Determining whether two graphs are structurally identical is a fundamental problem with applications spanning mathematics, computer science, chemistry, and network science. Despite decades of study, graph isomorphism remains a challenging algorithmic task, particularly for highly symmetric structures. Here we introduce a new algorithmic approach based on ideas from spectral graph theory and geometry that constructs candidate correspondences between vertices using their curvatures. Any correspondence produced by the algorithm is explicitly verified, ensuring that non-isomorphic graphs are never incorrectly identified as isomorphic. Although the method does not yet guarantee success on all isomorphic inputs, we find that it correctly resolves every instance tested in deterministic polynomial time, including a broad collection of graphs known to be difficult for classical spectral techniques. These results demonstrate that enriched spectral methods can be far more powerful than previously understood, and suggest a promising direction for the practical resolution of the complexity of the graph isomorphism problem.
Franco Pellegrini, Stefano de Gironcoli, Emine Küçükbenli
We propose a new descriptor for local atomic environments, to be used in combination with machine learning models for the construction of interatomic potentials. The Local Atomic Tensors Trainable Expansion (LATTE) allows for the efficient construction of a variable number of many-body terms with learnable parameters, resulting in a descriptor that is efficient, expressive, and can be scaled to suit different accuracy and computational cost requirements. We compare this new descriptor to existing ones on several systems, showing it to be competitive with very fast potentials at one end of the spectrum, and extensible to an accuracy close to the state of the art.
Amirhossein Rezaei, Mahmood Hasani, Alireza Rezaei
et al.
In this study, we present a novel analytical approach to solving large-scale Ising problems by reformulating the discrete Ising Hamiltonian into a continuous framework. This transformation enables us to derive exact solutions for a non-trivial class of fully connected Ising models. To validate our method, we conducted numerical experiments comparing our analytical solutions with those obtained from a quantum-inspired Ising algorithm and a quantum Ising machine. The results demonstrate that the quantum-inspired algorithm and brute-force method successfully align with our solutions, while the quantum Ising machine exhibits notable deviations. Our method offers promising avenues for analytically solving diverse Ising problem instances, while the class of Ising problems addressed here provides a robust framework for assessing the fidelity of Ising machines.
The Ornstein-Zernike (OZ) equation is the fundamental equation for pair correlation function computations in the modern integral equation theory for liquids. In this work, machine learning models, notably physics-informed neural networks and physics-informed neural operator networks, are explored to solve the OZ equation. The physics-informed machine learning models demonstrate great accuracy and high efficiency in solving the forward and inverse OZ problems of various bulk fluids. The results highlight the significant potential of physics-informed machine learning for applications in thermodynamic state theory.
This paper investigates subcycling of particle orbits in variational, geometric particle-in-cell methods addressing the Vlasov--Maxwell system in magnetized plasmas. The purpose of subcycling is to allow different time steps for different particle species and, ideally, time steps longer than the electron gyroperiod for the global field solves while sampling the local cyclotron orbits accurately. The considered algorithms retain the electromagnetic gauge invariance of the discrete action, guaranteeing a local charge conservation law, while the variational approach provides a bounded long-time energy behavior.
Christos Kotsalos, Karim Zouaoui Boudjeltia, Ritabrata Dutta
et al.
The transport of platelets in blood is commonly assumed to obey an advection-diffusion equation. Here we propose a disruptive view, by showing that the random part of their velocity is governed by a fat-tailed probability distribution, usually referred to as a Lévy flight. Although for small spatio-temporal scales, it is hard to distinguish it from the generally accepted "red blood cell enhanced" Brownian motion, for larger systems this effect is dramatic as the standard approach may underestimate the flux of platelets by several orders of magnitude, compromising in particular the validity of current platelet function tests.
We propose a method to extend the fast on-the-fly weight determination scheme for simulated tempering to two-dimensional space including not only temperature but also pressure. During the simulated tempering simulation, weight parameters for temperature-update and pressure-update are self-updated independently according to the trapezoidal rule. In order to test the effectiveness of the algorithm, we applied our proposed method to a peptide, chignolin, in explicit water. After setting all weight parameters to zero, the weight parameters were quickly determined during the simulation. The simulation realised a uniform random walk in the entire temperature-pressure space.
With the identification of two distinct classes of high affinity, physiologically relevant, ligands for PH domains, it appears reasonable to assume that additional specific high affinity ligands for other PH domains will be identified in the future. It is not clear, however, whether each of the 90 proposed PH domains will have its own specific ligand. Possible candidates for specific PH domain ligands include various inositol polyphosphates, phosphorylated membrane components, as well as specific protein sequences containing phosphorylated tyrosine, serine, threonine, or histidine residues. It appears unlikely that the low affinity interactions of phosphoinositides described for several PH domains are physiologically relevant. It is difficult to imagine why such a large and diverse family of PH domains (with just 10-15% sequence identity) would exist in order to bind with a similar low affinity to PtdInsP2-containing membranes. Rather, we suggest that these interactions represent limited binding to noncognate ligands - the physiologically relevant ligands have yet to be identified. It is likely that many, if not all, PH domains have their own high affinity, cell membrane-associated, ligands and operate according to the paradigms described for the PH domains of PLCδ1 and Shc (Figure 2Figure 2A and Figure 2Figure 2B). The structural homology between PH domains might reflect a particularly stable protein scaffold of β sheets that can present variable ligand-binding loops in a manner analogous to that seen in the immunoglobulin superfamily.
The electronic absorption spectrum, susceptibility to fluoride inhibition, redox potential, and substrate turnover of several fungal laccases have been explored as a function of pH. The laccases showed a single spectrally detectable acid-base transition at pH 6-9 and a fluoride inhibition that diminished by increased pH (indicating a competition with hydroxide inhibition). Relatively small changes in the redox potentials (≤0.1 V) of laccase were observed over the pH 2.7-11. Under the catalysis of laccase, the apparent oxidation rates (kcat and kcat/Km) of two nonphenolic substrates, potassium ferrocyanide and 2,2′-azinobis-(3-ethylbenzthiazoline-6-sulfonic acid),decreased monotonically as the pH increased. In contrast, the apparent oxidation rates (kcat and kcat/Km) of three 2,6-dimethoxyphenols (whose pKa values range from 7.0 to 8.7) exhibited bell-shaped pH profiles whose maxima were distinct for each laccase but independent of the substrate. By correlating these pH dependences, it is proposed that the balance of two opposing effects, one generated by the redox potential difference between a reducing substrate and the type 1 copper of laccase (which correlates to the electron transfer rate and is favored for a phenolic substrate by higher pH) and another generated by the binding of a hydroxide anion to the type 2/type 3 coppers of laccase (which inhibits the activity at higher pH), contributes to the pH activity profile of the fungal laccases.
Engineered biomedical nanoparticles (NP) administered via intravenous routes are prone to associate to serum proteins. The protein corona can mask the NP surface functionalization and hamper the delivery of the NP to its biological target. The design of corona-free NPs relies on our understanding of the chemical-physical features of the NP surface driving the interaction with serum proteins. Here we address, by computational means, the interaction between human serum albumin (HSA) and a prototypical monolayer-protected Au nanoparticle. We show that both the chemical composition (charge, hydrophobicity) and the conformational preferences of the ligands decorating the NP surface affect the NP propensity to bind HSA.
Human serum albumin (HSA) is a protein of 66.5 kDa that is composed of three homologous domains, each of which displays specific structural and functional characteristics. HSA is known to undergo different pH-dependent structural transitions, the N-F and F-E transitions in the acid pH region and the N-B transition at slightly alkaline pH. In order to elucidate the structural behavior of the recombinant HSA domains as stand-alone proteins and to investigate the molecular and structural origins of the pH-induced conformational changes of the intact molecule, we have employed fluorescence and circular dichroic methods. Here we provide evidence that the loosening of the HSA structure in the N-F transition takes place primarily in HSA-DOM III and that HSA-DOM I undergoes a structural rearrangement with only minor changes in secondary structure, whereas HSA-DOM II transforms to a molten globule-like state as the pH is reduced. In the pH region of the N-B transition of HSA, HSA-DOM I and HSA-DOM II experience a tertiary structural isomerization, whereas with HSA-DOM III no alterations in tertiary structure are observed, as judged from near-UV CD and fluorescence measurements.
The finite difference time domain (FDTD) method has been successfully applied to obtain energies and wave functions for two electrons in a quantum dot modeled by a three dimensional harmonic potential. The FDTD method uses the time-dependent Schrödinger equation (TDSE) in imaginary time. The TDSE is numerically solved with an initial random wave function and after enough simulation time, the wave function converges to the ground state wave function. The excited states are determined by using the same procedure for the ground state with additional constraints that the wave function must be orthogonal with all lower energy wave functions. The numerical results for energies and wave functions for different parameters of confinement potentials are given and compared with published results using other numerical methods. It is shown that the FDTD method gives accurate energies and wave functions.