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Biophysical model fitting plays a key role in obtaining quantitative parameters from physiological signals and images. However, the model complexity for molecular magnetic resonance imaging (MRI) often translates into excessive computation time, which makes clinical use impractical. Here, we present a generic computational approach for solving the parameter extraction inverse problem posed by ordinary differential equation (ODE) modeling coupled with experimental measurement of the system dynamics. This is achieved by formulating a numerical ODE solver to function as a step-wise analytical one, thereby making it compatible with automatic differentiation-based optimization. This enables efficient gradient-based model fitting, and provides a new approach to parameter quantification based on self-supervised learning from a single data observation. The neural-network-based train-by-fit pipeline was used to quantify semisolid magnetization transfer (MT) and chemical exchange saturation transfer (CEST) amide proton exchange parameters in the human brain, in an in-vivo molecular MRI study (n=4). The entire pipeline of the first whole brain quantification was completed in 18.3$\pm$8.3 minutes, which is an order-of-magnitude faster than comparable alternatives. Reusing the single-subject-trained network for inference in new subjects took 1.0$\pm$0.2 s, to provide results in agreement with literature values and scan-specific fit results (Pearson's r>0.98, p<0.0001)., Comment: This project was funded by the European Union (ERC, BabyMagnet, project no. 101115639), the Ministry of Innovation, Science and Technology, Israel, and a grant from the Tel Aviv University Center for AI and Data Science (TAD, The Blavatnik AI and Data Science Fund). None of above can be held responsible for views and opinions expressed, which are those of the authors alone

A multidimensional nonnegative matrix is called polystochastic if the sum of its entries over each line is equal to $1$. The permanent of a multidimensional matrix is the sum of products of entries over all diagonals. We prove that if $d$ is even, then the permanent of a $d$-dimensional polystochastic matrix of order $4$ is positive, and for odd $d$, we give a complete characterization of $d$-dimensional polystochastic matrices with zero permanent., Comment: 17 pages

This paper is concerned with open quantum harmonic oscillators with position-momentum system variables, whose internal dynamics and interaction with the environment are governed by linear quantum stochastic differential equations. A recently proposed approach to such systems as Heisenberg picture quantum memories exploits their ability to approximately retain initial conditions over a decoherence horizon. Using the quantum memory decoherence time defined previously in terms of a fidelity threshold on a weighted mean-square deviation of the system variables from their initial values, we apply this approach to a partially isolated subsystem of the oscillator, which is not directly affected by the external fields. The partial isolation leads to an appropriate system decomposition and a qualitatively different short-horizon asymptotic behaviour of the deviation, which yields a longer decoherence time in the high-fidelity limit. The resulting approximate decoherence time maximization over the energy parameters for improving the quantum memory performance is discussed for a coherent feedback interconnection of such systems., Comment: 9 pages, 3 figures, submitted to ANZCC 2025

We present a comprehensive study of the angular structure functions for Drell-Yan leptons in $Z/\gamma$-boson production within the framework of the transverse momentum dependent (TMD) factorization theorem, including kinematic power corrections (KPCs). We find good agreement with the data in the applicability region of the TMD factorization theorem. The inclusion of KPCs allows us to describe all angular coefficients in a frame-independent manner using only the leading-twist TMD distributions: the unpolarized and the Boer-Mulders functions. The value of the Boer-Mulders function is determined using the ATLAS measurement of the $A_2$ angular coefficient. The analysis is performed at N$^4$LL perturbative order. Additionally, we discuss the technical implementation and impact of KPCs on the phenomenology of TMD distributions., Comment: 43 pages, 14 figures

We address the problem of finite products that attain the joint spectral radius of a finite number of square matrices. Up to date the problem of existence of "forbidden products" remained open. We prove that the product $AABABABB$ (together with its circular shifts and their mirror images) never delivers the strict maximum to the joint spectral radius if we restrict consideration to pairs $\{A,B\}$ of real $2\by 2$ matrices. Under this restriction circular shifts and their mirror images constitute the class of isospectral products and hence they all have the same spectral radius for any pair $\{A,B\}$ of $2\by 2$ matrices, even complex. For pairs of complex matrices we have numerical evidence that $AABABABB$ is still a fobidden product. A couple of binary words that encode products from this isospectral class also happen to be the shortest forbidden patterns in the parametric family of double rotations.

This paper presents a review of the NTIRE 2024 challenge on night photography rendering. The goal of the challenge was to find solutions that process raw camera images taken in nighttime conditions, and thereby produce a photo-quality output images in the standard RGB (sRGB) space. Unlike the previous year's competition, the challenge images were collected with a mobile phone and the speed of algorithms was also measured alongside the quality of their output. To evaluate the results, a sufficient number of viewers were asked to assess the visual quality of the proposed solutions, considering the subjective nature of the task. There were 2 nominations: quality and efficiency. Top 5 solutions in terms of output quality were sorted by evaluation time (see Fig. 1). The top ranking participants' solutions effectively represent the state-of-the-art in nighttime photography rendering. More results can be found at https://nightimaging.org., Comment: 10 pages, 10 figures

Twist-3 collinear parton distribution functions (PDFs) are matrix elements of quark-gluon-quark or three-gluons light-cone operators. They depend on three momentum fraction variables, which are restricted to a hexagon region, and the evolution kernels are defined via two-dimensional convolution in these variables. We present the numerical realisation of the twist-3 evolution equations at leading order in the strong coupling for all kinds of twist-3 PDF (quark, gluon, chiral-even/odd, etc). We provide two independent codes (in C and Fortran) that have been extensively cross-checked, and are ready-to-use. We supplement the paper with a review of known properties of twist-3 PDFs., Comment: 8 figures; 34 pages

The second "Mineral Detection of Neutrinos and Dark Matter" (MDvDM'24) meeting was held January 8-11, 2024 in Arlington, VA, USA, hosted by Virginia Tech's Center for Neutrino Physics. This document collects contributions from this workshop, providing an overview of activities in the field. MDvDM'24 was the second topical workshop dedicated to the emerging field of mineral detection of neutrinos and dark matter, following a meeting hosted by IFPU in Trieste, Italy in October 2022. Mineral detectors have been proposed for a wide variety of applications, including searching for dark matter, measuring various fluxes of astrophysical neutrinos over gigayear timescales, monitoring nuclear reactors, and nuclear disarmament protocols; both as paleo-detectors using natural minerals that could have recorded the traces of nuclear recoils for timescales as long as a billion years and as detectors recording nuclear recoil events on laboratory timescales using natural or artificial minerals. Contributions to this proceedings discuss the vast physics potential, the progress in experimental studies, and the numerous challenges lying ahead on the path towards mineral detection. These include a better understanding of the formation and annealing of recoil defects in crystals; identifying the best classes of minerals and, for paleo-detectors, understanding their geology; modeling and control of the relevant backgrounds; developing, combining, and scaling up imaging and data analysis techniques; and many others. During the last years, MDvDM has grown rapidly and gained attention. Small-scale experimental efforts focused on establishing various microscopic readout techniques are underway at institutions in North America, Europe and Asia. We are looking ahead to an exciting future full of challenges to overcome, surprises to be encountered, and discoveries lying ahead of us., Comment: Summary and proceedings of the MDvDM'24 conference, Jan 8-11 2024

A numerical and analytical study was conducted to investigate the bifurcation mechanisms that cause desynchronization between the soliton repetition frequency and the frequency of external pulsed injection in a Kerr cavity described by the Lugiato-Lefever equation. The results suggest that desynchronization typically occurs through an Andronov-Hopf bifurcation. Additionally, a simple and intuitive criterion for this bifurcation to occur is proposed.

We establish robust relations between Transverse Momentum Dependent distributions (TMDs) and collinear distributions. We define weighted integrals of TMDs that we call Transverse Momentum Moments (TMMs) and prove that TMMs are equal to collinear distributions evaluated in some minimal subtraction scheme. The conversion to the $\bar{MS}$-scheme can be done by a calculable factor, which we derive up to three loops for some cases. We discuss in detail the zeroth, the first, and the second TMMs and provide phenomenological results for them based on the current extractions of TMDs. The results of this paper open new avenues for theoretical and phenomenological investigation of the three-dimensional and collinear hadron structures., Comment: 24 pages, 6 figures

This paper is concerned with a class of multivariable stochastic Hamiltonian systems whose generalised position is related by an ordinary differential equation to the momentum governed by an Ito stochastic differential equation. The latter is driven by a standard Wiener process and involves both conservative and viscous damping forces. With the mass, diffusion and damping matrices being position-dependent, the resulting nonlinear model of Langevin dynamics describes dissipative mechanical systems (possibly with rotational degrees of freedom) or their electromechanical analogues subject to external random forcing. We study the time evolution of the joint position-momentum probability distribution for the system and its convergence to equilibrium by decomposing the Fokker-Planck-Kolmogorov equation (FPKE) and the Kullback-Leibler relative entropy with respect to the invariant measure into those for the position distribution and the momentum distribution conditioned on the position. This decomposition reveals a manifestation of the Barbashin-Krasovskii-LaSalle principle and higher-order dissipation inequalities for the relative entropy as a Lyapunov functional for the FPKE., Comment: 34 pages, 3 figures, 1 table

A new definition of discrete-time negative imaginary (NI) systems is provided. This definition characterizes the dissipative property of a zero-order hold sampled continuous-time NI system. Under some assumptions, asymptotic stability can be guaranteed for the closed-loop interconnection of an NI system and an output strictly negative imaginary system, with one of them having a one step advance. In the case of linear systems, we also provide necessary and sufficient frequency-domain and LMI conditions under which the definition is satisfied. Also provided is a simple DC gain condition for the stability results in the linear case., Comment: 8 pages, 4 figures. 26th International Symposium on Mathematical Theory of Networks and Systems

This paper is concerned with open quantum systems whose dynamic variables have an algebraic structure, similar to that of the Pauli matrices for finite-level systems. The Hamiltonian and the operators of coupling of the system to the external bosonic fields depend linearly on the system variables. The fields are represented by quantum Wiener processes which drive the system dynamics according to a quasilinear Hudson-Parthasarathy quantum stochastic differential equation whose drift vector and dispersion matrix are affine and linear functions of the system variables. This setting includes the zero-Hamiltonian isolated system dynamics as a particular case, where the system variables are constant in time, which makes them potentially applicable as a quantum memory. In a more realistic case of nonvanishing system-field coupling, we define a memory decoherence time when a mean-square deviation of the system variables from their initial values becomes relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the decoherence time maximization over the energy parameters of the system and obtain a condition under which the zero Hamiltonian provides a suboptimal solution. This optimization problem is also discussed for a direct energy coupling interconnection of such systems., Comment: 11 pages, 2 figures. arXiv admin note: text overlap with arXiv:2310.17232

This paper is concerned with open quantum harmonic oscillators (OQHOs) described by linear quantum stochastic differential equations. This framework includes isolated oscillators with zero Hamiltonian, whose system variables remain unchanged (in the Heisenberg picture of quantum dynamics) over the course of time, making such systems potentially applicable as quantum memory devices. In a more realistic case of system-environment coupling, we define a memory decoherence horizon as a typical time for a mean-square deviation of the system variables from their initial values to become relatively significant as specified by a weighting matrix and a fidelity parameter. We consider the maximization of the decoherence time over the energy and coupling matrices of the OQHO as a memory system in its storage phase and obtain a condition under which the zero Hamiltonian delivers a suboptimal solution. This optimization problem is also discussed for an interconnection of OQHOs., Comment: 10 pages, 3 figures

This paper proposes the option-implied Fourier-cosine method, iCOS, for non-parametric estimation of risk-neutral densities, option prices, and option sensitivities. The iCOS method leverages the Fourier-based COS technique, proposed by Fang and Oosterlee (2008), by utilizing the option-implied cosine series coefficients. Notably, this procedure does not rely on any model assumptions about the underlying asset price dynamics, it is fully non-parametric, and it does not involve any numerical optimization. These features make it rather general and computationally appealing. Furthermore, we derive the asymptotic properties of the proposed non-parametric estimators and study their finite-sample behavior in Monte Carlo simulations. Our empirical analysis using S&P 500 index options and Amazon equity options illustrates the effectiveness of the iCOS method in extracting valuable information from option prices under different market conditions. Additionally, we apply our methodology to dissect and quantify observation and discretization errors in the VIX index.

This paper considers a risk-sensitive optimal control problem for a field-mediated interconnection of a quantum plant with a coherent (measurement-free) quantum controller. The plant and the controller are multimode open quantum harmonic oscillators governed by linear quantum stochastic differential equations, which are coupled to each other and driven by multichannel quantum Wiener processes modelling the external bosonic fields. The control objective is to internally stabilize the closed-loop system and minimize the infinite-horizon asymptotic growth rate of a quadratic-exponential functional which penalizes the plant variables and the controller output. We obtain first-order necessary conditions of optimality for this problem by computing the partial Frechet derivatives of the cost functional with respect to the energy and coupling matrices of the controller in frequency domain and state space. An infinitesimal equivalence between the risk-sensitive and weighted coherent quantum LQG control problems is also established. In addition to variational methods, we employ spectral factorizations and infinite cascades of auxiliary classical systems. Their truncations are applicable to numerical optimization algorithms (such as the gradient descent) for coherent quantum risk-sensitive feedback synthesis., Comment: 29 pages, 3 figures

Immunotherapy constitutes a paradigm shift in cancer treatment. Its FDA approval for several indications has yielded improved prognosis for cases where traditional therapy has shown limited efficiencey. However, many patients still fail to benefit from this treatment modality, and the exact mechanisms responsible for tumor response are unknown. Noninvasive treatment monitoring is crucial for longitudinal tumor characterization and the early detection of non-responders. While various medical imaging techniques can provide a morphological picture of the lesion and its surrounding tissue, a molecular-oriented imaging approach holds the key to unraveling biological effects that occur much earlier in the immunotherapy timeline. Magnetic resonance imaging (MRI) is a highly versatile imaging modality, where the image contrast can be tailored to emphasize a particular biophysical property of interest using advanced engineering of the imaging pipeline. In this review, recent advances in molecular-MRI based cancer immunotherapy monitoring are described. Next, the presentation of the underlying physics, computational, and biological features are complemented by a critical analysis of the results obtained in preclinical and clinical studies. Finally, emerging artificial intelligence (AI)-based strategies to further distill, quantify, and interpret the image-based molecular MRI information are discussed in terms of perspectives for the future., Comment: 25 pages, 7 figures

The correlation properties of a random system of densely packed disks, obeying a power-law size distribution, are analyzed in reciprocal space in the thermodynamic limit. This limit assumes that the total number of disks increases infinitely, while the mean density of the disk centers and the range of the size distribution are kept constant. We investigate the structure factor dependence on momentum transfer across various number of disks and extrapolate these findings to the thermodynamic limit. The fractal power-law decay of the structure factor is recovered in reciprocal space within the fractal range, which corresponds to the range of the size distribution in real space. The fractal exponent coincides with the exponent of the power-law size distribution as was shown previously by the authors [A. Yu. Cherny, E. M. Anitas, V. A. Osipov, J. Chem. Phys. 158, 044114 (2023)]. The dependence of the structure factor on density is examined. As is found, the power-law exponent remains unchanged but the fractal range shrinks when the packing fraction decreases. Additionally, the finite-size effects are studied at extremely low momenta of the order of the inverse system size. We show that the structure factor is parabolic in this region and calculate the prefactor analytically. The obtained results reveal fractal-like properties of the packing and can be used to analyze small-angle scattering from such systems., Comment: 8 pages, 7 figures

A neutral delay differential equation (NDDE) model of a Kerr cavity with external coherent injection is developed that can be considered as a generalization of the Ikeda map with second and higher order dispersion being taken into account. It is shown that this model has solutions in the form of dissipative solitons both in the limit, where the model can be reduced to the Lugiato-Lefever equation (LLE), and beyond this limit, where the soliton is eventually destroyed by the Cherenkov radiation. Unlike the standard LLE the NDDE model is able to describe the overlap of multiple resonances associated with different cavity modes., Comment: 9 pages, 9 figures

This work is dedicated to the study of power expansion in the transverse momentum dependent (TMD) factorization theorem. Each genuine term in this expansion gives rise to a series of kinematic power corrections (KPCs). All terms of this series exhibit the same properties as the leading term and share the same nonperturbative content. Among various power corrections, KPCs are especially important since they restore charge conservation and frame invariance, which are violated at a fixed power order. I derive and sum a series of KPCs associated with the leading-power term of the TMD factorization theorem. The resulting expression resembles a hadronic tensor computed with free massless quarks while still satisfying a proven factorization statement. Additionally, I provide an explicit check of this novel form of factorization theorem at the next-to-leading order (NLO) and demonstrate the restoration of the frame-invariant argument of the leading-power coefficient function. Numerical estimations show that incorporating the summed KPCs into the cross-section leads to an almost constant shift, which may help to explain the observed challenges in the TMD phenomenology., Comment: 35 pages, 4 figures; ver.2, corrections of misprints

Ti and Cr beryllides are materials of potential importance as neutron multipliers for tritium breeding in nuclear fusion reactors. The n-to-2n transmutation reaction also produces tritium and helium, which form bubbles. Neutron irradiation from fusion plasma also introduces point defects. The effect on beryllides' microstructure is important for understanding their mechanical properties and evolution in the fusion reactor environment. This study determines and describes the microstructural features that occur in TiBe12 and CrBe12 when He and fast-particle-induced point defects are introduced at fusion reactor neutron breeder relevant temperatures. Beryllide samples were implanted with 300kV He at temperatures between $387-900^{\circ}C$, sectioned down through the implantation surface with a focused ion beam post-irradiation, and the resulting microstructures examined using transmission electron microscopy, electron-dispersive spectroscopy (EDS) and precession diffraction mapping. Nanometre bubbles grew in both TiBe12 and CrBe12 at $600^{\circ}C$; larger (100 nm and over) bubbles, some faceted, grew at $900^{\circ}C$. Some bubbles in CrBe12 were lined with Cr, some oxidised. TiBe12 developed planar faults, on $\{110\}$ planes at $600^{\circ}C$ and below but on $\{111\}$ at $900^{\circ}C$. Faults were preferentially associated with large bubbles. The displacement vectors of faults on the $\{110\}$ planes had some commonality with previous studies that found displacement vectors of families $R=\langle 011\rangle$ and $R= \langle 110\rangle$; the present study also found faults that matched neither previously found type. CrBe12 also developed planar faults with an appearance quite different from the typical striped appearance of planar stacking faults; their nature remains unknown. Oxide particles were found in both beryllides, most prominently in CrBe12., Comment: 35 pages, 25 figures. Paper writing: Jo Sharp. Paper editing: everybody. Manufacture of beryllide material: Ramil Gaisin. FIB sample prep: Viacheslav Kuksenko. Irradiation: Jo Sharp and Graeme Greaves. Characterisation: Jo Sharp. Obtaining funding: Jonathan Hinks, Graeme Greaves, Stephen Donnelly, Pavel Vladimirov. Submitted to Journal of Nuclear Materials

The semi-inclusive deep-inelastic scattering (SIDIS) is the golden process for investigating the nucleon's transverse momentum-dependent (TMD) structure. We present the complete expression for SIDIS structure functions in the TMD factorization formalism at the next-to-leading power. All perturbative elements of the factorization theorem -- coefficient functions and evolution kernels -- are presented at one-loop accuracy. We found several differences with earlier derivations, which are due to accounting for nontrivial kinematics of the quark-gluon interference terms. As a side result, we present the definition and evolution of twist-three TMD fragmentation functions, including the leading-order evolution kernel., Comment: 36 pages, 2 figures

This document presents the initial scientific case for upgrading the Continuous Electron Beam Accelerator Facility (CEBAF) at Jefferson Lab (JLab) to 22 GeV. It is the result of a community effort, incorporating insights from a series of workshops conducted between March 2022 and April 2023. With a track record of over 25 years in delivering the world's most intense and precise multi-GeV electron beams, CEBAF's potential for a higher energy upgrade presents a unique opportunity for an innovative nuclear physics program, which seamlessly integrates a rich historical background with a promising future. The proposed physics program encompass a diverse range of investigations centered around the nonperturbative dynamics inherent in hadron structure and the exploration of strongly interacting systems. It builds upon the exceptional capabilities of CEBAF in high-luminosity operations, the availability of existing or planned Hall equipment, and recent advancements in accelerator technology. The proposed program cover various scientific topics, including Hadron Spectroscopy, Partonic Structure and Spin, Hadronization and Transverse Momentum, Spatial Structure, Mechanical Properties, Form Factors and Emergent Hadron Mass, Hadron-Quark Transition, and Nuclear Dynamics at Extreme Conditions, as well as QCD Confinement and Fundamental Symmetries. Each topic highlights the key measurements achievable at a 22 GeV CEBAF accelerator. Furthermore, this document outlines the significant physics outcomes and unique aspects of these programs that distinguish them from other existing or planned facilities. In summary, this document provides an exciting rationale for the energy upgrade of CEBAF to 22 GeV, outlining the transformative scientific potential that lies within reach, and the remarkable opportunities it offers for advancing our understanding of hadron physics and related fundamental phenomena., Comment: Updates to the list of authors; Preprint number changed from theory to experiment; Updates to sections 4 and 6, including additional figures

Model-driven analysis of biophysical phenomena is gaining increased attention and utility for medical imaging applications. In magnetic resonance imaging (MRI), the availability of well-established models for describing the relations between the nuclear magnetization, tissue properties, and the externally applied magnetic fields has enabled the prediction of image contrast and served as a powerful tool for designing the imaging protocols that are now routinely used in the clinic. Recently, various advanced imaging techniques have relied on these models for image reconstruction, quantitative tissue parameter extraction, and automatic optimization of acquisition protocols. In molecular MRI, however, the increased complexity of the imaging scenario, where the signals from various chemical compounds and multiple proton pools must be accounted for, results in exceedingly long model simulation times, severely hindering the progress of this approach and its dissemination for various clinical applications. Here, we show that a deep-learning-based system can capture the nonlinear relations embedded in the molecular MRI Bloch-McConnell model, enabling a rapid and accurate generation of biologically realistic synthetic data. The applicability of this simulated data for in-silico, in-vitro, and in-vivo imaging applications is then demonstrated for chemical exchange saturation transfer (CEST) and semisolid macromolecule magnetization transfer (MT) analysis and quantification. The proposed approach yielded 78%-99% acceleration in data synthesis time while retaining excellent agreement with the ground truth (Pearson's r$>$0.99, p$<$0.0001, normalized root mean square error $<$3%).

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance., Comment: 44 pages, ReVTeX, White Paper on EIC Theory Alliance

This paper is concerned with stochastic systems whose state is a diffusion process governed by an Ito stochastic differential equation (SDE). In the framework of a nominal white-noise model, the SDE is driven by a standard Wiener process. For a scenario of statistical uncertainty, where the driving noise acquires a state-dependent drift and thus deviates from its idealised model, we consider the perturbation of the invariant probability density function (PDF) as a steady-state solution of the Fokker-Planck-Kolmogorov equation. We discuss an upper bound on a logarithmic Dirichlet form for the ratio of the invariant PDF to its nominal counterpart in terms of the Kullback-Leibler relative entropy rate of the actual noise distribution with respect the Wiener measure. This bound is shown to be achievable, provided the PDF ratio is preserved by the nominal steady-state probability flux. The logarithmic Dirichlet form bound is used in order to obtain an upper bound on the relative entropy of the perturbed invariant PDF in terms of quadratic-exponential moments of the noise drift in the uniform ellipticity case. These results are illustrated for perturbations of Gaussian invariant measures in linear stochastic systems involving linear noise drifts., Comment: 14 pages, 2 figures

We present the extraction of unpolarized transverse momentum dependent parton distributions functions (TMDPDFs) and Collins-Soper kernel from the fit of Drell-Yan and weak-vector boson production data. The TMDPDF are parameterized, as commonly done, using their (large transverse momentum) asymptotic matching to PDF. The analysis is done at the next-to-next-to-next-to-next-to leading logarithmic accuracy (N$^4$LL) (performed only approximately because PDF evolution is known so far at next-to-next-to leading order (NNLO)). The non-perturbative model used for TMDPDF is flavor dependent to reduce the colllinear PDF bias. The estimation of uncertainties is done with the replica method and, for the first time, it includes the propagation of uncertainties due to the collinear distributions., Comment: 39 pages, many figures: v2. Added extra discussions on PDF uncertainties, normalization, and text corrections. Matching the journal version

The partons' transverse momentum can be explored with QCD lattice simulations by studying the quasi-transverse-momentum-dependent parton distribution functions (qTMDPDFs), which are factorized in terms of physical TMDPDFs and soft factors in the limit of the large hadron's momentum. We present the next-to-next-to-leading order (NNLO) calculation of the coefficient function for this factorization. Together with already known expressions for anomalous dimensions, this result allows analysis of lattice data at NNLO perturbative accuracy., Comment: 8 pages, 2 figures; v2: N3LO logarithms added in appendix; v3: Corrected misprint on (33), and misprints

Weak interaction of temporal cavity solitons due to gain saturation and recovery in a delay differential model of a long cavity semiconductor laser is studied numerically and analytically using an asymptotic approach. It is shown that in addition to the usual soliton repulsion leading to a harmonic mode-locking regimes a soliton attraction is also possible in a laser with nonzero linewidth enhancement factor. It is shown numerically that this attraction can lead either to a pulse merging or to a pulse bound state formation., Comment: 8 pages, 6 figures

In this paper, we extend nonlinear negative imaginary (NI) systems theory to switched systems. Switched nonlinear NI systems and switched nonlinear output strictly negative imaginary (OSNI) systems are defined. We show that the interconnection of two switched nonlinear NI systems is still switched nonlinear NI. The interconnection of a switched nonlinear NI system and a switched nonlinear OSNI system is asymptotically stable under some assumptions. This stability result is then illustrated using a numerical example., Comment: 7 pages, 4 figures. Full archive version for the paper of the same title to appear in the proceedings of IFAC World Congress 2023