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We compute the multiplicity of the irreducible representations in the decomposition of the tensor product of an arbitrary number $n$ of fundamental representations of $SU(N)$, and we identify a duality in the representation content of this decomposition. Our method utilizes the mapping of the representations of $SU(N)$ to the states of free fermions on the circle, and can be viewed as a random walk on a multidimensional lattice. We also derive the large-$n$ limit and the response of the system to an external non-abelian magnetic field. These results can be used to study the phase properties of non-abelian ferromagnets and to take various scaling limits., Some relevant references added; 24 pages, no figures

The Neyman-Pearson strategy for hypothesis testing can be employed for goodness of fit if the alternative hypothesis $\rm H_1$ is generic enough not to introduce a significant bias while at the same time avoiding overfitting. A practical implementation of this idea (dubbed NPLM) has been developed in the context of high energy physics, targeting the detection in collider data of new physical effects not foreseen by the Standard Model. In this paper we initiate a comparison of this methodology with other approaches to goodness of fit, and in particular with classifier-based strategies that share strong similarities with NPLM. NPLM emerges from our comparison as more sensitive to small departures of the data from the expected distribution and not biased towards detecting specific types of anomalies while being blind to others. These features make it more suited for agnostic searches for new physics at collider experiments. Its deployment in other contexts should be investigated.

There has been a recent explosion in research into machine-learning-based generative modeling to tackle computational challenges for simulations in high energy physics (HEP). In order to use such alternative simulators in practice, we need well-defined metrics to compare different generative models and evaluate their discrepancy from the true distributions. We present the first systematic review and investigation into evaluation metrics and their sensitivity to failure modes of generative models, using the framework of two-sample goodness-of-fit testing, and their relevance and viability for HEP. Inspired by previous work in both physics and computer vision, we propose two new metrics, the Fr\'echet and kernel physics distances (FPD and KPD, respectively), and perform a variety of experiments measuring their performance on simple Gaussian-distributed, and simulated high energy jet datasets. We find FPD, in particular, to be the most sensitive metric to all alternative jet distributions tested and recommend its adoption, along with the KPD and Wasserstein distances between individual feature distributions, for evaluating generative models in HEP. We finally demonstrate the efficacy of these proposed metrics in evaluating and comparing a novel attention-based generative adversarial particle transformer to the state-of-the-art message-passing generative adversarial network jet simulation model. The code for our proposed metrics is provided in the open source JetNet Python library., Comment: 11 pages, 5 figures, 3 tables, and a 5 page appendix

We consider the Topological String/Spectral theory duality on toric Calabi-Yau threefolds obtained from the resolution of the cone over the $Y^{N,0}$ singularity. Assuming Kyiv formula, we demonstrate this duality in a special regime thanks to an underlying connection between spectral determinants of quantum mirror curves and the non-autonomous (q)-Toda system. We further exploit this link to connect small and large time expansions in Toda equations. In particular we provide an explicit expression for their tau functions at large time in terms of a strong coupling version of irregular $W_N$ conformal blocks at $c=N-1$. These are related to a special class of multi-cut matrix models which describe the strong coupling regime of four dimensional, $\mathcal{N}=2$ $SU(N)$ super Yang-Mills., Comment: 62 pages

RooFit is a toolkit for statistical modeling and fitting used by most experiments in particle physics. Just as data sets from next-generation experiments grow, processing requirements for physics analysis become more computationally demanding, necessitating performance optimizations for RooFit. One possibility to speed-up minimization and add stability is the use of Automatic Differentiation (AD). Unlike for numerical differentiation, the computation cost scales linearly with the number of parameters, making AD particularly appealing for statistical models with many parameters. In this paper, we report on one possible way to implement AD in RooFit. Our approach is to add a facility to generate C++ code for a full RooFit model automatically. Unlike the original RooFit model, this generated code is free of virtual function calls and other RooFit-specific overhead. In particular, this code is then used to produce the gradient automatically with Clad. Clad is a source transformation AD tool implemented as a plugin to the clang compiler, which automatically generates the derivative code for input C++ functions. We show results demonstrating the improvements observed when applying this code generation strategy to HistFactory and other commonly used RooFit models. HistFactory is the subcomponent of RooFit that implements binned likelihood models with probability densities based on histogram templates. These models frequently have a very large number of free parameters and are thus an interesting first target for AD support in RooFit., 6 pages, 5 figures, 21st International Workshop on Advanced Computing and Analysis Techniques in Physics Research

The estimation of probability density functions is a non trivial task that over the last years has been tackled with machine learning techniques. Successful applications can be obtained using models inspired by the Boltzmann machine (BM) architecture. In this manuscript, the product Jacobi-Theta Boltzmann machine (pJTBM) is introduced as a restricted version of the Riemann-Theta Boltzmann machine (RTBM) with diagonal hidden sector connection matrix. We show that score matching, based on the Fisher divergence, can be used to fit probability densities with the pJTBM more efficiently than with the original RTBM., 7 pages, 3 figures, ACAT22 proceedings

There is a generalization of Heegaard-Floer theory from ${\mathfrak{gl}}_{1|1}$ to other Lie (super)algebras $^L{\mathfrak{g}}$. The corresponding category of A-branes is solvable explicitly and categorifies quantum $U_q(^L{\mathfrak{g}})$ link invariants. The theory was discovered in \cite{A1,A2}, using homological mirror symmetry. It has novel features, including equivariance and, if $^L{\mathfrak{g}} \neq {\mathfrak{gl}}_{1|1}$, coefficients in categories. In this paper, we describe the theory and how it is solved in detail in the two simplest cases: the ${\mathfrak{gl}}_{1|1}$ theory itself, categorifying the Alexander polynomial, and the ${\mathfrak{su}}_{2}$ theory, categorifying the Jones polynomial. Our approach to solving the theory is new, even in the familiar ${\mathfrak{gl}}_{1|1}$ case., Comment: 146 pages

We examine two types of half-BPS surface defects $-$ regular monodromy surface defect and canonical surface defect $-$ in four-dimensional gauge theory with $\mathcal{N}=2$ supersymmetry and $\Omega_{\varepsilon_1,\varepsilon_2}$-background. Mathematically, we investigate integrals over the moduli spaces of parabolic framed sheaves over $\mathbb{P}^2$. Using analytic methods of $\mathcal{N}=2$ theories, we demonstrate that the former gives a twisted $\mathcal{D}$-module on $\text{Bun}_{G_{\mathbb{C}}}$ while the latter acts as a Hecke operator. In the limit $\varepsilon_2 \to 0$, the cluster decomposition implies the Hecke eigensheaf property for the regular monodromy surface defect. The eigenvalues are given by the opers associated to the canonical surface defect. We derive, in our $\mathcal{N}=2$ gauge theoretical framework, that the twisted $\mathcal{D}$-modules assigned to the opers in the geometric Langlands correspondence represent the spectral equations for quantum Hitchin integrable system. A duality to topologically twisted four-dimensional $\mathcal{N}=4$ theory is discussed, in which the two surface defects are mapped to Dirichlet boundary and 't Hooft line defect. This is consistent with earlier works on the $\mathcal{N}=4$ theory approach to the geometric Langlands correspondence., Comment: 89+23 pages, 3 figures; v2. typos corrected, references added

Journal of high energy physics 2023(6), 062 (2023). doi:10.1007/JHEP06(2023)062, We present a method to calculate the $x$--space expressions of massless or massive operatormatrix elements in QCD and QED containing local composite operator insertions, depending onthe discrete Mellin index $N$, directly without computing the Mellin--space expressions inexplicit form analytically. Here $N$ belongs either to the even or odd positive integers. Themethod is based on the resummation of the operators into effective propagators and relies onan analytic continuation between two continuous variables. We apply it to iterative integralsas well as to the case of iterative non--iterative integrals, generalizing the former ones.The $x$--space expressions are needed to derive the small--$x$ behaviour of the respectivequantities, which can usually not be accessed in $N$--space. We illustrate the method fordifferent (iterative) alphabets, including non--iterative $_2F_1$ and elliptic structures,as examples, occurring in different massless and massive three--loop calculations. Likewisethe method applies even to the closed analytic solutions of more general cases of differentialequations not factorizing in first order., Published by SISSA, Trieste

Jackiw-Teitelboim dilaton-quantum-gravity localizes on a double-scaled random-matrix model, whose perturbative free energy is an asymptotic series. Understanding the resurgent properties of this asymptotic series, including its completion into a full transseries, requires understanding the nonperturbative instanton sectors of the matrix model for Jackiw-Teitelboim gravity. The present work addresses this question by setting-up instanton calculus associated to eigenvalue tunneling (or ZZ-brane contributions), directly in the matrix model. In order to systematize such calculations, a nonperturbative extension of the topological recursion formalism is required -- which is herein both constructed and applied to the present problem. Large-order tests of the perturbative genus expansion validate the resurgent nature of Jackiw-Teitelboim gravity, both for its free energy and for its (multi-resolvent) correlation functions. Both ZZ and FZZT nonperturbative effects are required by resurgence, and they further display resonance upon the Borel plane. Finally, the resurgence properties of the multi-resolvent correlation functions yield new and improved resurgence formulae for the large-genus growth of Weil-Petersson volumes., Comment: 63 pages, 52 plots in 16 figures, jheppub-nosort.sty

We study the thermodynamics of a non-abelian ferromagnet consisting of "atoms" each carrying a fundamental representation of $SU(N)$, coupled with long-range two-body quadratic interactions. We uncover a rich structure of phase transitions from non-magnetized, global $SU(N)$-invariant states to magnetized ones breaking global invariance to $SU(N-1) \times U(1)$. Phases can coexist, one being stable and the other metastable, and the transition between states involves latent heat exchange, unlike in usual $SU(2)$ ferromagnets. Coupling the system to an external non-abelian magnetic field further enriches the phase structure, leading to additional phases. The system manifests hysteresis phenomena both in the magnetic field, as in usual ferromagnets, and in the temperature, in analogy to supercooled water. Potential applications are in fundamental situations or as a phenomenological model., Comment: 49 pages, 17 figures, 2 appendices; references added

We provide details on the implementation of a machine-learning based particle flow algorithm for CMS. The standard particle flow algorithm reconstructs stable particles based on calorimeter clusters and tracks to provide a global event reconstruction that exploits the combined information of multiple detector subsystems, leading to strong improvements for quantities such as jets and missing transverse energy. We have studied a possible evolution of particle flow towards heterogeneous computing platforms such as GPUs using a graph neural network. The machine-learned PF model reconstructs particle candidates based on the full list of tracks and calorimeter clusters in the event. For validation, we determine the physics performance directly in the CMS software framework when the proposed algorithm is interfaced with the offline reconstruction of jets and missing transverse energy. We also report the computational performance of the algorithm, which scales approximately linearly in runtime and memory usage with the input size., 12 pages, 6 figures. Presented at the ACAT 2021: 20th International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Daejeon, Kr, 29 Nov - 3 Dec 2021

Orbifold singularities of M-theory constitute the building blocks of a broad class of supersymmetric quantum field theories (SQFTs). In this paper we show how the local data of these geometries determines global data on the resulting higher symmetries of these systems. In particular, via a process of cutting and gluing, we show how local orbifold singularities encode the 0-form, 1-form and 2-group symmetries of the resulting SQFTs. Geometrically, this is obtained from the possible singularities which extend to the boundary of the non-compact geometry. The resulting category of boundary conditions then captures these symmetries, and is equivalently specified by the orbifold homology of the boundary geometry. We illustrate these general points in the context of a number of examples, including 5D superconformal field theories engineered via orbifold singularities, 5D gauge theories engineered via singular elliptically fibered Calabi-Yau threefolds, as well as 4D SQCD-like theories engineered via M-theory on non-compact $G_2$ spaces., v4: 78 pages, 9 figures, typos corrected, clarifications added

Root bundles appear prominently in studies of vector-like spectra of 4d F-theory compactifications. Of particular importance to phenomenology are the Quadrillion F-theory Standard Models (F-theory QSMs). In this work, we analyze a superset of the physical root bundles whose cohomologies encode the vector-like spectra for the matter representations $(\mathbf{3}, \mathbf{2})_{1/6}$, $(\mathbf{\overline{3}}, \mathbf{1})_{-2/3}$ and $(\mathbf{1}, \mathbf{1})_{1}$. For the family $B_3( \Delta_4^\circ )$ consisting of $\mathcal{O}(10^{11})$ F-theory QSM geometries, we argue that more than $99.995\%$ of the roots in this superset have no vector-like exotics. This indicates that absence of vector-like exotics in those representations is a very likely scenario. The QSM geometries come in families of toric 3-folds $B_3( \Delta^\circ )$ obtained from triangulations of certain 3-dimensional polytopes $\Delta^\circ$. The matter curves in $X_\Sigma \in B_3( \Delta^\circ )$ can be deformed to nodal curves which are the same for all spaces in $B_3( \Delta^\circ )$. Therefore, one can probe the vector-like spectra on the entire family $B_3( \Delta^\circ )$ from studies of a few nodal curves. We compute the cohomologies of all limit roots on these nodal curves. In our applications, for the majority of limit roots the cohomologies are determined by line bundle cohomology on rational tree-like curves. For this, we present a computer algorithm. The remaining limit roots, corresponding to circuit-like graphs, are handled by hand. The cohomologies are independent of the relative position of the nodes, except for a few circuits. On these \emph{jumping circuits}, line bundle cohomologies can jump if nodes are specially aligned. This mirrors classical Brill-Noether jumps. $B_3( \Delta_4^\circ )$ admits a jumping circuit, but the root bundle constraints pick the canonical bundle and no jump happens., Comment: 37 pages + appendix; fixes to computational mistakes; typos corrected

Resonant slow extraction is used at the Super Proton Synchrotron (SPS) for the extraction of a beam of particles by exciting a 1/3rd integer resonance. A stable flux of particles is necessary for the correct functioning of the particles' detection process. However, the variations in power converter currents introduce ripples which are responsible for the harmonics present on the extracted beam profile and potentially introduce discontinuities in the flux. In this project, we will model how perturbations in the machine parameters affect the spill of particles, as a function of time, while keeping the computational cost minimal.

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory., 29 pages, revtex format; to match published version

In the Large Hadron Collider, the beam losses are continuously measured for machine protection. By design, most of the particle losses occur in the collimation system, where the particles with high oscilla-tion amplitudes or large momentum error are scraped from the beams. The particle loss level is typically optimized manually by changing control parameters, among which are currents in the focusing and defocusing magnets. It is generally challenging to model and predict losses based only on the control parameters, due to the presence of various (non-linear) effects in the system, such as electron clouds, resonance effects, etc., and multiple sources of uncertainty. At the same time understanding the influence of control parameters on the losses is extremely important in order to improve the operation and performance, and future design of accelerators. Prior work [1] showed that modeling the losses as an instantaneous function of the control parameters does not generalize well to data from a different year, which is an indication that the leveraged statistical associations are not capturing the actual mechanisms which should be invariant from 1 year to the next. Given that this is most likely due to lagged effects, we propose to model the losses as a function of not only instantaneous but also previously observed control parameters as well as previous loss values. Using a standard reparameterization, we reformulate the model as a Kalman Filter (KF) which allows for a flexible and efficient estimation procedure. We consider two main variants: one with a scalar loss output, and a second one with a 4D output with loss, horizontal and vertical emittances, and aggregated heatload as components. The two models once learned can be run for a number of steps in the future, and the second model can forecast the evolution of quantities that are relevant to predicting the loss itself. Our results show that the proposed models trained on the beam loss data from 2017 are able to predict the losses on a time horizon of several minutes for the data of 2018 as well and successfully identify both local and global trends in the losses., Frontiers in Physics, 10, ISSN:2296-424X

Recurrent neural networks have been shown to be effective architectures for many tasks in high energy physics, and thus have been widely adopted. Their use in low-latency environments has, however, been limited as a result of the difficulties of implementing recurrent architectures on field-programmable gate arrays (FPGAs). In this paper we present an implementation of two types of recurrent neural network layers -- long short-term memory and gated recurrent unit -- within the hls4ml framework. We demonstrate that our implementation is capable of producing effective designs for both small and large models, and can be customized to meet specific design requirements for inference latencies and FPGA resources. We show the performance and synthesized designs for multiple neural networks, many of which are trained specifically for jet identification tasks at the CERN Large Hadron Collider., 12 pages, 6 figures, 5 tables

In this paper, results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps and Hamiltonians with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This makes possible to determine explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation, as well as an extension of the work by Neishtadt et al. [Regul. Chaotic Dyn. 18, 686 (2013)] on a restricted class of quasi-integrable systems with time-dependent exciters. In this paper, new results concerning the phenomenon of adiabatic trapping into resonance for a class of quasi-integrable maps with a time-dependent exciter are presented and discussed in detail. The applicability of the results about trapping efficiency for Hamiltonian systems to the maps considered is proven by using perturbation theory. This allows determining explicit scaling laws for the trapping properties. These findings represent a generalization of previous results obtained for the case of quasi-integrable maps with parametric modulation as well as an extension of the work by Neishtadt \textit{et al.} on a restricted class of quasi-integrable systems with time-dependent exciters.

We present an exact formula for the thermal scalar two-point function in four-dimensional holographic conformal field theories. The problem of finding it reduces to the analysis of the wave equation on the AdS-Schwarzschild background. The two-point function is computed from the connection coefficients of the Heun equation, which can be expressed in terms of the Nekrasov-Shatashvili partition function of an SU(2) supersymmetric gauge theory with four fundamental hypermultiplets. The result is amenable to numerical evaluation upon truncating the number of instantons in the convergent expansion of the partition function. We also examine it analytically in various limits. At large spin the instanton expansion of the thermal two-point function directly maps to the light-cone bootstrap analysis of the heavy-light four-point function. Using this connection, we compute the OPE data of heavy-light double-twist operators. We compare our prediction to the perturbative results available in the literature and find perfect agreement., 9 pages + appendices, 2 figures. v2: typos corrected, references added

We investigate infinite distance limits in the complex structure moduli space of F-theory compactified on K3 to eight dimensions. While this is among the simplest possible arenas to test ideas about the Swampland Distance Conjecture, it is nevertheless non-trivial enough to improve our understanding of the physics for these limiting geometries, including phenomena of emergence. It also provides a perspective on infinite distance limits from the viewpoint of open strings. The paper has two quite independent themes. In the main part we show that all degenerations of elliptic K3 surfaces at infinite distance as analysed in a companion paper can be interpreted as (partial) decompactification or emergent string limits in F-theory, in agreement with the Emergent String Conjecture. We present a unified geometric picture of the possible towers of states that can become light and illustrate our general claims via the connection between Kulikov models of degenerating K3 surfaces and the dual heterotic string. As an application we classify the possible maximal non-abelian Lie algebras and their Kac-Moody and loop extensions that can arise in the infinite distance limits. In the second part we discuss the infinite distance behaviour of certain exact quartic gauge couplings. We encounter a tension with the hypothesis that effective couplings should be fully generated by integrating out massive states. We show that by appropriately renormalizing the string coupling, at least partial emergence can be achieved., 57 pages, 11 figures

We compute the leading term of the tripartite information at long distances for three spheres in a CFT. This falls as $r^{-6\Delta}$, where $r$ is the typical distance between the spheres, and $\Delta$, the lowest primary field dimension. The coefficient turns out to be a combination of terms coming from the two- and three-point functions and depends on the OPE coefficient of the field. We check the result with three-dimensional free scalars in the lattice finding excellent agreement. When the lowest-dimensional field is a scalar, we find that the mutual information can be monogamous only for quite large OPE coefficients, far away from a perturbative regime. When the lowest-dimensional primary is a fermion, we argue that the scaling must always be faster than $r^{-6\Delta_f}$. In particular, lattice calculations suggest a leading scaling $ r^{-(6\Delta_f+1)}$. For free fermions in three dimensions, we show that mutual information is also non-monogamous in the long-distance regime., Comment: 25 pages and 5 figures. V2: References added, a paragraph with comments on $d=2$ results was included and it matches the version to appear in SciPost

We propose and demonstrate the use of a model-assisted generative adversarial network (GAN) to produce fake images that accurately match true images through the variation of the parameters of the model that describes the features of the images. The generator learns the model parameter values that produce fake images that best match the true images. Two case studies show excellent agreement between the generated best match parameters and the true parameters. The best match model parameter values can be used to retune the default simulation to minimize any bias when applying image recognition techniques to fake and true images. In the case of a real-world experiment, the true images are experimental data with unknown true model parameter values, and the fake images are produced by a simulation that takes the model parameters as input. The model-assisted GAN uses a convolutional neural network to emulate the simulation for all parameter values that, when trained, can be used as a conditional generator for fast fake-image production.

Given a closed oriented surface S we describe those cohomology classes which appear as the period characters of abelian differentials for some choice of complex structure on S consistent with the orientation. The proof is based upon Ratner's solution of Raghunathan's conjecture., Comment: A revision of my 2000 preprint

Feynman integrals are central to all calculations in perturbative Quantum Field Theory. They often give rise to iterated integrals of dlog-forms with algebraic arguments, which in many cases can be evaluated in terms of multiple polylogarithms. This has led to certain folklore beliefs in the community stating that all such integrals evaluate to polylogarithms. Here we discuss a concrete example of a double iterated integral of two dlog-forms that evaluates to a period of a cusp form. The motivic versions of these integrals are shown to be algebraically independent from all multiple polylogarithms evaluated at algebraic arguments. From a mathematical perspective, we study a mixed elliptic Hodge structure arising from a simple geometric configuration in $\mathbb{P}^2$, consisting of a modular plane elliptic curve and a set of lines which meet it at torsion points, which may provide an interesting worked example from the point of view of periods, extensions of motives, and L-functions., 25 pages, 4 figures. To appear in the proceedings of "Mathemamplitudes", held in Padova in December 2019

We study machine learning of phenomenologically relevant properties of string compactifications, which arise in the context of heterotic line bundle models. Both supervised and unsupervised learning are considered. We find that, for a fixed compactification manifold, relatively small neural networks are capable of distinguishing consistent line bundle models with the correct gauge group and the correct chiral asymmetry from random models without these properties. The same distinction can also be achieved in the context of unsupervised learning, using an auto-encoder. Learning non-topological properties, specifically the number of Higgs multiplets, turns out to be more difficult, but is possible using sizeable networks and feature-enhanced data sets., Comment: 10 pages

We propose a connection between 3d-5d exponential networks and exact WKB for difference equations associated to five dimensional Seiberg-Witten curves, or equivalently, to quantum mirror curves to toric Calabi-Yau threefolds $X$: the singularities in the Borel planes of local solutions to such difference equations correspond to central charges of 3d-5d BPS KK-modes, and the central charges of 5d BPS KK-modes are related to the singularities in the Borel planes of the closed topological string free energy on $X$. It follows that there should be distinguished local solutions of the difference equation in each domain of the complement of the exponential network, and these solutions jump at the walls of the network. We verify this picture in detail in two simple examples of 3d-5d systems, corresponding to taking the toric Calabi-Yau $X$ to be either $\mathbb{C}^3$ or the resolved conifold. We provide the full list of local solutions in each sector of the Borel plane and in each domain of the complement of the exponential network, and find that local solutions in disconnected domains correspond to non-perturbative open topological string amplitudes on $X$ with insertions of branes at different positions of the toric diagram. We also study the Borel summation of the closed refined topological string free energy on $X$ and the corresponding non-perturbative effects., 47 pages, 9 figures

The article contains a detailed proof of the famous Belyi theorem on geometry of complex algebraic curves defined over number fields. It also includes the discussion of several constructions and conjectures inspired by Belyi’s result which where brought up by the first author during his colloquium talks at different universities within the period from 1979 to 1984.

Magnetic fields generated by normal or superconducting electromagnets are used to guide and focus particle beams in storage rings, synchrotron light sources, mass spectrometers, and beamlines for radiotherapy. The accurate determination of the magnetic field by measurement is critical for the prediction of the particle beam trajectory and hence the design of the accelerator complex. In this context, state-of-the-art numerical field computation makes use of boundary-element methods (BEM) to express the magnetic field. This enables the accurate computation of higher-order partial derivatives and local expansions of magnetic potentials used in efficient numerical codes for particle tracking. In this paper, we present an approach to infer the boundary data of an indirect BEM formulation from magnetic field measurements by ensemble Kálmán filtering. In this way, measurement uncertainties can be propagated to the boundary data, magnetic field and potentials, and to the beam related quantities derived from particle tracking. We provide results obtained from real measurement data of a curved dipole magnet using a Hall probe mapper system.

Analytical expressions are derived for the position of irreducible fractions in the Farey sequence $F_N$ of order $N$ for a particular choice of $N$. The asymptotic behaviour is derived obtaining a lower error bound than in previous results when these fractions are in the vicinity of $0/1$, $1/2$ or $1/1$. Franel's famous formulation of Riemann's hypothesis uses the summation of distances between irreducible fractions and evenly spaced points in $[0,1]$. A partial Franel sum is defined here as a summation of these distances over a subset of fractions in $F_N$. The partial Franel sum in the range $[0, i/N]$, with $N={\rm lcm}(1,2,...,i)$ is shown here to grow as $O(\log(N)\delta_B(\log N))$, where $\delta_B(x)$ is a decreasing function. Other partial Franel sums are also explored., Comment: 10 pages

We study in detail the Schr\"{o}dinger equation corresponding to the four dimensional $SU(2)$ $\mathcal{N}=2$ SQCD theory with one flavour. We calculate the Voros symbols, or quantum periods, in four different ways: Borel summation of the WKB series, direct computation of Wronskians of exponentially decaying solutions, the TBA equations of Gaiotto-Moore-Neitzke/Gaiotto, and instanton counting. We make computations by all of these methods, finding good agreement. We also study the exact quantization condition for the spectrum, and we compute the Fredholm determinant of the inverse of the Schr\"odinger operator using the TS/ST correspondence and Zamolodchikov's TBA, again finding good agreement. In addition, we explore two aspects of the relationship between singularities of the Borel transformed WKB series and BPS states: BPS states of the 4d theory are related to singularities in the Borel transformed WKB series for the quantum periods, and BPS states of a coupled 2d+4d system are related to singularities in the Borel transformed WKB series for local solutions of the Schr\"odinger equation., Comment: 63 pages, 18 figures

In a recent paper, the adiabatic theory of Hamiltonian systems was successfully applied to study the crossing of the linear coupling resonance, $Q_x-Q_y=0$. A detailed explanation of the well-known phenomena that occur during the resonance-crossing process, such as emittance exchange and its dependence on the adiabaticity of the process was obtained. In this paper, we consider the crossing of the resonance of nonlinear coupling $2 Q_x -2 Q_y = 0$ using the same theoretical framework. We perform the analysis using a Hamiltonian model in which the nonlinear coupling resonance is excited and the corresponding dynamics is studied in detail, in particular looking at the phase-space topology and its evolution, in view of characterizing the emittance exchange phenomena. The theoretical results are then tested using a symplectic map. Thanks to this approach, scaling laws of general interest for applications are derived.

Particle identification (PID) is one of the main strengths of the ALICE experiment at the LHC. It is a crucial ingredient for detailed studies of the strongly interacting matter formed in ultrarelativistic heavy-ion collisions. ALICE provides PID information via various experimental techniques, allowing for the identification of particles over a broad momentum range (from around 100 MeV/$c$ to around 50 GeV/$c$). The main challenge is how to combine the information from various detectors effectively. Therefore, PID represents a model classification problem, which can be addressed using Machine Learning (ML) solutions. Moreover, the complexity of the detector and richness of the detection techniques make PID an interesting area of research also for the computer science community. In this work, we show the current status of the ML approach to PID in ALICE. We discuss the preliminary work with the Random Forest approach for the LHC Run 2 and a more advanced solution based on Domain Adaptation Neural Networks, including a proposal for its future implementation within the ALICE computing software for the upcoming LHC Run 3., Comment: 11 pages, 4 figures, proceedings from the Workshop: AI4EIC-Exp - Experimental Applications of Artificial Intelligence for the Electron Ion Collider, accepted for publication in JINST

We define a variant of real-analytic polylogarithms that are single-valued and that satisfy ''clean'' functional relations that do not involve any products of lower weight functions. We discuss the basic properties of these functions and, for depths one and two, we present some explicit formulas and results. We also give explicit formulas for the single-valued and clean single-valued version attached to the Nielsen polylogarithms $S_{n,2}(x)$, and we show how the clean single-valued functions give new evaluations of multiple polylogarithms at certain algebraic points., Special Issue on Algebraic Structures in Perturbative Quantum Field Theory in honor of Dirk Kreimer for his 60th birthday

Entanglement represents "the" key resource for several applications of quantum information processing, ranging from quantum communications to distributed quantum computing. Despite its fundamental importance, deterministic generation of maximally entangled qubits represents an on-going open problem. Here, we design a novel generation scheme exhibiting two attractive features, namely, i) deterministically generating genuinely multipartite entangled states, ii) without requiring any direct interaction between the qubits. Indeed, the only necessary condition is the possibility of coherently controlling -- according to the indefinite causal order framework -- the causal order among some unitaries acting on the qubits. Through the paper, we analyze and derive the conditions on the unitaries for deterministic generation, and we provide examples for unitaries practical implementation. We conclude the paper by discussing the scalability of the proposed scheme to higher dimensional GME states and by introducing some possible applications of the proposal for quantum networks.

We propose an effective framework for computing the prepotential of the topological B-model on a class of local Calabi--Yau geometries related to the circle compactification of five-dimensional $\mathcal{N}=1$ super Yang--Mills theory with simple gauge group. In the simply-laced case, we construct Picard--Fuchs operators from the Dubrovin connection on the Frobenius manifolds associated to the extended affine Weyl groups of type $\mathrm{ADE}$. In general, we propose a purely algebraic construction of Picard--Fuchs ideals from a canonical subring of the space of regular functions on the ramification locus of the Seiberg--Witten curve, encompassing non-simply-laced cases as well. We offer several precision tests of our proposal. Whenever a candidate spectral curve is known from string theory/brane engineering, we perform non-perturbative comparisons with the gauge theory prepotentials obtained from the K-theoretic blow-up equations, finding perfect agreement. We also employ our formalism to rule out some proposals from the theory of integrable systems of Seiberg--Witten geometries for non-simply laced gauge groups., 42 pages

The report discusses main steps of retrieving RPC (Resistive Plate Chambers) data of multiple LHC (Large Hadron Collider) runs. The retrieved data contains different metrics that are being analyzed by the help of the main statistical methods. Once the data becomes familiar, different Machine Learning and Deep Learning models are trained to predict the fiducial efficiency of each chamber based on the measurable detector quantities collected. Data of CMS experiment of 2018 is used to train the models. For the work, Python scikit-learn and Keras libraries are used to train the models. The predicted results are then compared against the initial fiducial efficiency values

We discuss two realizations of the colored Jones polynomials of a knot, one from an unnoticed work of the second author in 1994 on quantum R-matrices at roots of unity obtained from solutions of the pentagon identity, and another one from recent work of D. Zagier and the first author regarding the Refined Quantum Modularity Conjecture, more precisely, the mysterious top row of a matrix of conjectured knot invariants., 19 pages

The Landau–Lifshitz (LL) equation has been proposed as the classical equation to describe the dynamics of a charged particle in a strong electromagnetic field when influenced by radiation reaction. Until recently, there has been no clear experimental verification. However, aligned crystals have remedied the situation: here, as in Nielsen et al CERN NA63 Collaboration (2020 Phys. Rev. D 102 052004), we report on a quantitative experimental test of the LL equation by measuring the emission spectra of electrons and positrons penetrating aligned single crystals. The recorded spectra are in remarkable agreement with simulations based on the LL equation of motion with moderate quantum corrections for recoil and, in the case of electrons in axially aligned crystals, spin and reduced radiation intensity.

We establish a precise relation between the modular bootstrap, used to constrain the spectrum of 2D CFTs, and the sphere packing problem in Euclidean geometry. The modular bootstrap bound for chiral algebra $U(1)^c$ maps exactly to the Cohn-Elkies linear programming bound on the sphere packing density in $d=2c$ dimensions. We also show that the analytic functionals developed earlier for the correlator conformal bootstrap can be adapted to this context. For $c=4$ and $c=12$, these functionals exactly reproduce the "magic functions" used recently by Viazovska [1] and Cohn et al. [2] to solve the sphere packing problem in dimensions 8 and 24. The same functionals are also applied to general 2D CFTs, with only Virasoro symmetry. In the limit of large central charge, we relate sphere packing to bounds on the black hole spectrum in 3D quantum gravity, and prove analytically that any such theory must have a nontrivial primary state of dimension $\Delta_0 \lesssim c/8.503$., Comment: 70 pages, 7 figures

In this article, we present and analyze the numerical stability of two coupled finite element formulations. The first one is the $h$ - $a$ -formulation and is well suited for modeling systems with superconductors and ferromagnetic materials. The second one, the so-called $t$ - $a$ -formulation with thin-shell approximation, applies for systems with thin superconducting domains. Both formulations involve two coupled unknown fields and are mixed on the coupling interfaces. Function spaces in mixed formulations must satisfy compatibility conditions to ensure stability of the problem and reliability of the numerical solution. We propose stable choices of function spaces using hierarchical basis functions and demonstrate the effectiveness of the approach on simple 2D examples.

We introduce natural language processing into the study of knot theory, as made natural by the braid word representation of knots. We study the UNKNOT problem of determining whether or not a given knot is the unknot. After describing an algorithm to randomly generate $N$-crossing braids and their knot closures and discussing the induced prior on the distribution of knots, we apply binary classification to the UNKNOT decision problem. We find that the Reformer and shared-QK Transformer network architectures outperform fully-connected networks, though all perform well. Perhaps surprisingly, we find that accuracy increases with the length of the braid word, and that the networks learn a direct correlation between the confidence of their predictions and the degree of the Jones polynomial. Finally, we utilize reinforcement learning (RL) to find sequences of Markov moves and braid relations that simplify knots and can identify unknots by explicitly giving the sequence of unknotting actions. Trust region policy optimization (TRPO) performs consistently well for a wide range of crossing numbers and thoroughly outperformed other RL algorithms and random walkers. Studying these actions, we find that braid relations are more useful in simplifying to the unknot than one of the Markov moves., Comment: 51 pages, 16 figures, 6 algorithms, 2 tables

This review describes the composition of the Compact Muon Solenoid (CMS) detector and the methodology for modelling the heterogeneous CMS magnetic system, starting with the formulation of the magnetostatics problem for modelling the magnetic flux of the CMS superconducting solenoid enclosed in a steel flux-return yoke. The review includes a section on the magnetization curves of various types of steel used in the CMS magnet yoke. The evolution of the magnetic system model over 20 years is presented in the discussion section and is well illustrated by the CMS model layouts and the magnetic flux distribution., 17 pages, 9 figures, 67 references

We describe the outcome of a data challenge conducted as part of the Dark Machines Initiative and the Les Houches 2019 workshop on Physics at TeV colliders. The challenged aims at detecting signals of new physics at the LHC using unsupervised machine learning algorithms. First, we propose how an anomaly score could be implemented to define model-independent signal regions in LHC searches. We define and describe a large benchmark dataset, consisting of >1 Billion simulated LHC events corresponding to $10~\rm{fb}^{-1}$ of proton-proton collisions at a center-of-mass energy of 13 TeV. We then review a wide range of anomaly detection and density estimation algorithms, developed in the context of the data challenge, and we measure their performance in a set of realistic analysis environments. We draw a number of useful conclusions that will aid the development of unsupervised new physics searches during the third run of the LHC, and provide our benchmark dataset for future studies at https://www.phenoMLdata.org. Code to reproduce the analysis is provided at https://github.com/bostdiek/DarkMachines-UnsupervisedChallenge., v1: 54 pages, 24 figures. v2: 56 pages, citations added, extend discussion of look-elsewhere-effect, results unchanged; v3. minor typos and updated references

We develop a self-consistent approach to study the spectral properties of a class of quantum mechanical operators by using the knowledge about monodromies of $2\times 2$ linear systems (Riemann-Hilbert correspondence). Our technique applies to a variety of problems, though in this paper we only analyse in detail two examples. First we review the case of the (modified) Mathieu operator, which corresponds to a certain linear system on the sphere and makes contact with the Painlev\'e $\mathrm{III}_3$ equation. Then we extend the analysis to the 2-particle elliptic Calogero-Moser operator, which corresponds to a linear system on the torus. By using the Kiev formula for the isomonodromic tau functions, we obtain the spectrum of such operators in terms of self-dual Nekrasov functions ($\epsilon_1+\epsilon_2=0$). Through blowup relations, we also find Nekrasov-Shatashvili type of quantizations ($\epsilon_2=0$). In the case of the torus with one regular singularity we obtain certain results which are interesting by themselves. Namely, we derive blowup equations (filling some gaps in the literature) and we relate them to the bilinear form of the isomonodromic deformation equations. In addition, we extract the $\epsilon_2\to 0$ limit of the blowup relations from the regularized action functional and CFT arguments., Comment: 62 pages, minor corrections, references added

In general-purpose particle detectors, the particle-flow algorithm may be used to reconstruct a comprehensive particle-level view of the event by combining information from the calorimeters and the trackers, significantly improving the detector resolution for jets and the missing transverse momentum. In view of the planned high-luminosity upgrade of the CERN Large Hadron Collider (LHC), it is necessary to revisit existing reconstruction algorithms and ensure that both the physics and computational performance are sufficient in an environment with many simultaneous proton-proton interactions (pileup). Machine learning may offer a prospect for computationally efficient event reconstruction that is well-suited to heterogeneous computing platforms, while significantly improving the reconstruction quality over rule-based algorithms for granular detectors. We introduce MLPF, a novel, end-to-end trainable, machine-learned particle-flow algorithm based on parallelizable, computationally efficient, and scalable graph neural networks optimized using a multi-task objective on simulated events. We report the physics and computational performance of the MLPF algorithm on a Monte Carlo dataset of top quark-antiquark pairs produced in proton-proton collisions in conditions similar to those expected for the high-luminosity LHC. The MLPF algorithm improves the physics response with respect to a rule-based benchmark algorithm and demonstrates computationally scalable particle-flow reconstruction in a high-pileup environment., 15 pages, 10 figures

The thermal equilibrium properties of physical systems can be described using Gibbs states. It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regions are small. In this work, we consider 1D quantum spin systems with local, finite-range, translation-invariant interactions at any temperature. In this setting, we show that Gibbs states satisfy uniform exponential decay of correlations and, moreover, the mutual information between two regions decays exponentially with their distance, irrespective of the temperature. In order to prove the latter, we show that exponential decay of correlations of the infinite-chain thermal states, exponential uniform clustering and exponential decay of the mutual information are equivalent for 1D quantum spin systems with local, finite-range interactions at any temperature. In particular, Araki's seminal results yields that the three conditions hold in the translation-invariant case. The methods we use are based on the Belavkin-Staszewski relative entropy and on techniques developed by Araki. Moreover, we find that the Gibbs states of the systems we consider are superexponentially close to saturating the data-processing inequality for the Belavkin-Staszewski relative entropy., Final version: 40 pages; corrected typos, revised notation, added further comments to clarify some points

In this work, we investigate different machine learning-based strategies for denoising raw simulation data from the ProtoDUNE experiment. The ProtoDUNE detector is hosted by CERN and it aims to test and calibrate the technologies for DUNE, a forthcoming experiment in neutrino physics. The reconstruction workchain consists of converting digital detector signals into physical high-level quantities. We address the first step in reconstruction, namely raw data denoising, leveraging deep learning algorithms. We design two architectures based on graph neural networks, aiming to enhance the receptive field of basic convolutional neural networks. We benchmark this approach against traditional algorithms implemented by the DUNE collaboration. We test the capabilities of graph neural network hardware accelerator setups to speed up training and inference processes., 9 pages, 7 figures, 3 tables. Code available at https://github.com/marcorossi5/DUNEdn

We introduce an automated tool for deploying ultra low-latency, low-power deep neural networks with convolutional layers on FPGAs. By extending the hls4ml library, we demonstrate an inference latency of $5\,\mu$s using convolutional architectures, targeting microsecond latency applications like those at the CERN Large Hadron Collider. Considering benchmark models trained on the Street View House Numbers Dataset, we demonstrate various methods for model compression in order to fit the computational constraints of a typical FPGA device used in trigger and data acquisition systems of particle detectors. In particular, we discuss pruning and quantization-aware training, and demonstrate how resource utilization can be significantly reduced with little to no loss in model accuracy. We show that the FPGA critical resource consumption can be reduced by 97% with zero loss in model accuracy, and by 99% when tolerating a 6% accuracy degradation., Comment: 18 pages, 18 figures, 4 tables

Haar WaveletsThe Haar TransformConservation and Compaction of EnergyRemoving Noise from Audio SignalsHaar WaveletsMultiresolution AnalysisCompression of Audio SignalsRemoving Noise from Audio SignalsNotes and ReferencesDaubechies WaveletsThe Daub4 WaveletsConservation and Compaction of EnergyOther Daubechies WaveletsCompression of Audio SignalsQuantization, Entropy, and CompressionDenoising Audio SignalsTwo-Dimensional Wavelet TransformsCompression of ImagesFingerprint CompressionDenoising ImagesSome Topics in Image ProcessingNotes and ReferencesFrequency AnalysisDiscrete Fourier AnalysisCorrelation and Feature DetectionObject Detection in 2-D ImagesCreating Scaling Signals and WaveletsNotes and ReferencesBeyond WaveletsWavelet Packet TransformsApplications of Wavelet Packet TransformsContinuous Wavelet TransformsGabor Wavelets and Speech AnalysisNotes and ReferencesAppendix: Software for Wavelet Analysis