Search

We study the spontaneous breaking of diffeomorphism invariance using the proper-time non-perturbative flow equation in quantum gravity. In particular, we analyze the structure of the UV critical manifold of conformally reduced Einstein-Hilbert theory and observe the occurrence of a non-trivial minimum for the conformal factor at Planckian energies. We argue that our result can be interpreted as the occurrence of a dynamically generated minimal length in quantum gravity.

We characterize the self-assembly and phase behavior of Janus rods over a broad range of temperatures and volume fractions, using Langevin dynamics simulations and free energy calculations. The Janus rods consist of a line of fused overlapping spheres that interact via a soft-core repulsive potential, with the addition of an attractive pseudo-square-well tail to a fraction of the spheres (the coverage) ranging from 5\% to 100\% of sites. Competition between the stability of liquid crystal phases originating from shape anisotropy and assembly driven by directional interactions gives rise to a rich polymorphism that depends on the coverage. At low density near the Boyle temperature, we observe the formation of spherical and tubular micelles at low coverage, while at higher coverage randomly oriented monolayers form as the attractive parts of the rods overlap. At higher density, bilayer structures appear and merge to form smectic and crystalline lamellar phases. All of these structures gradually become unstable as the temperature is increased until eventually regular nematic and smectic phases appear, consistent with the hard rod limit. Our results indicate that the intermediate regime where shape-entropic effects compete with anisotropic attractions provided by site specificity is rich in structural possibilities, and should help guide the design of rod-like colloids for specific applications., Comment: 13 pages, 13 figures, SI not included

We report on extensive molecular dynamics atomistic simulations of a \textit{meta}-substituted \textit{poly}-phenylacetylene (pPA) foldamer dispersed in three solvents, water \ce{H2O}, cyclohexane \ce{cC6H12}, and \textit{n}-hexane \ce{nC6H14}, and for three oligomer lengths \textit{12mer}, \textit{16mer} and \textit{20mer}. At room temperature, we find a tendency of the pPA foldamer to collapse into a helical structure in all three solvents but with rather different stability character, stable in water, marginally stable in n-hexane, unstable in cyclohexane. In the case of water, the initial and final number of hydrogen bonds of the foldamer with water molecules is found to be unchanged, with no formation of intrachain hydrogen bonding, thus indicating that hydrogen bonding plays no role in the folding process. In all three solvents, the folding is found to be mainly driven by electrostatics, nearly identical in the three cases, and largely dominant compared to van der Waals interactions that are different in the three cases. This scenario is also supported by the analysis of distribution of the bond and dihedral angles and by a direct calculation of the solvation and transfer free energies via thermodynamic integration. The different stability in the case of cyclohexane and n-hexane notwithstanding their rather similar chemical composition can be traced back to the different entropy-enthalpy compensation that is found similar for water and n-hexane, and very different for cyclohexane. A comparison with the same properties for \textit{poly}-phenylalanine oligomers underscores the crucial differences between pPA and peptides. To highlight how these findings can hardly be interpreted in terms of a simple "good" and "poor" solvent picture, a molecular dynamics study of a bead-spring polymer chain in a Lennard-Jones fluid is also included., Comment: 24 pages, 16 Figures, to appear in Soft Matter. Supplementary Material not included

Symmetric Multi-Processing (SMP) based on cache coherency is crucial for high-end embedded systems like automotive applications. RISC-V is gaining traction, and open-source hardware (OSH) platforms offer solutions to issues such as IP costs and vendor dependency. Existing multi-core cache-coherent RISC-V platforms are complex and not efficient for small embedded core clusters. We propose an open-source SystemVerilog implementation of a lightweight snoop-based cache-coherent cluster of Linux-capable CVA6 cores. Our design uses the MOESI protocol via the Arm's AMBA ACE protocol. Evaluated with Splash-3 benchmarks, our solution shows up to 32.87% faster performance in a dual-core setup and an average improvement of 15.8% over OpenPiton. Synthesized using GF 22nm FDSOI technology, the Cache Coherency Unit occupies only 1.6% of the system area., Comment: 4 pages, 4 figures, DSD2024 and SEAA2024 Works in Progress Session AUG 2024; Updated the acknowledgments

We present a lattice model for polymer solutions, explicitly incorporating interactions with solvent molecules and the contribution of vacancies. By exploiting the well-known analogy between polymer systems and the $O(n)$-vector spin model in the limit $n \to 0$, we derive an exact field-theoretic expression for the partition function of the system. The latter is then evaluated at the saddle-point, providing a mean-field estimate of the free energy. The resulting expression, which conforms to the Flory-Huggins type, is then used to analyze the system's stability with respect to phase separation, complemented by a numerical approach based on convex hull evaluation. We demonstrate that this simple lattice model can effectively explain the behavior of polymer systems in explicit solvent, which has been predominantly investigated through numerical simulations. This includes both single-chain systems and polymer solutions. Our findings emphasize the fundamental role of vacancies whose presence, rendering the system a ternary mixture, is a crucial factor in the observed phase behavior., Comment: 7 pages, 4 figures (main); 11 pages, 4 figures (suppl info); submitted for publication

Using Langevin dynamics complemented by Wang-Landau Monte Carlo simulations, we study the phase behavior of single and multiple semiflexible polymer chains in solution under poor-solvent conditions. In the case of a single chain, we obtain the full phase diagram in the temperature-bending rigidity (stiffness) plane and we provide connections with a classical mean field result on a lattice as well as with past results on the same model. At low bending rigidity and upon cooling, we find a second order coil-globule transition, followed by a subsequent first order globule-crystal transition at lower temperatures. The obtained crystals have the shape of a twisted rod whose length increases with the increase of the stiffness of the chain. Above a critical value of the stiffness, we also find a direct first order globule-crystal transition, with the crystal having the form of a twisted toroid. Close to the triple point, we find a region with isoenergetic structures with frequent switching from rods to toroids, with the toroid eventually becoming the only observed stable phase at higher stiffness. The model is then extended to many thermally equilibrated chains in a box and the analogous phase diagram is deduced where the chains are observed to first fold into a globule bundle at low stiffness upon cooling, and then rearrange into a nematic bundle via a nucleation process involving an isotropic-nematic transition. As in the single chain counterpart, above a critical stiffness the chains are observed to undergo a direct transition from a gas of isotropically distributed chains to a nematic bundle as the temperature decreases in agreement with recent suggestions from mean field theory. The consequences of these findings for self-assembly of biopolymers in solutions are discussed., Comment: 59 pages, supporting information; published in Macromolecules (2024)

We define bipartite and monopartite relational networks of chemical elements and compounds using two different datasets of inorganic chemical and material compounds, as well as study their topology. We discover that the connectivity between elements and compounds is distributed exponentially for materials, and with a fat tail for chemicals. Compounds networks show similar distribution of degrees, and feature a highly-connected club due to oxygen. Chemical compounds networks appear more modular than material ones, while the communities detected reveal different dominant elements specific to the topology. We successfully reproduce the connectivity of the empirical chemicals and materials networks by using a family of fitness models, where the fitness values are derived from the abundances of the elements in the aggregate compound data. Our results pave the way towards a relational network-based understanding of the inherent complexity of the vast chemical knowledge atlas, and our methodology can be applied to other systems with the ingredient-composite structure., Comment: main manuscript with 3 Figures, and supplementary information with 8 figures

In this paper, we propose a general bi-objective model for portfolio selection, aiming to maximize both a diversification measure and the portfolio expected return. Within this general framework, we focus on maximizing a diversification measure recently proposed by Choueifaty and Coignard for the case of volatility as a risk measure. We first show that the maximum diversification approach is actually equivalent to the Risk Parity approach using volatility under the assumption of equicorrelated assets. Then, we extend the maximum diversification approach formulated for general risk measures. Finally, we provide explicit formulations of our bi-objective model for different risk measures, such as volatility, Mean Absolute Deviation, Conditional Value-at-Risk, and Expectiles, and we present extensive out-of-sample performance results for the portfolios obtained with our model. The empirical analysis, based on five real-world data sets, shows that the return-diversification approach provides portfolios that tend to outperform the strategies based only on a diversification method or on the classical risk-return approach.

We present a geometrical analysis of the protrusion statistics of side chains in more than 4,000 high-resolution protein structures. We employ a coarse-grained representation of the protein backbone viewed as a linear chain of C{\alpha} atoms and consider just the heavy atoms of the side chains. We study the large variety of behaviors of the amino acids based on both rudimentary structural chemistry as well as geometry. Our geometrical analysis uses a backbone Frenet coordinate system for the common study of all amino acids. Our analysis underscores the richness of the repertoire of amino acids that is available to nature to design protein sequences that fit within the putative native state folds., Comment: 46 pages, 6 figures, 4 tables

We have shown recently that the notion of poking pairwise interactions along a chain provides a unifying framework for understanding the formation of both secondary and the tertiary protein structure based on symmetry and geometry. $\alpha$-helices and $\beta$-sheets are found to be special geometries that have systematic poking contacts in a repetitive manner with the contacts being local along the $\alpha$-helix and non-local along a pair of adjacent strands within a $\beta$-sheet. Pairwise poking interactions also govern tertiary structure formation, but they are weaker and there are no special geometrical constraints as in secondary structure formation. Here we demonstrate that protein turns, the most prevalent non-repetitive structural element in proteins, are instances of local (as in $\alpha$-helices) and isolated (non-repetitive) poking pairwise contacts for which the geometrical constraints are partially relaxed. This simple and purely geometrical definition of protein turns (also sometimes known as reverse turns, $\beta$-turns, $\beta$-bends, hairpin bends, $3_{10}$ bends, kinks, widgets, ...) provides a simple framework for unifying them. We present the results of a systematic analysis and identify their structural classes as well as their respective amino acid preferences., Comment: 67 pages, 17 figures, 2 tables

The phase diagram of hard helices differs from its hard rods counterpart by the presence of chiral "screw" phases stemming from the characteristic helical shape, in addition to the conventional liquid crystal phases also found for rod-like particles. Using extensive Monte Carlo and Molecular Dynamics simulations, we study the effect of the addition of a short-range attractive tail representing solvent-induced interactions to a fraction of the sites forming the hard helices, ranging from a single-site attraction to fully attractive helices for a specific helical shape. Different temperature regimes exist for different fractions of the attractive sites, as assessed in terms of the relative Boyle temperatures, that are found to be rather insensitive to the specific shape of the helical particle. The temperature range probed by the present study is well above the corresponding Boyle temperatures, with the phase behaviour still mainly entropically dominated and with the existence and location of the various liquid crystal phases only marginally affected. The pressure in the equation of state is found to decrease upon increasing the fraction of attractive beads and/or on lowering the temperature at fixed volume fraction, as expected on physical grounds. All screw phases are found to be stable within the considered range of temperatures with the smectic phase becoming more stable on lowering the temperature. By contrast, the location of the transition lines do not display a simple dependence on the fraction of attractive beads in the considered range of temperatures., Comment: 17 pages, 13 figures, JCP in press, SI not included

We study a solution of interacting semiflexible polymers with curvature energy in poor-solvent conditions on the d-dimensional cubic lattice using mean-field theory and Monte Carlo computer simulations. Building upon past studies on a single chain, we construct a field-theory representation of the system and solve it within a mean-field approximation supported by Monte Carlo simulations in d=3. A gas-liquid transition is found in the temperature-density plane that is then interpreted in terms of real systems. Interestingly, we find this transition to be independent of the bending rigidity. Past classical Flory-Huggins and Flory mean-field results are shown to be particular cases of this more general framework. Perspectives in terms of guiding experimental results towards optimal conditions are also proposed., Comment: 19 pages, 10 figures, 3 appendices, accepted for publication

The growing interest in sustainable investing calls for an axiomatic approach to measures of risk and reward that focus not only on financial returns, but also on measures of environmental and social sustainability, i.e. environmental, social, and governance (ESG) scores. We propose definitions for ESG-coherent risk measures and ESG reward-risk ratios based on functions of bivariate random variables that are applied to financial returns and ESG scores, extending the traditional univariate measures to the ESG case. We provide examples and present an empirical analysis in which the ESG-coherent risk measures and ESG reward-risk ratios are used to rank stocks.

Recently, we presented a framework for understanding protein structure based on the idea that simple constructs of holding hands or touching of objects can be used to rationalize the common characteristics of globular proteins. We developed a consistent approach for understanding the formation of the two key common building blocks of helices and sheets as well as the compatible assembly of secondary structures into the tertiary structure through the notion of poking pairwise interactions. Here we benchmark our predictions with a detailed analysis of structural data of over 4000 proteins from the Protein Data Bank. We also present the results of detailed computer simulations of a simplified model demonstrating a pre-sculpted free energy landscape, determined by geometry and symmetry, comprising numerous minima corresponding to putative native state structures. We explore the consequences of our model. Our results suggest that symmetry and geometry are a powerful guide to capture the simplicity underlying protein complexity., Comment: 45 pages, 14 figures

We present a model, based on symmetry and geometry, for proteins. Using elementary ideas from mathematics and physics, we derive the geometries of discrete helices and sheets. We postulate a compatible solvent-mediated emergent pairwise attraction that assembles these building blocks, while respecting their individual symmetries. Instead of seeking to mimic the complexity of proteins, we look for a simple abstraction of reality that yet captures the essence of proteins. We employ analytic calculations and detailed Monte Carlo simulations to explore some consequences of our theory. The predictions of our approach are in accord with experimental data. Our framework provides a rationalization for understanding the common characteristics of proteins. Our results show that the free energy landscape of a globular protein is pre-sculpted at the backbone level, sequences and functionalities evolve in the fixed backdrop of the folds determined by geometry and symmetry, and that protein structures are unique in being simultaneously characterized by stability, diversity, and sensitivity., Comment: 47 pages, 9 figures, 1 table

In this paper, we propose an outlier detection algorithm for multivariate data based on their projections on the directions that maximize the Cumulant Generating Function (CGF). We prove that CGF is a convex function, and we characterize the CGF maximization problem on the unit n-circle as a concave minimization problem. Then, we show that the CGF maximization approach can be interpreted as an extension of the standard principal component technique. Therefore, for validation and testing, we provide a thorough comparison of our methodology with two other projection-based approaches both on artificial and real-world financial data. Finally, we apply our method as an early detector for financial crises.

Using molecular dynamics and thermodynamic integration, we report on the solvation process in water and in cyclohexane of seven polypeptides (GLY, ALA, ILE, ASN, LYS, ARG, GLU). The polypeptides are selected to cover the full hydrophobic scale while varying their chain length from tri- to undeca-homopeptides provide indications on possible non-additivity effects as well as the role of the peptide backbone in the overall stability of the polypeptides. The use of different solvents and different polypeptides allows us to investigate the relation between solvent quality -- the capacity of a given solvent to fold a given biopolymer often described on a scale ranging from "good" to "poor", and solvent polarity -- related to the specific interactions of any solvent with respect to a reference solvent. Undeca-glycine is found to be the only polypeptides to have a proper stable collapse in water (polar solvent), with the other hydrophobic polypetides displaying in water repeated folding and unfolding events and with polar polypeptides presenting a even more complex behavior. By contrast, all polypeptides but none are found to keep an extended conformation in cyclohexane, irrespective of their polarity. All considered polypeptides are also found to have a favorable solvation free energy independently of the solvent polarity and their intrinsic hydrophobicity, clearly highlighting the prominent stabilizing role of the peptide backbone, with the solvation process largely enthalpically dominated in polar polypeptides and partially entropically driven for hydrophobic polypeptides. Our study thus reveals the complexity of the solvation process of polypeptides defying the common view " like dissolves like", with the solute polarity playing the most prominent role. The absence of a mirror symmetry upon the inversion of polarities of both the solvent and the polypeptides is confirmed., Comment: 16 pages, 8 Figures, in press Physical Chemistry Chemical Physics 2023 with Supplementary information https://www.rsc.org/suppdata/d2/cp/d2cp05214h/d2cp05214h1.pdf

The propagation of chirality across scales is a common but poorly understood phenomenon in soft matter. In this work, we use computer simulations to study chiral monolayer assemblies formed by hard rod-like colloidal particles in the presence of non-adsorbing polymer and characterize the thermodynamic driving forces responsible for the twisting. Simulations show that straight (achiral) rods assemble into monolayers with a spontaneous twist that is either left- or right-handed, while helical (chiral) rods lead to assemblies with preferential chiral features that depend on their handedness and curliness. The onset of chirality in these monolayers can be traced back to small clusters formed at the initial stage of the self-assembly. In these microscopic monolayers, entropy drives twisting in ways that differ from the assumptions on which existing continuum theory is built. Depending on the geometry of the constituent rods, the preferred chiral twist can be driven by entropy gain of the polymers, or of the rods, or both. In addition, the variation of the polymer entropy with twist depends on changes in both the surface area and the volume of the monolayer. Rod fluctuations perpendicular to the monolayer also play an important role in stabilising the twisting., Comment: 14 pages, 12 figures

Proteins are the common constituents of all living cells. They are molecular machines that interact with each other as well as with other cell products and carry out a dizzying array of functions with distinction. These interactions follow from their native state structures and therefore understanding sequence-structure relationships is of fundamental importance. What is quite remarkable about proteins is that their understanding necessarily straddles several disciplines. The importance of geometry in defining protein native state structure, the constraints placed on protein behavior by mathematics and physics, the need for proteins to obey the laws of quantum chemistry, and the rich role of evolution and biology all come together in defining protein science. Here we review ideas from the literature and present an interdisciplinary framework that aims to marry ideas from Plato and Darwin and demonstrates an astonishing consilience between disciplines in describing proteins. We discuss the consequences of this framework on protein behavior., Comment: 18 pages; 1 table; 6 figures