibility, interoperability, and reusability of molecular dynamics simulation data. Such a development would democratize the field and significantly improve the impact of MD simulations on life science research. This will transform our working paradigm, pushing the field to a new frontier. We invite you to support our initiative at the MDDB community (https://mddbr.eu/community/)

Electron transfer is at the heart of many fundamental physical, chemical, and biochemical processes essential for life. Exact simulation of reactions in these systems is often hindered by the large number of degrees of freedom and by the essential role of quantum effects. In this work, we experimentally simulate a paradigmatic model of molecular electron transfer using a multi-species trapped-ion crystal, where the donor-acceptor gap, the electronic and vibronic couplings, and the bath relaxation dynamics can all be controlled independently. We employ the ground-state qubit of one ion to simulate the electronic degree of freedom and the optical qubit of another ion to perform reservoir engineering on a collective mode encoding a reaction coordinate. We observe the real-time dynamics of the spin excitation, measuring the transfer rate in several regimes of adiabaticity and relaxation dynamics. The setup allows access to the electron transfer dynamics in the non-perturbative regime, where there is no clear hierarchy among the energy scales in the model, as has been suggested to be optimal for many rate phenomena, including photosynthesis. Our results provide a testing ground for increasingly rich models of molecular excitation transfer processes that are relevant for molecular electronics and light-harvesting systems.

In this paper, we consider functionals related to mean curvature flow in an ambient space which evolves by an extended Ricci flow from the perspective introduced by Lott when studying a mean curvature flow in a Ricci flow background. One of them is a weighted extended version of the Gibbons-Hawking-York action on Riemannian metrics in compact manifolds with boundary. We compute its variational properties from which naturally arise boundary conditions to the analysis of its time-derivative under Perelman's modified extended Ricci flow. For instance, the boundary integrand term provides an extension of Hamilton's differential Harnack expression for mean curvature flows in Euclidean space. We also derive the evolution equations for both the second fundamental form and the mean curvature under mean curvature flow in an extended Ricci flow background. In the special case of gradient solitons to the extended Ricci flow, we discuss mean curvature solitons and establish a Huisken's monotonicity-type formula. We show how to construct a family of mean curvature solitons and establish a characterization of such a family. Also, we show how for constructing examples of mean curvature solitons in an extended Ricci flow background., Comment: 24 pages. Suggestions and comments are welcome

The integration of distributed energy resources (DER) makes active distribution networks (ADNs) natural providers of flexibility services. However, the optimal operation of flexible units in ADNs is highly complex, which poses challenges for distribution system operators (DSOs) in aggregating DER flexibility. For example, to maximise the provision of services, flexible units must be strongly coordinated to manage network constraints, e.g., perform power swaps. Furthermore, due to the nonlinearities of aggregated DER flexibility provision, some units may need to rapidly change their outputs to enable the services. To address these challenges, this paper brings together exact AC optimal power flow (OPF) models and a cooperative game formulation and presents a new framework for tracing, ranking, and valuation of aggregated DER flexibility in ADNs. Extensive tests and simulations performed for the 33-bus radial distribution network demonstrate that the framework enables translating complex DER interactions into useful information for DSOs by ranking the criticality of flexible units and performing flexibility valuation based on its cost or economic surplus. Additionally, the framework proposes no-swap constraints and a nonlinearity metric which can be used by DSOs to identify unreliable operating regions with power swaps or rapid changes in flexible unit dispatch.

In this paper, we obtain eigenvalue estimates for a larger class of elliptic differential operators in divergence form on a bounded domain in a complete Riemannian manifold isometrically immersed in Euclidean space. As an application, we give eigenvalue estimates in the Gaussian shrinking soliton, and we find a domain that makes the behavior of these estimates similar to the estimates for the case of the Laplacian. Moreover, we also give an answer to the generalized conjecture of P\'olya., Comment: Final version which has been accepted for publication in Zeitschrift f\"ur Angewandte Mathematik und Physik

The Notch-Delta signaling pathway mediates cell differentiation implicated in many regulatory processes including spatiotemporal patterning in tissues by promoting alternate cell fates between neighboring cells. At the multicellular level, this "lateral inhibition" principle leads to checkerboard patterns of Sender and Receiver cells. While it is well known that stochasticity modulates cell fate specification, little is known about how stochastic fluctuations at the cellular level propagate during multicell pattern formation. Here, we model stochastic fluctuations in the Notch-Delta pathway in the presence of two different noise types - shot and white - for a multicell system. The results show that intermediate fluctuations reduce disorder and guide the multicell lattice toward more checkerboard like patterns. By further analyzing cell fate transition events, we demonstrate that intermediate noise amplitudes provide enough perturbation to facilitate "proofreading" of disordered patterns and cause cells to switch to their correct ordered state. Conversely, high noise can override environmental signals coming from neighboring cells and lead to switching between ordered and disordered patterns. Therefore, in analogy with spin glass systems, intermediate noise levels allow the multicell Notch system to escape frustrated patterns and relax towards the lower energy checkerboard pattern while at large noise levels the system is unable to find this ordered base of attraction.

Let $\overline{M}^{n+1}$ be a semi-Riemannian manifold of constant sectional curvature, and endowed with a conformal vector field . Consider a Riemannian manifold $M^n$, isometrically immersed into $\overline{M}^{n+1}$. With these hypotheses in mind, the ultimate goal of this paper is to investigate the intimate relationship between conformal vector fields on $\overline{M}^{n+1}$ and the Ricci almost soliton structure on $M^n$. Assuming that the latter manifold is connected and totally umbilic, we prove that it is naturally given a Ricci almost soliton structure by means of the tangential part of a conformal vector field on the ambient manifold. This result is rather general in nature, and few concrete examples are worked out to illustrate its true power. Furthermore, with Tashiro's theorem in mind, we reach the climax of this paper with a classification of a class of Riemannian hypersurfaces that naturally inherit their Ricci almost soliton structure by the existence of a conformal vector field on the ambient manifold., Comment: 21 pages

The T cell arm of the adaptive immune system provides the host protection against unknown pathogens by discriminating between host and foreign material. This discriminatory capability is achieved by the creation of a repertoire of cells each carrying a T cell receptor (TCR) specific to non-self antigens displayed as peptides bound to the major histocompatibility complex (pMHC). The understanding of the dynamics of the adaptive immune system at a repertoire level is complex, due to both the nuanced interaction of a TCR-pMHC pair and to the number of different possible TCR-pMHC pairings, making computationally exact solutions currently unfeasible. To gain some insight into this problem, we study an affinity-based model for TCR-pMHC binding in which a crystal structure is used to generate a distance-based contact map that weights the pairwise amino acid interactions. We find that the TCR-pMHC binding energy distribution strongly depends both on the number of contacts and the repeat structure allowed by the topology of the contact map of choice; this in turn influences T cell recognition probability during negative selection, with higher variances leading to higher survival probabilities. In addition, we quantify the degree to which neoantigens with mutations in sites with higher contacts are recognized at a higher rate., Comment: 10 pages, 4 figures, to be submitted to Physical Review E

This paper proposes a framework to assess the flexibility of active distribution networks (ADNs) via P-Q area segmentation, considering the reliability of flexible units (FUs). A mixed-integer quadratically constrained programming (MIQCP) model is formulated to analyse flexible active and reactive power support at the interface with transmission networks, explicitly capturing the contributions and reliability of FUs that provide flexibility services within an ADN. The numerical simulations performed for a real 124-bus UK distribution network demonstrate the optimal flexibility provision by different FUs, as well as the corresponding reliability and the impact of network reconfiguration. Distribution system operators (DSOs) can use the proposed framework to identify critical units, select an adequate combination of flexibility volumes, and manage its reliability., Comment: Submitted to PSCC 2022, then resubmitted to IEEE PowerTech 2023 conference

We present a spectrum of the planetary nebula M 2-36 obtained using the Ultra Violet and Visual Echelle Spectrograph (UVES) at the Very Large Telescope (VLT). 446 emission lines are detected. We perform an analysis of the chemical composition using multiple electron temperature ($T_{e}$) and density ($n_{e}$) diagnostics. $T_{e}$ and $n_{e}$ are computed using a variety of methods, including collisionally excited line (CEL) ratios, O$^{++}$ optical recombination lines (ORLs), and measuring the intensity of the Balmer jump. Besides the classical CEL abundances, we also present robust ionic abundances from ORLs of heavy elements. From CELs and ORLs of O$^{++}$, we obtain a new value for the Abundance Discrepancy Factor (ADF) of this nebula, being ADF(O$^{++})=$ 6.76 $\pm$ 0.50. From all the different line ratios that we study, we find that the object cannot be chemically homogeneous; moreover, we find that two-phased photoionization models are unable to simultaneously reproduce critical \ion{O}{ii} and [\ion{O}{iii}] line ratios. However, we find a three-phased model able to adequately reproduce such ratios. While we consider this to be a toy model, it is able to reproduce the observed temperature and density line diagnostics. Our analysis shows that it is important to study high ADF PNe with high spectral resolution, since its physical and chemical structure may be more complicated than previously thought., Comment: 20 pages, 6 figures. Accepted for publication in MNRAS

In this note, we prove triviality and nonexistence results for gradient Ricci soliton warped metrics. The proofs stem from the construction of gradient Ricci solitons that are realized as warped products, from which we know that the base spaces of these products are Ricci-Hessian type manifolds. We study this latter class of manifolds as the most appropriate setting to prove our results., Comment: 12 pages

With the availability of large datasets and ever-increasing computing power, there has been a growing use of data-driven artificial intelligence systems, which have shown their potential for successful application in diverse areas. However, many of these systems are not able to provide information about the rationale behind their decisions to their users. Lack of understanding of such decisions can be a major drawback, especially in critical domains such as those related to cybersecurity. In light of this problem, in this paper we make three contributions: (i) proposal and discussion of desiderata for the explanation of outputs generated by AI-based cybersecurity systems; (ii) a comparative analysis of approaches in the literature on Explainable Artificial Intelligence (XAI) under the lens of both our desiderata and further dimensions that are typically used for examining XAI approaches; and (iii) a general architecture that can serve as a roadmap for guiding research efforts towards the development of explainable AI-based cybersecurity systems -- at its core, this roadmap proposes combinations of several research lines in a novel way towards tackling the unique challenges that arise in this context.

We show how a Bochner type formula can be used to establish universal inequalities for the eigenvalues of the drifted Cheng-Yau operator on a bounded domain in a pinched Cartan-Hadamard manifold with the Dirichlet boundary condition. In the first theorem, the hyperbolic space case is treated in an independent way. For the more general setting, we first establish a Rauch comparison theorem for the Cheng-Yau operator and two estimates associated with the Bochner type formula for this operator. Next, we get some integral estimates of independent interest. As an application, we compute our universal inequalities. In particular, we obtain the corresponding inequalities for both Cheng-Yau operator and drifted Laplacian cases, and we recover the known inequalities for the Laplacian case. We also obtain a rigidity result for a Cheng-Yau operator on a class of bounded annular domains in a pinched Cartan-Hadamard manifold. In particular, we can use, e.g., the potential function of the Gaussian shrinking soliton to obtain such a rigidity for the Euclidean space case. The fundamental gap conjecture is also addressed in this paper., Comment: In this version, we address the fundamental gap conjecture in a new section of the paper

Cancer cells have the plasticity to adjust their metabolic phenotypes for survival and metastasis. During metastasis, a developmental program known as the epithelial-mesenchymal transition (EMT) plays a critical role. There is extensive cross-talk between metabolism and EMT, but how this leads to coordinated physiological changes is still uncertain. The elusive connection between metabolism and EMT compromises the efficacy of metabolic therapies targeting metastasis. In this review, we aim for clarifying causation between metabolism and EMT based on recent experimental studies and propose integrated theoretical-experimental efforts to better understand the coupled decision-making of metabolism and EMT., Comment: 31 pages, 3 figures

In this paper, we compute universal estimates of eigenvalues of a coupled system of elliptic differential equations in divergence form on a bounded domain in Euclidean space. As an application, we show an interesting case of rigidity inequalities of the eigenvalues of the Laplacian, more precisely, we consider a countable family of bounded domains in Gaussian shrinking soliton that makes the behavior of known estimates of the eigenvalues of the Laplacian invariant by a first-order perturbation of the Laplacian. We also address the Gaussian expanding soliton case in two different settings. We finish with the special case of divergence-free tensors which is closely related to the Cheng-Yau operator., Comment: Final version which has been accepted for publication in Zeitschrift f\"ur Angewandte Mathematik und Physik

Based on the connection between the categorical derivation of classical programs from specifications and the category-theoretic approach to quantum physics, this paper contributes to extending the laws of classical program algebra to quantum programming. This aims at building correct-by-construction quantum circuits to be deployed on quantum devices such as those available at the IBM Q Experience. Quantum circuit reversibility is ensured by minimal complements, extended recursively. Measurements are postponed to the end of such recursive computations, termed "quantamorphisms", thus maximising the quantum effect. Quantamorphisms are classical catamorphisms which, extended to ensure quantum reversibility, implement quantum cycles (vulg. for-loops) and quantum folds on lists. By Kleisli correspondence, quantamorphisms can be written as monadic functional programs with quantum parameters. This enables the use of Haskell, a monadic functional programming language, to perform the experimental work. Such calculated quantum programs prepared in Haskell are pushed through Quipper to the Qiskit interface to IBM Q quantum devices. The generated quantum circuits - often quite large - exhibit the predicted behaviour. However, running them on real quantum devices incurs into a significant amount of errors. As quantum devices are constantly evolving, an increase in reliability is likely in the near future, allowing for our programs to run more accurately., Comment: 18 pages

Stem cells can precisely and robustly undergo cellular differentiation and lineage commitment, referred to as stemness. However, how the gene network underlying stemness regulation reliably specifies cell fates is not well understood. To address this question, we applied a recently developed computational method, Random Circuit Perturbation (RACIPE), to a nine-component gene regulatory network (GRN) governing stemness, from which we identified fifteen robust gene states. Among them, four out of the five most probable gene states exhibit gene expression patterns observed in single mouse embryonic cells at 32-cell and 64-cell stages. These gene states can be robustly predicted by the stemness GRN but not by randomized versions of the stemness GRN. Strikingly, we found a hierarchical structure of the GRN with the Oct4/Cdx2 motif functioning as the first decision-making module followed by Gata6/Nanog. We propose that stem cell populations, instead of being viewed as all having a specific cellular state, can be regarded as a heterogeneous mixture including cells in various states. Upon perturbations by external signals, stem cells lose the capacity to access certain cellular states, thereby becoming differentiated. The findings demonstrate that the functions of the stemness GRN is mainly determined by its well-evolved network topology rather than by detailed kinetic parameters., Comment: 28 pages, 8 figures

Cancer cells can acquire a spectrum of stable hybrid epithelial/mesenchymal (E/M) states during epithelial-mesenchymal transition (EMT). Cells in these hybrid E/M phenotypes often combine epithelial and mesenchymal features and tend to migrate collectively commonly as small clusters. Such collectively migrating cancer cells play a pivotal role in seeding metastases and their presence in cancer patients indicates an adverse prognostic factor. Moreover, cancer cells in hybrid E/M phenotypes tend to be more associated with stemness which endows them with tumor-initiation ability and therapy resistance. Most recently, cells undergoing EMT have been shown to promote immune suppression for better survival. A systematic understanding of the emergence of hybrid E/M phenotypes and the connection of EMT with stemness and immune suppression would contribute to more effective therapeutic strategies. In this review, we first discuss recent efforts combining theoretical and experimental approaches to elucidate mechanisms underlying EMT multi-stability (i.e. the existence of multiple stable phenotypes during EMT) and the properties of hybrid E/M phenotypes. Following we discuss non-cell-autonomous regulation of EMT by cell cooperation and extracellular matrix. Afterwards, we discuss various metrics that can be used to quantify EMT spectrum. We further describe possible mechanisms underlying the formation of clusters of circulating tumor cells. Last but not least, we summarize recent systems biology analysis of the role of EMT in the acquisition of stemness and immune suppression., Comment: 50 pages, 6 figures