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In this proceedings article we survey the results in [5] and their motivation, as presented at the 50th Journ\'ees EDP 2024. With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality of a family of generalized Riemann's non-differentiable functions. These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow, the classical model for vortex filaments dynamics. We explain how we determined their spectrum of singularities through a careful design of Diophantine sets, which we study by using the Duffin-Schaeffer theorem and the Mass Transference Principle.

The structural and chemical properties of metal nanoparticles are often dictated by their interactions with molecular ligand shells. These interactions are highly material-specific and can vary significantly even among elements within the same group or materials with similar crystal structure. Precise characterization of ligand-metal interactions is crucial for the rational design of ligands and the functionalization of nanoparticles. In this study, we found that the ligation behavior with m-terphenyl isocyanide molecule differs significantly between Au and Ag nanoparticles, with distinct ligand extraction efficiencies and size dependencies. Surface-enhanced Raman spectroscopy measurements revealed unique enhancement factors for two molecular vibrational modes between two metal surfaces, indicating different ligand binding geometries. Molecular-level characterization using scanning tunneling microscopy allowed us to directly visualize these variations between Ag and Au surfaces, which we assign as two distinct binding mechanisms. This molecular-scale visualization provides clear insights into the different ligand-metal interactions, as well as the chemical behavior and spectroscopic characteristics of isocyanide-functionalized nanoparticles.

Several long-period binaries with a carbon-rich Wolf-Rayet star and an O star produce dust in their wind collisions. In eccentric binaries, this is seen most strongly near periastron passage. The exact conditions leading to dust creation require orbital properties to be determined, which is difficult owing to their long periods. Recently, the binary system WR 125 (WC7+O9III) began a dust creation episode seen through an infrared outburst first detected by NEOWISE-R, which was the first outburst detected since 1991. We present new near- and mid-infrared photometry, which we use to show consistency between the two outbursts and derive an orbital period of 28.12$^{+0.10}_{-0.05}$ yr. We use a long time-series of optical spectra to place the first constraints on its orbital elements, on the assumption that this system will produce dust near periastron. The orbit has a mild eccentricity of 0.29$\pm$0.12 and is only derived for the Wolf-Rayet component, as the O star's radial velocities have noise that is likely larger than the expected semi-amplitude of the orbit. We also present SOFIA/FORCAST grism spectroscopy to examine the infrared spectral energy distribution (SED) of the dust during this outburst, comparing its properties to other WCd binaries, deriving a dust temperature of 580 K in 2021. This collection of observations will allow us to plan future observations of this system and place the system in the context of dust-creating Wolf-Rayet binaries., Comment: accepted to ApJ

Virtual screening is a technique used in drug discovery to select the most promising molecules to test in a lab. To perform virtual screening, we need a large set of molecules as input, and storing these molecules can become an issue. In fact, extreme-scale high-throughput virtual screening applications require a big dataset of input molecules and produce an even bigger dataset as output. These molecules' databases occupy tens of TB of storage space, and domain experts frequently sample a small portion of this data. In this context, SMILES is a popular data format for storing large sets of molecules since it requires significantly less space to represent molecules than other formats (e.g., MOL2, SDF). This paper proposes an efficient dictionary-based approach to compress SMILES-based datasets. This approach takes advantage of domain knowledge to provide a readable output with separable SMILES, enabling random access. We examine the benefits of storing these datasets using ZSMILES to reduce the cold storage footprint in HPC systems. The main contributions concern a custom dictionary-based approach and a data pre-processing step. From experimental results, we can notice how ZSMILES leverage domain knowledge to compress x1.13 more than state of the art in similar scenarios and up to $0.29$ compression ratio. We tested a CUDA version of ZSMILES targetting NVIDIA's GPUs, showing a potential speedup of 7x.

With the aim of quantifying turbulent behaviors of vortex filaments, we study the multifractality and intermittency of the family of generalized Riemann's non-differentiable functions \begin{equation} R_{x_0}(t) = \sum_{n \neq 0} \frac{e^{2\pi i ( n^2 t + n x_0 ) } }{n^2}, \qquad x_0 \in [0,1]. \end{equation} These functions represent, in a certain limit, the trajectory of regular polygonal vortex filaments that evolve according to the binormal flow. When $x_0$ is rational, we show that $R_{x_0}$ is multifractal and intermittent by completely determining the spectrum of singularities of $R_{x_0}$ and computing the $L^p$ norms of its Fourier high-pass filters, which are analogues of structure functions. We prove that $R_{x_0}$ has a multifractal behavior also when $x_0$ is irrational. The proofs rely on a careful design of Diophantine sets that depend on $x_0$, which we study by crucially using the Duffin-Schaeffer theorem and the Mass Transference Principle., Comment: 43 pages, 3 figures. v2: Introduction rewritten. Overview rewritten in Section 2. Appendix B added. v3: Small corrections

We consider the 2D incompressible Euler equation on a bounded simply connected domain $\Omega$. We give sufficient conditions on the domain $\Omega$ so that for all initial vorticity $\omega_0 \in L^{\infty}(\Omega)$ the weak solutions are unique. Our sufficient condition is slightly more general than the condition that $\Omega$ is a $C^{1,\alpha}$ domain for some $\alpha>0$, with its boundary belonging to $H^{3/2}(\mathbb{S}^1)$. As a corollary we prove uniqueness for $C^{1,\alpha}$ domains for $\alpha >1/2$ and for convex domains which are also $C^{1,\alpha}$ domains for some $\alpha >0$. Previously uniqueness for general initial vorticity in $L^{\infty}(\Omega)$ was only known for $C^{1,1}$ domains with possibly a finite number of acute angled corners. The fundamental barrier to proving uniqueness below the $C^{1,1}$ regularity is the fact that for less regular domains, the velocity near the boundary is no longer log-Lipschitz. We overcome this barrier by defining a new change of variable which we then use to define a novel energy functional., Comment: 33 pages, comments welcome

In this note we further discuss the probabilistic scaling introduced by the authors in [21, 22]. In particular we do a case study comparing the stochastic heat equation, the nonlinear wave equation and the nonlinear Schrodinger equation., Comment: Expository paper, 14 pages

Direct imaging of single molecules at nanostructured interfaces is a grand challenge, with potential to enable new, precise material architectures and technologies. Of particular interest are the structural morphology and spectroscopic signatures of the adsorbed molecule, where modern probes are only now being developed with the necessary spatial and energetic resolution to provide detailed information at molecule-surface interface. Here, we directly visualize the binding of individual m-terphenyl isocyanide ligands to a reconstructed Au(111) surface through scanning tunneling microscopy (STM) and inelastic electron tunneling spectroscopy (IETS). The site-dependent steric pressure of the various surface features alters the vibrational fingerprints of the m-terphenyl isocyanides, which is characterized with single-molecule precision through joint experimental and theoretical approaches. This study for the first time provides molecular-level insights into the steric-pressure-enabled surface binding selectivity, as well as its effect on the chemical properties of individual surface-binding ligands.

Today digital revolution is having a dramatic impact on the pharmaceutical industry and the entire healthcare system. The implementation of machine learning, extreme-scale computer simulations, and big data analytics in the drug design and development process offers an excellent opportunity to lower the risk of investment and reduce the time to the patient. Within the LIGATE project, we aim to integrate, extend, and co-design best-in-class European components to design Computer-Aided Drug Design (CADD) solutions exploiting today's high-end supercomputers and tomorrow's Exascale resources, fostering European competitiveness in the field. The proposed LIGATE solution is a fully integrated workflow that enables to deliver the result of a virtual screening campaign for drug discovery with the highest speed along with the highest accuracy. The full automation of the solution and the possibility to run it on multiple supercomputing centers at once permit to run an extreme scale in silico drug discovery campaign in few days to respond promptly for example to a worldwide pandemic crisis., Comment: Paper Accepted to the 20th ACM International Conference on Computing Frontiers (CF'23)

COVID-19 has shown the importance of having a fast response against pandemics. Finding a novel drug is a very long and complex procedure, and it is possible to accelerate the preliminary phases by using computer simulations. In particular, virtual screening is an in-silico phase that is needed to filter a large set of possible drug candidates to a manageable number. This paper presents the implementations and a comparative analysis of two GPU-optimized implementations of a virtual screening algorithm targeting novel GPU architectures. The first adopts a traditional approach that spreads the computation required to evaluate a single molecule across the entire GPU. The second uses a batched approach that exploits the parallel architecture of the GPU to evaluate more molecules in parallel, without considering the latency to process a single molecule. The paper describes the advantages and disadvantages of the proposed solutions, highlighting implementation details that impact the performance. Experimental results highlight the different performance of the two methods on several target molecule databases while running on NVIDIA A100 GPUs. The two implementations have a strong dependency with respect to the data to be processed. For both cases, the performance is improving while reducing the dimension of the target molecules (number of atoms and rotatable bonds). The two methods demonstrated a different behavior with respect to the size of the molecule database to be screened. While the latency one reaches sooner (with fewer molecules) the performance plateau in terms of throughput, the batched one requires a larger set of molecules. However, the performances after the initial transient period are much higher (up to 5x speed-up). Finally, to check the efficiency of both implementations we deeply analyzed their workload characteristics using the instruction roof-line methodology.

We consider the Vlasov equation in any spatial dimension, which has long been known to be an infinite-dimensional Hamiltonian system whose bracket structure is of Lie-Poisson type. In parallel, it is classical that the Vlasov equation is a mean-field limit for a pairwise interacting Newtonian system. Motivated by this knowledge, we provide a rigorous derivation of the Hamiltonian structure of the Vlasov equation, both the Hamiltonian functional and Poisson bracket, directly from the many-body problem. One may view this work as a classical counterpart to arXiv:1908.03847, which provided a rigorous derivation of the Hamiltonian structure of the cubic nonlinear Schr\"odinger equation from the many-body problem for interacting bosons in a certain infinite particle number limit, the first result of its kind. In particular, our work settles a question of Marsden, Morrison, and Weinstein on providing a "statistical basis" for the bracket structure of the Vlasov equation., Comment: 54 pages

We prove the invariance of the Gibbs measure under the dynamics of the three-dimensional cubic wave equation, which is also known as the hyperbolic $\Phi^4_3$-model. This result is the hyperbolic counterpart to seminal works on the parabolic $\Phi^4_3$-model by Hairer '14 and Hairer-Matetski '18. The heart of the matter lies in establishing local in time existence and uniqueness of solutions on the statistical ensemble, which is achieved by using a para-controlled Ansatz for the solution, the analytical framework of the random tensor theory, and the combinatorial molecule estimates. The singularity of the Gibbs measure with respect to the Gaussian free field brings out a new caloric representation of the Gibbs measure and a synergy between the parabolic and hyperbolic theories embodied in the analysis of heat-wave stochastic objects. Furthermore from a purely hyperbolic standpoint our argument relies on key new ingredients that include a hidden cancellation between sextic stochastic objects and a new bilinear random tensor estimate., Comment: Added remarks and corrected typographical errors

In this paper we consider the defocusing Hartree nonlinear Schr\"odinger equations on $\mathbb T^3$ with real valued and even potential $V$ and Fourier multiplier decaying like $|k|^{-\beta}$. By relying on the method of random averaging operators in arXiv:1910.08492, we show that there exists $\frac{1}{2} \ll \beta_0 <1 $ such that for $ \beta > \beta_0 $ we have invariance of the associated Gibbs measure and global existence of strong solutions in its statistical ensemble. In this way we extend Bourgain's seminal result [7] which requires $\beta >2$ in this case., Comment: 46 pages

We consider the 2D incompressible Euler equation on a corner domain $\Omega$ with angle $\nu\pi$ with $\frac{1}{2}<\nu<1$. We prove that if the initial vorticity $\omega_0 \in L^{1}(\Omega)\cap L^{\infty}(\Omega)$ and if $\omega_0$ is non-negative and supported on one side of the angle bisector of the domain, then the weak solutions are unique. This is the first result which proves uniqueness when the velocity is far from Lipschitz and the initial vorticity is nontrivial around the boundary., Comment: 41 pages. Published in Nonlinearity

Abstract. The purpose of this paper is twofold. We introduce the theory of random tensors, which naturally extends the method of random averaging operators in our earlier work arXiv:1910.08492, to study the propagation of randomness under nonlinear dispersive equations. By applying this theory we also solve Conjecture 1.7 in arXiv:1910.08492, and establish almost-sure local well-posedness for semilinear Schr\"{o}dinger equations in spaces that are subcritical in the probabilistic scaling. The solution we find has an explicit expansion in terms of multilinear Gaussians with adapted random tensor coefficients. In the random setting, the probabilistic scaling is the natural scaling for dispersive equations, and is different from the natural scaling for parabolic equations. Our theory, which covers the full subcritical regime in the probabilistic scaling, can be viewed as the dispersive counterpart of the existing parabolic theories (regularity structure, para-controlled calculus and renormalization group techniques).

The stray- and demagnetization tensor field for a homogeneously magnetized tetrahedron is found analytically. The tetrahedron is a special case of four triangular faces with constant magnetization-charge surface density, for which we also determine the tensor field. The tensor field is implemented in the open source micromagnetic and magnetostatic simulation framework MagTense and compared with the obtained magnetic field from an FEM solution, showing excellent agreement. This result is important for modeling magnetostatics in general and for micromagnetism in particular as the demagnetizing field of an arbitrary body discretized using conventional meshing techniques is significantly simplified with this approach., Comment: 5 pages, 4 figures

We consider the defocusing nonlinear Schr\"odinger equation on $\mathbb{T}^2$ with Wick ordered power nonlinearity, and prove almost sure global well-posedness with respect to the associated Gibbs measure. The heart of the matter is the uniqueness of the solution as limit of solutions to canonically truncated systems. The invariance of the Gibbs measure under the global dynamics follows as a consequence. The proof relies on the novel idea of random averaging operators., Comment: 61 pages. [V2] Final version. To appear in Ann. of Math

We consider the cubic Gross-Pitaevskii (GP) hierarchy in one spatial dimension. We establish the existence of an infinite sequence of observables such that the corresponding trace functionals, which we call ``energies,'' commute with respect to the weak Lie-Poisson structure defined by the authors in arXiv:1908.03847. The Hamiltonian equation associated to the third energy functional is precisely the GP hierarchy. The equations of motion corresponding to the remaining energies generalize the well-known nonlinear Schr\"odinger hierarchy, the third element of which is the one-dimensional cubic nonlinear Schr\"odinger equation. This work provides substantial evidence for the GP hierarchy as a new integrable system., Comment: 97 pages

We consider the cubic nonlinear Schr\"odinger equation (NLS) in any spatial dimension, which is a well-known example of an infinite-dimensional Hamiltonian system. Inspired by the knowledge that the NLS is an effective equation for a system of interacting bosons as the particle number tends to infinity, we provide a derivation of the Hamiltonian structure, which is comprised of both a Hamiltonian functional and a weak symplectic structure, for the nonlinear Schr\"odinger equation from quantum many-body systems. Our geometric constructions are based on a quantized version of the Poisson structure introduced by Marsden, Morrison and Weinstein for a system describing the evolution of finitely many indistinguishable classical particles., Comment: 81 pages

We prove local well-posedness for the periodic derivative nonlinear Schrodinger's equation, which is L^2 critical, in Fourier-Lebesgue spaces which scale like H^s(T) for s>0. In particular we close the existing gap in the subcritical theory by improving the result of Grunrock and Herr [25], which established local well-posedness in Fourier-Lebesgue spaces which scale like H^s(T) for s>1 . We achieve this result by a delicate analysis of the structure of the solution and the construction of an adapted nonlinear submanifold of a suitable function space. Together these allow us to construct the unique solution to the given subcritical data. This constructive procedure is inspired by the theory of para-controlled distributions developed by Gubinelli-Imkeller-Perkowski [26] and Cantellier-Chouk [10] in the context of stochastic PDE. Our proof and results however, are purely deterministic.

The drug discovery process involves several tasks to be performed in vivo, in vitro and in silico. Molecular docking is a task typically performed in silico. It aims at finding the three-dimensional pose of a given molecule when it interacts with the target protein binding site. This task is often done for virtual screening a huge set of molecules to find the most promising ones, which will be forwarded to the later stages of the drug discovery process. Given the huge complexity of the problem, molecular docking cannot be solved by exploring the entire space of the ligand poses. State-of-the-art approaches face the problem by sampling the space of the ligand poses to generate results in a reasonable time budget. In this work, we improve the geometric approach to molecular docking by introducing tunable approximations. In particular, we analyzed and enriched the original implementation with tunable software knobs to explore and control the performance-accuracy tradeoffs. We modeled time-to-solution of the virtual screening task as a function of software knobs, input data features, and available computational resources. Therefore, the application can autotune its configuration according to a user-defined time budget. We used a Mini-App derived by LiGenDock - a state-of-the-art molecular docking application - to validate the proposed approach. We run the enhanced Mini-App on an HPC system by using a very large database of pockets and ligands. The proposed approach exposes a time-to-solution interval spanning more than one order of magnitude with accuracy degradation up to 30%, more in general providing different accuracy levels according to the needs of the virtual screening campaign.

The ANTAREX project relies on a Domain Specific Language (DSL) based on Aspect Oriented Programming (AOP) concepts to allow applications to enforce extra functional properties such as energy-efficiency and performance and to optimize Quality of Service (QoS) in an adaptive way. The DSL approach allows the definition of energy-efficiency, performance, and adaptivity strategies as well as their enforcement at runtime through application autotuning and resource and power management. In this paper, we present an overview of the key outcome of the project, the ANTAREX DSL, and some of its capabilities through a number of examples, including how the DSL is applied in the context of the project use cases.

For certain non linear evolution equations, existence of global in time flows for large data is a fundamental and difficult question. In general, for dispersive and wave equations high regularity of the data does not automatically guarantee the existence of a global flow. One first needs to prove a global result at a level of regularity that matches that of a conserved quantity. Then, preservation of regularity allows to prove that the global flow exists for all smoother data. This mechanism cannot be applied in the non deterministic setting, such as the global well-posedness on the statistical ensemble of an invariant (Gibbs) measure, first obtained by Bourgain. We present a new and general technique to prove that data smoother than those in the statistical ensemble give rise to global flows, despite the fact that the measures carried by such smoother data are no longer invariant. As a consequence we close an important gap in the existence of global solutions for certain nonlinear Schr\"odinger equations., Comment: This paper has been withdrawn since the manner in which we state Theorem 3.1 is not correct. Since this carries through the main argument in sections 4 and 5, the paper needs a major revision

In this paper we prove an optimal local well-posedness result for the 1+2 dimensional system of nonlinear wave equations (NLW) with quadratic null-form derivative nonlinearities $Q_{\mu\nu}$. The Cauchy problem for these equations is known to be ill-possed for data in the Sobolev space $H^s$ with $s<5/4$ for all the basic null-forms, except $Q_0$. However, the scaling analysis predicts local well-posedness all the way to the critical regularity of $s_c=1$. Following Gr\"{u}nrock's result for the quadratic derivative NLW, we consider initial data in the Fourier-Lebesgue spaces $\^{H}_s^r$, which coincide with the Sobolev spaces of the same regularity for $r=2$, but scale like lower regularity Sobolev spaces for $11+{1}{r}$, $1

In this paper we show that after suitable data randomization there exists a large set of super-critical periodic initial data, in $H^{-\alpha}({\mathbb T}^d)$ for some $\alpha(d) > 0$, for both 2d and 3d Navier-Stokes equations for which global energy bounds are proved. As a consequence, we obtain almost sure super-critical global weak solutions. We also show that in 2d these global weak solutions are unique., Comment: 22 pages, a revised argument in Section 5, the $d=3$ case

We prove absolute continuity of Gaussian measures associated to complex Brownian bridges under certain gauge transformations. As an application we prove that the invariant measure for the periodic derivative nonlinear Schr\"odinger equation obtained by Nahmod, Oh, Rey-Bellet and Staffilani in [20], and with respect to which they proved almost surely global well-posedness, coincides with the weighted Wiener measure constructed by Thomann and Tzvetkov [24]. Thus, in particular we prove the invariance of the measure constructed in [24]., Comment: 12 pages. Submitted

We prove a T(1) theorem for bilinear singular integral operators (trilinear forms) with a one-dimensional modulation symmetry., Comment: 62 pages, 1 figure

A method based on Maximum-Entropy (ME) principle to infer photon distribution from on/off measurements performed with few and low values of quantum efficiency is addressed. The method consists of two steps: at first some moments of the photon distribution are retrieved from on/off statistics using Maximum-Likelihood estimation, then ME principle is applied to infer the quantum state and, in turn, the photon distribution. Results from simulated experiments on coherent and number states are presented., Comment: 4 figures, to appear in EPJD

We show how to obtain the photon distribution of a single-mode field using only avalanche photodetectors. The method is based on measuring the field at different quantum efficiencies and then inferring the photon distribution by maximum-likelihood estimation. The convergence of the method and its robustness against fluctuations are illustrated by means of numerically simulated experiments., Comment: references added, new figures

We address the propagation of twin-beam of radiation through Gaussian phase-sensitive channels, i.e. noisy channels with squeezed fluctuations. We find that squeezing the environment always reduces the survival time of entanglement in comparison to the case of simple dissipation and thermal noise. We also show that the survival time is further reduced if the squeezing phase of the fluctuations is different from the twin-beam phase., Comment: to be published in the special issue of J. Mod. Opt. (April 2004) edited by R. Bonifacio, B.G. Englert and M.G.A. Paris, devoted to the 2003 Garda Lake Workshop on "Mysteries, Puzzles and Paradoxes in Quantum Mechanics"

Reduction criteria for distillability is applied to general depolarized states and an explicit condition is found in terms of a characteristic polynomial of the density matrix. 3 $\times$ 3 bipartite systems are analyzed in some details., Comment: 5 pages, 1 figure

We address continuous variable quantum teleportation in Gaussian quantum noisy channels, either thermal or squeezed-thermal. We first study the propagation of twin-beam and evaluate a threshold for its separability. We find that the threshold for purely thermal channels is always larger than for squeezed-thermal ones. On the other hand, we show that squeezing the channel improves teleportation of squeezed states and, in particular, we find the class of squeezed states that are better teleported in a given noisy channel. Finally, we find regimes where optimized teleportation of squeezed states improves amplitude-modulated communication in comparison with direct transmission.

Worker rights advocates seeking to improve labor conditions in global supply chains have engaged in private political strategies prompting transnational corporations (TNCs) to adopt codes of conduct and monitor their suppliers for compliance, but it is not clear whether organizational structures established by TNCs to protect their reputations can actually raise labor standards. We extend the literature on private politics and organizational self-regulation by identifying several conditions under which codes and monitoring are more likely to be associated with improvements in supply chain working conditions. We find that suppliers are more likely to improve when they face external compliance pressure in their domestic institutional environment, when their buyers take a cooperative approach to monitoring, and when their auditors are highly trained. We find, further, that a cooperative approach to monitoring enhances the impact of auditor training, and that auditor training has a greater impact on improvement when coupled with a cooperative approach than with external compliance pressures. These findings suggest key considerations that should inform the design and implementation of monitoring strategies aimed at improving conditions in global supply chains as well as theory and empirical research on the organizational outcomes of private political activism for social change.