We developed a low-energy model that can be used at any time to describe the dynamics of DNA bubbles at temperatures below the melting point. The Schrödinger equation associated with this problem is solved in imaginary time with a quantum Coulomb potential, and we obtain an approximate expression for its more general physical solution as a linear combination of the states whose energies are close to the lower bound energy. We can then determine the probability density, the first-passage time density, and the correlation functions in terms of Bessel functions. Our findings are consistent with results obtained directly from the Fokker-Planck equation. Comparisons with the Gamma and Diffusion models are discussed.

In this study, we apply 1D quantum convolution to address the task of time series forecasting. By encoding multiple points into the quantum circuit to predict subsequent data, each point becomes a feature, transforming the problem into a multidimensional one. Building on theoretical foundations from prior research, which demonstrated that Variational Quantum Circuits (VQCs) can be expressed as multidimensional Fourier series, we explore the capabilities of different architectures and ansatz. This analysis considers the concepts of circuit expressibility and the presence of barren plateaus. Analyzing the problem within the framework of the Fourier series enabled the design of an architecture that incorporates data reuploading, resulting in enhanced performance. Rather than a strict requirement for the number of free parameters to exceed the degrees of freedom of the Fourier series, our findings suggest that even a limited number of parameters can produce Fourier functions of higher degrees. This highlights the remarkable expressive power of quantum circuits. This observation is also significant in reducing training times. The ansatz with greater expressibility and number of non-zero Fourier coefficients consistently delivers favorable results across different scenarios, with performance metrics improving as the number of qubits increases.

September 7, 2025 marked the 80th anniversary of the birth of Oleg Marichev. Marichev is known mathematician which has developed many of Mathematica's algorithms for the calculation of definite and indefinite integrals and hypergeometric functions including Meijer G-function.

This work introduces Federated Adaptive Gain via Dual Signal Trust (FedAgain), a novel federated learning algorithm designed to enhance anomaly detection in medical imaging under decentralized and heterogeneous conditions. Focusing on the task of kidney stone classification, FedAgain addresses the common challenge of corrupted or low-quality client data in real-world clinical environments by implementing a dual-signal trust mechanism based on reconstruction error and model divergence. This mechanism enables the central server to dynamically down-weight updates from untrustworthy clients without accessing their raw data, thereby preserving both model integrity and data privacy. FedAgain employs deep convolutional autoencoders trained in two diverse kidney stone datasets and is evaluated in 16 types of endoscopy-specific corruption at five severity levels. Extensive experiments demonstrate that FedAgain effectively suppresses "expert forger" clients, enhances robustness to image corruptions, and offers a privacy-preserving solution for collaborative medical anomaly detection. Compared to traditional FedAvg, FedAgain achieves clear improvements in all 16 types of corruption, with precision gains of up to +14.49\% and F1 score improvements of up to +10.20\%, highlighting its robustness and effectiveness in challenging imaging scenarios.

This is the third out of five chapters of the final report [1] of the Workshop on Physics at HL-LHC, and perspectives on HE-LHC [2]. It is devoted to the study of the potential, in the search for Beyond the Standard Model (BSM) physics, of the High Luminosity (HL) phase of the LHC, defined as $3~\mathrm{ab}^{-1}$ of data taken at a centre-of-mass energy of $14~\mathrm{TeV}$, and of a possible future upgrade, the High Energy (HE) LHC, defined as $15~\mathrm{ab}^{-1}$ of data at a centre-of-mass energy of $27~\mathrm{TeV}$. We consider a large variety of new physics models, both in a simplified model fashion and in a more model-dependent one. A long list of contributions from the theory and experimental (ATLAS, CMS, LHCb) communities have been collected and merged together to give a complete, wide, and consistent view of future prospects for BSM physics at the considered colliders. On top of the usual standard candles, such as supersymmetric simplified models and resonances, considered for the evaluation of future collider potentials, this report contains results on dark matter and dark sectors, long lived particles, leptoquarks, sterile neutrinos, axion-like particles, heavy scalars, vector-like quarks, and more. Particular attention is placed, especially in the study of the HL-LHC prospects, to the detector upgrades, the assessment of the future systematic uncertainties, and new experimental techniques. The general conclusion is that the HL-LHC, on top of allowing to extend the present LHC mass and coupling reach by $20-50\%$ on most new physics scenarios, will also be able to constrain, and potentially discover, new physics that is presently unconstrained. Moreover, compared to the HL-LHC, the reach in most observables will generally more than double at the HE-LHC, which may represent a good candidate future facility for a final test of TeV-scale new physics.

The first measurement of the charged-particle multiplicity density at mid-rapidity in Pb-Pb collisions at a centre-of-mass energy per nucleon pair $\sqrt{s_{\rm NN}}$ = 2.76 TeV is presented. For an event sample corresponding to the most central 5% of the hadronic cross section the pseudo-rapidity density of primary charged particles at mid-rapidity is 1584 $\pm$ 4 (stat) $\pm$ 76 (sys.), which corresponds to 8.3 $\pm$ 0.4 (sys.) per participating nucleon pair. This represents an increase of about a factor 1.9 relative to pp collisions at similar collision energies, and about a factor 2.2 to central Au-Au collisions at $\sqrt{s_{\rm NN}}$ = 0.2 TeV. This measurement provides the first experimental constraint for models of nucleus-nucleus collisions at LHC energies.

The first and second-order supersymmetry transformations are used to generate Hamiltonians with known spectra departing from the trigonometric Poschl-Teller potentials. The several possibilities of manipulating the initial spectrum are fully explored, and it is shown how to modify one or two levels, or even to leave the spectrum unaffected. The behavior of the new potentials at the boundaries of the domain is studied.

Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems, can help to understand observables that otherwise show a puzzling behavior. Furthermore, when these fields are comparable to or stronger than \Lambda_QCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. In this work we provide a comprehensive review of recent developments on the description of QED and QCD systems where magnetic field driven effects are important. These include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work represents a state-of-the-art review of the field, motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.

We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. In this paper, we give a relationship between the Laplacian spectra of any two token graphs of a given graph. In particular, we show that, for any integers $h$ and $k$ such that $1\le h\le k\le \frac{n}{2}$, the Laplacian spectrum of $F_h(G)$ is contained in the Laplacian spectrum of $F_k(G)$. We also show that the double odd graphs and doubled Johnson graphs can be obtained as token graphs of the complete graph $K_n$ and the star $S_{n}=K_{1,n-1}$, respectively. Besides, we obtain a relationship between the spectra of the $k$-token graph of $G$ and the $k$-token graph of its complement $\overline{G}$. This generalizes a well-known property for Laplacian eigenvalues of graphs to token graphs. Finally, the double odd graphs and doubled Johnson graphs provide two infinite families, together with some others, in which the algebraic connectivities of the original graph and its token graph coincide. Moreover, we conjecture that this is the case for any graph $G$ and its token graph.

Diffractive electroproduction of rho and phi mesons is measured at HERA with the H1 detector in the elastic and proton dissociative channels. The data correspond to an integrated luminosity of 51 pb^-1. About 10500 rho and 2000 phi events are analysed in the kinematic range of squared photon virtuality 2.5 < Q^2 < 60 GeV^2, photon-proton centre of mass energy 35 < W < 180 GeV and squared four-momentum transfer to the proton |t| < 3 GeV^2. The total, longitudinal and transverse cross sections are measured as a function of Q^2, W and |t|. The measurements show a transition to a dominantly "hard" behaviour, typical of high gluon densities and small q\bar{q} dipoles, for Q^2 larger than 10 to 20 GeV^2. They support flavour independence of the diffractive exchange, expressed in terms of the scaling variable (Q^2 + M_V^2)/4, and proton vertex factorisation. The spin density matrix elements are measured as a function of kinematic variables. The ratio of the longitudinal to transverse cross sections, the ratio of the helicity amplitudes and their relative phases are extracted. Several of these measurements have not been performed before and bring new information on the dynamics of diffraction in a QCD framework. The measurements are discussed in the context of models using generalised parton distributions or universal dipole cross sections.

We define a time-dependent extension of the quantum geometric tensor to describe the geometry of the time-parameter space for a quantum state, by considering small variations in both time and wave function parameters. Compared to the standard quantum geometric tensor, this tensor introduces new temporal components, enabling the analysis of systems with non-time-separable or explicitly time-dependent quantum states and encoding new information about these systems. In particular, the time-time component of this tensor is related to the energy dispersion of the system. We applied this framework to a harmonic/inverted oscillator, a time-dependent harmonic oscillator, and a chain of generalized harmonic/inverted oscillators. We show some results on the scalar curvature associated with the time-dependent quantum geometric tensor and the generalized Berry curvature behavior on the transition from harmonic oscillators to inverted ones. Furthermore, we analyze the entanglement for the chain through purity analysis, obtaining that the purity for any excited state is zero in the mentioned transitions.

Face Anti-Spoofing (FAS) is crucial to safeguard Face Recognition (FR) Systems. In real-world scenarios, FRs are confronted with both physical and digital attacks. However, existing algorithms often address only one type of attack at a time, which poses significant limitations in real-world scenarios where FR systems face hybrid physical-digital threats. To facilitate the research of Unified Attack Detection (UAD) algorithms, a large-scale UniAttackData dataset has been collected. UniAttackData is the largest public dataset for Unified Attack Detection, with a total of 28,706 videos, where each unique identity encompasses all advanced attack types. Based on this dataset, we organized a Unified Physical-Digital Face Attack Detection Challenge to boost the research in Unified Attack Detections. It attracted 136 teams for the development phase, with 13 qualifying for the final round. The results re-verified by the organizing team were used for the final ranking. This paper comprehensively reviews the challenge, detailing the dataset introduction, protocol definition, evaluation criteria, and a summary of published results. Finally, we focus on the detailed analysis of the highest-performing algorithms and offer potential directions for unified physical-digital attack detection inspired by this competition. Challenge Website: this https URL.

We study the quantum metric tensor and its scalar curvature for a particular version of the Lipkin-Meshkov-Glick model. We build the classical Hamiltonian using Bloch coherent states and find its stationary points. They exhibit the presence of a ground state quantum phase transition, where a bifurcation occurs, showing a change of stability associated with an excited state quantum phase transition. Symmetrically, for a sign change in one Hamiltonian parameter, the same phenomenon is observed in the highest energy state. Employing the Holstein-Primakoff approximation, we derive analytic expressions for the quantum metric tensor and compute the scalar and Berry curvatures. We contrast the analytic results with their finite-size counterparts obtained through exact numerical diagonalization and find an excellent agreement between them for large sizes of the system in a wide region of the parameter space, except in points near the phase transition where the Holstein-Primakoff approximation ceases to be valid.

In this study, we revisit the Schwinger-Dyson equation for the electron propagator in QED in three and four space-time dimensions. Our analysis addresses the non-perturbative phenomenon of dynamical chiral symmetry breaking, which requires a critical value of the coupling for the dynamical generation of electron masses, encoded in the infrared behavior of the corresponding Green function. With a minimalistic truncation of the infinite tower of equations and adopting standard assumptions, the resulting gap equation is linearized and transformed into a Schrödinger-like equation with an auxiliary potential barrier (or well) subjected to boundary conditions for both high and low momenta. The dynamical mass is then associated with the zero mode of the corresponding Schrödinger-like operator and follows the Miransky scaling law, as expected.

Recent progress in AutoML has lead to state-of-the-art methods (e.g., AutoSKLearn) that can be readily used by non-experts to approach any supervised learning problem. Whereas these methods are quite effective, they are still limited in the sense that they work for tabular (matrix formatted) data only. This paper describes one step forward in trying to automate the design of supervised learning methods in the context of text mining. We introduce a meta learning methodology for automatically obtaining a representation for text mining tasks starting from raw text. We report experiments considering 60 different textual representations and more than 80 text mining datasets associated to a wide variety of tasks. Experimental results show the proposed methodology is a promising solution to obtain highly effective off the shell text classification pipelines.

We revisit the connection between trajectories of accelerated mirrors and spacetime metrics. We present the general (1+1)D effective metric that can be obtained with a fibre-optical analogue through the Kerr effect. Then we introduce a new connection between accelerated mirrors and the optical metric. In particular, we connect them for two specific trajectories: The first one is the black mirror that perfectly recreates the Schwarzchild spacetime. The second one is the Schwarzschild-Planck metric that is a regularized version of the Schwarzschild case. The regularization depends on a length scale that has a clear physical interpretation in the fibre-optical analogue system. We study the geometric properties and the Hawking radiation produced in these new analogue metrics.

Analytical expressions are derived for the distribution rates of spatial coincidences in the counting of photons produced by spontaneous parametric down conversion (SPDC). Gaussian profiles are assumed for the wave function of the idler and signal light created in type-I SPDC. The distribution rates describe ellipses on the detection planes that are oriented at different angles according to the photon coincidences in either horizontal-horizontal, vertical-vertical, horizontal-vertical or vertical-horizontal position variables. The predictions are in agreement with the experimental data obtained with a type-I BBO crystal that is illuminated by a 100 mW violet pump laser as well as with the results obtained from the geometry defined by the phase-matching conditions.

Network Function Virtualization (NFV) has recently received significant attention as an innovative way of deploying network services. By decoupling network functions from the physical equipment on which they run, NFV has been proposed as passage towards service agility, better time-to-market, and reduced Capital Expenses (CAPEX) and Operating Expenses (OPEX). One of the main selling points of NFV is its promise for better energy efficiency resulting from consolidation of resources as well as their more dynamic utilization. However, there are currently no studies or implementations which attach values to energy savings that can be expected, which could make it hard for Telecommunication Service Providers (TSPs) to make investment decisions. In this paper, we utilize Bell Labs' GWATT tool to estimate the energy savings that could result from the three main NFV use cases Virtualized Evolved Packet Core (VEPC), Virtualized Customer Premises Equipment (VCPE) and Virtualized Radio Access Network (VRAN). We determine that the part of the mobile network with the highest energy utilization prospects is the Evolved Packet Core (EPC) where virtualization of functions leads to a 22% reduction in energy consumption and a 32% enhancement in energy efficiency.

The inverse problem of recovery of a potential on a quantum tree graph from Weyl's matrix given at a number of points is considered. A method for its numerical solution is proposed. The overall approach is based on the leaf peeling method combined with Neumann series of Bessel functions (NSBF) representations for solutions of Sturm-Liouville equations. In each step, the solution of the arising inverse problems reduces to dealing with the NSBF coefficients. The leaf peeling method allows one to localize the general inverse problem to local problems on sheaves, while the approach based on the NSBF representations leads to splitting the local problems into two-spectra inverse problems on separate edges and reduce them to systems of linear algebraic equations for the NSBF coefficients. Moreover, the potential on each edge is recovered from the very first NSBF coefficient. The proposed method leads to an efficient numerical algorithm that is illustrated by numerical tests.

A new form to construct complex superpotentials that produce real energy spectra in supersymmetric quantum mechanics is presented. This is based on the relation between the nonlinear Ermakov equation and a second order differential equation of the Schroedinger type. The superpotentials so constructed are characterized by the Ermakov parameters in such a way that they are always complex-valued and lead to non-Hermitian Hamiltonians with real spectra, whose eigenfunctions form a bi-orthogonal system. As applications we present new complex supersymmetric partners of the free particle that are PT-symmetric and can be either periodic or regular (of the Poeschl-Teller form). A new family of complex oscillators with real frequencies that have the energies of the harmonic oscillator plus an additional real eigenvalue is introduced.