Explicit Calculation Research Articles

Accurate machine learning of rate coefficients for state-to-state transitions in molecular collisions.

We present an algorithm that combines quantum scattering calculations with probabilistic machine-learning models to predict quantum dynamics rate coefficients for a large number of state-to-state transitions in molecule-molecule collisions much faster than with direct solutions of the Schrödinger equation. By utilizing the predictive power of Gaussian process regression with kernels, optimized to make accurate predictions outside of the input parameter space, the present strategy reduces the computational cost by about 75%, with an accuracy within 5%. Our method uses temperature dependences of rate coefficients for transitions from the isolated states of initial rotational angular momentum j, determined via explicit calculations, to predict the temperature dependences of rate coefficients for other values of j. The approach, demonstrated here for rovibrational transitions of SiO due to thermal collisions with H2, uses different prediction models and is thus adaptive to various time and accuracy requirements. The procedure outlined in this work can be used to extend multiple inelastic molecular collision databases without exponentially large computational resources required for conventional rigorous quantum dynamics calculations.

Replica wormholes and entanglement islands in the Karch-Randall braneworld

The Karch-Randall braneworld provides a natural set-up to study the Hawking radiation from a black hole using holographic tools. Such a black hole lives on a brane and is highly quantum yet has a holographic dual as a higher dimensional classical theory that lives in the ambient space. Moreover, such a black hole is coupled to a nongravitational bath which is absorbing its Hawking radiation. This allows us to compute the entropy of the Hawking radiation by studying the bath using the quantum extremal surface prescription. The quantum extremal surface geometrizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface in time from connecting different portions of the bath to the one connecting the bath and the brane gives the Page curve of the Hawking radiation that is consistent with unitarity. Nevertheless, there doesn’t exit a derivation of the quantum extremal surface prescription and its geometrization in the Karch-Randall braneworld. In this paper, we fill this gap. We mainly focus on the case that the ambient space is (2+1)-dimensional for which explicit computations can be done in each description of the set-up. We show that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of the replica wormhole on the Karch-Randall brane as the dominant contribution to the replica path integral. For higher dimensional situations, we show that the geometry of the brane satisfies Einstein’s equation coupled with conformal matter. We comment on possible implications to the general rule of gravitational path integral from this equation.

Bayesian technique to combine independently-trained machine-learning models applied to direct dark matter detection

We carry out a Bayesian analysis of dark matter (DM) direct detection data to determine particle model parameters using the Truncated Marginal Neural Ratio Estimation (TMNRE) machine learning technique. TMNRE avoids an explicit calculation of the likelihood, which instead is estimated from simulated data, unlike in traditional Markov Chain Monte Carlo (MCMC) algorithms. This considerably speeds up, by several orders of magnitude, the computation of the posterior distributions, which allows to perform the Bayesian analysis of an otherwise computationally prohibitive number of benchmark points. In this article we demonstrate that, in the TMNRE framework, it is possible to include, combine, and remove different datasets in a modular fashion, which is fast and simple as there is no need to re-train the machine learning algorithm or to define a combined likelihood. In order to assess the performance of this method, we consider the case of WIMP DM with spin-dependent and independent interactions with protons and neutrons in a xenon experiment. After validating our results with MCMC, we employ the TMNRE procedure to determine the regions where the DM parameters can be reconstructed. Finally, we present CADDENA, a Python package that implements the modular Bayesian analysis of direct detection experiments described in this work.

Pluripotential homotopy theory

We build free, bigraded bidifferential algebra models for the forms on a complex manifold, with respect to a strong notion of quasi-isomorphism and compatible with the conjugation symmetry. This answers a question of Sullivan. The resulting theory naturally accomodates higher operations involving double primitives. As applications, we obtain various refinements of the homotopy groups, sensitive to the complex structure. Under a simple connectedness assumption, one obtains minimal models which are unique up to isomorphism and allow for explicit computations of the new invariants.

Flow‐Based Electromagnetic Information Recovery for Inaccessible Area and Low‐Resolution Detection

AbstractMetasurfaces are widely applied in various applications, such as none‐line‐of‐sight detection, radar imaging enhancement, and non‐invasive monitoring. However, electromagnetic (EM) information recovery in inaccessible and occluded areas is of great importance to obtain complete EM picture, albeit challenging. Conventional methods to this end typically necessitate specific prior knowledge and suffer from performance degradation due to implicit computation mechanism. Here a flow‐based framework is proposed to facilitate the explicit computation of conditional distribution between the partially accessible EM field and complete EM field. The adjacent distributions in a hierarchical architecture exhibit similarity and seamless convertibility between each other, facilitating a smooth transition without performance degradation. The method is benchmarked through two typical scenarios, i.e., resolution enhancement and field recovery in randomly occluded areas. Even in an entirely unseen scene, the EM information recovery maintains consistence with the ground truth, with maximum error below 10%. The work provides a key advance for EM information recovery in complex real‐world environment, offering fresh insights on information access and detection even in extreme cases.

Connection Matrices on the Siegel-Jacobi Upper Half Space and Extended Siegel-Jacobi Upper Half Space

" The inverse of the metric matrices on the Siegel-Jacobi upper half space XJn , invariant to the restricted real Jacobi group GJn (R)0 and extended Siegel-Jacobi XJn upper half space, invariant to the action of the real Jacobi GJ n(R), are presented. The results are relevant for Berezin quantization of the manifolds XJn and X˜Jn . Explicit calculations in the case n = 2 are given."

Magnetically modulated superconductor-graphene-superconductor (SGS) Josephson junctions and their tunability

Abstract Graphene-based Josephson junctions \cite{Heersche2007, Du2008, Popinciuc2012, Mizuno2013, Efetov2016, bretheau2017, Borzenets2016} played an important role in various quantum devices from their inception. 
 Magnetic tunnel junctions or vertical devices \cite{Cobas2012, Meng2013,Chen2013,Huang2024} were also made out of graphene by exposing the graphene layer to localised pattern of strong magnetic field created by hard ferromagnetic material.
 By combining the essence of these different methods for constructing graphene based junctions, in this work we propose that the temperature-dependent Josephson current in such junctions can be tuned 
 by exposing the graphene regions to a combination of highly localised non-uniform magnetic field, dubbed as magnetic barrier, and spatially modulated gate voltage. Within the framework of Dirac-Bogoliubov-de-Gennes (DBDG) theory, we show by explicit calculation 
 that in such magnetically modulated Josephson Junctions, the band structure of graphene gets significantly altered, which results in the change of the Andreev reflections in such junctions. This leads to a significant modulation of the Josephson current. 
 We numerically evaluated the Josephson current as a function of the strength of the magnetic barrier and the gate voltage and discussed the practical consequences of such controlling of Josephson currents

Study of the stability of the linearized compressible Navier-Stokes system

A deep analytic analysis of the stability for the one-dimensional linearized compressible Navier-Stokes system (LNSS) is presented. A very detailed study of the spectrum of the unbounded linear differential operator associated with LNSS has been completed. A Fourier analysis method and an explicit calculation using the eigenvalues of the linear operator make it possible to obtain exponential stability results with a decay rate determined solely according to the parameters of LNSS. Consequently, some exponential stability results are proved in different Hilbert spaces, (in [Formula: see text]-norm and [Formula: see text]-norm). Finally, numerical experiments are presented to verify the theoretical results.

Numerical investigation of the effects of pre-dilatation on paravalvular leakage during transcatheter aortic valve implantation

Abstract Due to promising results, the patient cohort for transcather aortic valve replacement (TAVR) has been extended in recent years to include patients with a bicuspid aortic valve (BAV). There are different types of BAV. One variant is the tricommisural bicuspid aortic valve (TBAV). BAV have an increased risk of post-TAVR complications such as paravalvular leakage. In the case of paravalvular leakage, blood flows past the prosthesis back into the ventricle during diastole. Clinically, patients with BAV are often pre-dilated. For this reason, we want to investigate how pre-dilatation of BAV can affect the leakage rate. A simplified model is used for pre-dilatation, where the calcification nodule is cut along the free edge of the leaflets before the deployment. In order to evaluate the effects of this method, a deployment simulation was carried out for both geometries using an explicit calculation. A flow simulation was then performed to determine the paravalvular leakage. The pre-dilatation allows the leaflets to move independently of each other. Without pre-dilatation, the TAVR cannot fully expanded. The leakage rate is higher for the BAV than for the pre-dilated geometry (53.1mLs−1 vs. 19.4mLs−1). In this model, we have shown the effect of pre-dilatation on implantation results.

The Distributions and Dependences of 3D Particle Morphology Characteristics for Crushed and Natural Sands by X-Ray uCT Investigations.

The morphology of an individual particulate refers to its shape characteristics and size properties, which both play important roles for granular matter in physics, mechanics, chemistry, and biology. In this study, ellipsoidality is defined as a 3D shape index for evaluating particle roundness, and an explicit calculation method is applied. The dependences of 3D shape characteristics (aspect ratios, sphericity, and ellipsoidal degree) on particle size (ranges from 0.063 mm to 5.0 mm) are adequately investigated with the X-ray micro-computed microtomography (uCT) imaging for hundreds of thousands of particles of crushed and natural sands. This study focuses on comparing and evaluating the specific surface area and equivalent diameter, suggesting that particle segregation and changes in surface area may explain the strong dependence of particle shape on size. The correlation between different shape metrics was analyzed by comparing crushed sand with natural sand to provide theoretical support for material filling and mechanical behaviour. The significant differences in the microscale particle size indexes of different sands by single grading are used to provide data references for further analyses of the effect of material microscale on material properties in future discrete element particle simulations.

(Invited) Voltage Controlled First-Principles Simulations of Li Ion Transport at Battery Interfaces Using the Quantum Continuum Approximation (QCA)

Voltage has traditionally been difficult to include in Density Functional Theory (DFT) calculations of electrochemical interfaces which include large semiconducting/insulating sections, as is common in battery applications with the Solid Electrolyte Interface (SEI). This is due to the limited length scale available for full atomistic treatment with DFT. In this talk, I will outline a novel approach, the Quantum Continuum Approximation (QCA), which self-consistently pairs explicit DFT calculations of relevant interfaces with analytic treatment of the electrostatics within bulk semiconducting/insulating regions such as the SEI. This approach enables electronic voltage to be included within DFT calculations of battery interfaces. I demonstrate this methodology by examining potential barriers to Li transport within the Solid Electrolyte Interphase (SEI) in Li-ion batteries, demonstrating that changing voltages can lead to shifts in diffusion barriers, which make certain paths and SEI chemistries more favorable than would be expected under typically simulated neutral conditions. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525

Element-wise and recursive solutions for the power spectral density of biological stochastic dynamical systems at fixed points

Stochasticity plays a central role in nearly every biological process, and the noise power spectral density (PSD) is a critical tool for understanding variability and information processing in living systems. In steady state, many such processes can be described by stochastic linear time-invariant (LTI) systems driven by Gaussian white noise, whose PSD is a complex rational function of the frequency that can be concisely expressed in terms of their Jacobian, dispersion, and diffusion matrices, fully defining the statistical properties of the system's dynamics at steady state. Here, we arrive at compact, element-wise solutions of the rational function coefficients for the auto- and cross-spectrum that enable the explicit analytical computation of the PSD in dimensions n=2,3,4. We further present a recursive Leverrier-Faddeev-type algorithm for the exact computation of the rational function coefficients. Crucially, both solutions are free of matrix inverses. We illustrate our element-wise and recursive solutions by considering the stochastic dynamics of neural systems models, namely, FitzHugh-Nagumo (n=2), Hindmarsh-Rose (n=3), Wilson-Cowan (n=4), and the stabilized supralinear network (n=22), as well as an evolutionary game-theoretic model with mutations (n=5,31). We extend our approach to derive a recursive method for calculating the coefficients in the power-series expansion of the integrated covariance matrix for interacting spiking neurons modeled as Hawkes processes on arbitrary directed graphs. Published by the American Physical Society 2024

Rate coefficients for C and O2 reactive collisions relevant to interstellar clouds from QCT and machine learning.

The chemical reactions between certain interstellar molecules are exothermic in nature and barrierless in the entrance channel, allowing these reactions to occur rapidly even at low astronomical temperatures, e.g., C and O2 interaction. Obtaining detailed rovibrational transition parameters for the reaction between C and O2, such as state-selected rate coefficients, is crucial for studying the associated atmospheric and astronomical environments. Hence, this work presents an approach that combines quasi-classical trajectory calculations with machine learning techniques based on Neural Network (NN) and Gaussian Process Regression (GPR) to determine state-selected rate coefficients. Employing this approach, we significantly reduced the computational requirements while simultaneously obtaining the accurate state-selected reaction cross sections and rate coefficients for the collision of C and O2. Both the NN-based and GPR-based models established in this work accurately predict the results calculated from explicit numerical calculations in the explored temperature range of 50-1500K, achieving a coefficient of determination R2 > 0.96. Most importantly, the current work provides the most comprehensive dataset of rovibrational rate coefficients of v = 0-4, j = 0-70 → v' = 0-15 for the astrophysical modeling of the C-O2 collision system.

Optimizing marked power spectra for cosmology

ABSTRACT Marked power spectra provide a computationally efficient way to extract non-Gaussian information from the matter density field using the usual analysis tools developed for the power spectrum without the need for explicit calculation of higher-order correlators. In this work, we explore the optimal form of the mark function used for re-weighting the density field, to maximally constrain cosmology. We show that adding to the mark function or multiplying it by a constant leads to no additional information gain, which significantly reduces our search space for optimal marks. We quantify the information gain of this optimal function and compare it against mark functions previously proposed in the literature. We find that we can gain around $\sim 2$ times smaller errors in $\sigma _8$ and $\sim 4$ times smaller errors in $\Omega _\mathrm{m}$ compared to using the traditional power spectrum alone, an improvement of $\sim 60~{{\ \rm per\ cent}}$ compared to other proposed marks when applied to the same data set.

Conformal field theories in a magnetic field

We study the properties of 2+1d conformal field theories (CFTs) in a background magnetic field. Using generalized particle-vortex duality, we argue that in many cases of interest the theory becomes gapped, which allows us to make a number of predictions for the magnetic response, background monopole operators, and more. Explicit calculations at large N for Wilson-Fisher and Gross-Neveu CFTs support our claim, and yield the spectrum of background (defect) monopole operators. Finally, we point out that other possibilities exist: certain CFTs can become metallic in a magnetic field. Such a scenario occurs, for example, with a Dirac fermion coupled to a Chern-Simons gauge field, where a non-Fermi liquid is argued to emerge. Published by the American Physical Society 2024

Flavor factorization at two-loops

Recently, a factorization theorem was proposed for partonic flavor evolution as defined by the net flavor of the Winner-Take-All axis of a jet. We validate the factorization theorem through explicit calculation at two-loop order, and in the process extract all anomalous dimensions and renormalization factors for any ultraviolet-to-infrared flavor transition at this order. These results can then be used to extract the renormalized hard function for flavored jet production at next-to-next-to-leading order for any process of interest.

Relational Lorentzian Asymptotically Safe Quantum Gravity: Showcase Model

In a recent contribution, we identified possible points of contact between the asymptotically safe and canonical approaches to quantum gravity. The idea is to start from the reduced phase space (often called relational) formulation of canonical quantum gravity, which provides a reduced (or physical) Hamiltonian for the true (observable) degrees of freedom. The resulting reduced phase space is then canonically quantized, and one can construct the generating functional of time-ordered Wightman (i.e., Feynman) or Schwinger distributions, respectively, from the corresponding time-translation unitary group or contraction semigroup, respectively, as a path integral. For the unitary choice, that path integral can be rewritten in terms of the Lorentzian Einstein–Hilbert action plus observable matter action and a ghost action. The ghost action depends on the Hilbert space representation chosen for the canonical quantization and a reduction term that encodes the reduction of the full phase space to the phase space of observables. This path integral can then be treated with the methods of asymptotically safe quantum gravity in its Lorentzian version. We also exemplified the procedure using a concrete, minimalistic example, namely Einstein–Klein–Gordon theory, with as many neutral and massless scalar fields as there are spacetime dimensions. However, no explicit calculations were performed. In this paper, we fill in the missing steps. Particular care is needed due to the necessary switch to Lorentzian signature, which has a strong impact on the convergence of “heat” kernel time integrals in the heat kernel expansion of the trace involved in the Wetterich equation and which requires different cut-off functions than in the Euclidian version. As usual we truncate at relatively low order and derive and solve the resulting flow equations in that approximation.

Computational approaches and the epistemology of scholarly editing

AbstractDigital Scholarly Editing has followed a fundamentally conservative model over the last forty years. As a result, the epistemological advantages of digital possibilities have not yet been fully explored. The current article proposes that alternative models for editions (e.g. graphs) provide new conceptual and practical opportunities, importantly moving scholarly editing from a static result-oriented practice towards a dynamic knowledge process oriented one. By means of a concrete example, which uses the glyph as its key building block, we suggest that part of the reasoning in the constitution of digital scholarly editions will shift from implicit in the scholar to explicit in forms of code and explicit analysis, calculation, reasoning and logic, and that this will necessarily have significant implications for the nature of authority, the requirement for transparency, the operationalisation of workflow and, ultimately, the very nature and conceptualising of the works that we study.

Trading Place for Space: Increasing Location Resolution Reduces Contextual Capacity in Hippocampal Codes.

Many animals learn cognitive maps of their environment - a simultaneous representation of context, experience, and position. Place cells in the hippocampus, named for their explicit encoding of position, are believed to be a neural substrate of these maps, with place cell "remapping" explaining how this system can represent different contexts. Briefly, place cells alter their firing properties, or "remap", in response to changes in experiential or sensory cues. Substantial sensory changes, produced, e.g., by moving between environments, cause large subpopulations of place cells to change their tuning entirely. While many studies have looked at the physiological basis of remapping, we lack explicit calculations of how the contextual capacity of the place cell system changes as a function of place field firing properties. Here, we propose a geometric approach to understanding population level activity of place cells. Using known firing field statistics, we investigate how changes to place cell firing properties affect the distances between representations of different environments within firing rate space. Using this approach, we find that the number of contexts storable by the hippocampus grows exponentially with the number of place cells, and calculate this exponent for environments of different sizes. We identify a fundamental trade-off between high resolution encoding of position and the number of storable contexts. This trade-off is tuned by place cell width, which might explain the change in firing field scale along the dorsal-ventral axis of the hippocampus. We demonstrate that clustering of place cells near likely points of confusion, such as boundaries, increases the contextual capacity of the place system within our framework and conclude by discussing how our geometric approach could be extended to include other cell types and abstract spaces.

π-π scattering lengths: Electric corrections in the linear sigma model

In the frame of the linear sigma model and working in the weak field approximation, we discuss the role played by an external electric field on the behavior of π-π scattering lengths. For this purpose, we have considered all relevant one-loop diagrams in the s, t, and u channels where we have Schwinger propagators for charged pions. An important novelty of our analysis, compared with previous existing discussions in the literature, is the explicit calculation of box diagrams which were previously not considered in discussions regarding magnetic corrections to π-π scattering lengths. Our analysis shows that electric field corrections have an opposite effect with respect to the previously calculated magnetic corrections.