The objective of this work is to develop a framework that exploits the lattice structure of the $k$-th Volterra--Bogoyavlensky equations ($k\in\mathbb N$, $k>1$) to generate rational solutions of higher symmetric Painlevé equations. For $k=2$, we show that the Volterra lattice, equipped with suitable initial conditions, exactly models the one- and two-dimensional orbits generated by half-translation operators of the $A_2^{(1)}$ symmetric Painlevé IV equations. This correspondence yields explicit closed-form expressions for all solution components in terms of generalized Okamoto polynomials and leads to new algebraic recurrence relations among these polynomials. We present two generalizations of the above Volterra lattice. One is derived from a fractional translation of the $A_{4}^{(1)}$ symmetric Painlevé equations. It generalizes Volterra lattice structure in the multi-compneent setup of the affine $A_{4}^{(1)}$ group and it is shown to generate solutions of the $A_{4}^{(1)}$ symmetric Painlevé equations from the seed solutions invariant under dihedral group $D_{5}$. The other is the $k=3$ Bogoyavlensky lattice structure. It satisfies recurrence relations that naturally extend recurrence relations of the Volterra lattice.

In the Born-Oppenheimer approximation for QCD, the exotic hidden-charm tetraquark meson $χ_{c1}(3872)$ is a near-threshold bound state in Born-Oppenheimer potentials associated with an isospin-0 adjoint meson. The $χ_{c1}(3872)$ is the $1^{++}$ member of a heavy-quark spin-symmetry multiplet whose other members have $J^{PC}$ quantum numbers $0^{++}$, $1^{+-}$, and $2^{++}$. We introduce a simple model for the Born-Oppenheimer potentials that interpolates between the adjoint-meson potential at short distances and the triplet-meson-pair potential at large distances. We take into account the spin splittings of charm mesons nonperturbatively for the first time by solving the diabatic Schrödinger equation. We also take into account the spin splittings of the adjoint meson as well as a narrow avoided crossing with the quarkonium potential. We tune the energy of $χ_{c1}(3872)$ to the $D^* \bar{D}$ threshold and then calculate the spin splittings of the other members of the multiplet and their decay widths into charm-meson pairs. We also calculate the energies and decay widths of the corresponding multiplet of hidden-bottom tetraquarks. These calculations provide a template for the quantitative analysis of all hidden-heavy hadrons using the Born-Oppenheimer approximation for QCD.

Witten recently proposed a background-independent algebraic framework for quantum gravity, wherein an observer endowed with a Hamiltonian defines a diffeomorphism invariant worldline algebra manifested by the modified Hamiltonian constraint. In the semiclassical limit, this construction admits a lift to a von Neumann algebra acting on a Hilbert space defined by geodesic in a fixed background. Motivated by this, we revisit quantization of certain class of deformed CFT Hamiltonian on a cylinder to capture non-perturbative aspects of black holes. We construct a type-I Von-Neuman algebra by imposing conformal boundary conditions on cut-offs near fixed points of Hamiltonian flow, acting on a GNS Hilbert space built from highest-weight representation of `emergent modular Virasoro algebra'. Upon identifying the Hamiltonian with the modular Hamiltonian of a sharp subregion associated to a fixed reference KMS (vacuum) state, the algebra changes to type-III$_{1}$ factor. We also discuss the structure of emergent Hilbert spaces using `open-closed string' duality after incorporating an emergent non-trivial center made out of scalars at fixed points. We further employ this modular quantization of a single holographic CFT to demonstrate how the boundary limit of exact Hartle-Hawking correlator of smooth BTZ background emerge in the strict semiclassical limit in an alternative dual description, while at finite $G_{N}$, the corresponding description is intrinsically non-smooth, featuring both a stretched horizon and a boundary cutoff. The exact correlator has also been precisely reproduced from the vacuum correlators in modular quantization. We further discuss the effect of incorporating gravity by including the center via AdS/CFT on boundary correlators, for which the description of a smooth horizon is replaced by a (stretched) horizon containing explicit microstructures embedded within it.

Hyperspectral standoff detection systems such as Focal Plane Array (FPA) Fourier Transform Infrared (FTIR) spectrometers provide high spatial resolution in detecting airborne chemical contaminants that are invisible to the human eye but potentially hazardous. When two such systems are operated simultaneously with a suitable opening angle, they enable tomographic reconstruction of contaminant plumes with improved spatial and temporal accuracy. This work presents a mathematical model of these measurement capabilities and an algorithm to identify, localize, and quantify contaminant release sources. The objective is to develop a a tool that reconstructs release locations and predict the future plume evolution from standoff measurement data, thereby supporting early warning and situational awareness in hazardous material release scenarios. The transport of contaminants is modeled by an advection-diffusion equation, and the corresponding inverse problem for source identification is formulated accordingly. Owing to the severe ill-posedness and underdetermination of the problem, a sparsity-promoting regularization approach is employed together with a high-performance optimization algorithm. To incorporate the tomographic measurement data into the discrete formulation, a level-set description of a threshold concentration is used, allowing the measurements to be represented independently of the computational mesh and avoiding costly remeshing procedures.

We give a dynamical proof of Benoist's non-arithmeticity theorem for Jordan spectra of Zariski dense subgroups of connected semisimple real algebraic groups. After passing to a Zariski dense Schottky subgroup, we use the coding of the limit set to realize Jordan projections as periods of a vector-valued Busemann return map for an expanding map on the Furstenberg boundary. The key step is to prove that a suitable two-branch asymptotic discrepancy is not locally constant on the limit set. We also show that the same criterion applies beyond Lie groups; in particular, it yields a direct density result for multiplier spectra of hyperbolic rational maps whose Julia set is not contained in a circle.

Multipartite entanglement is a uniquely quantum form of correlation that captures collective properties of a composite quantum state beyond those encoded in its bipartite subsystems. We investigate this phenomenon in the process $e^+e^-\to t\bar tZ$ at a future lepton collider, where the final state spins span the tripartite Hilbert space $\mathscr{H} = \mathbb{C}^2 \otimes \mathbb{C}^2 \otimes \mathbb{C}^3$. Starting from the Standard Model helicity amplitudes, we reconstruct the full $12\times 12$ spin density matrix and characterise its entanglement structure through one-to-one negativities, one-to-other negativities, and the genuine multipartite negativity, evaluated at three increasingly inclusive levels of phase space integration. Pairwise entanglement is generally suppressed relative to the collective (one-to-other) and the genuine multipartite entanglement, and all measures decrease as more kinematic information is integrated out. Assuming quantum tomography in the fully leptonic decay channel at $\sqrt{s}=1$ TeV, we find that collective entanglement should be accessible at a realistic high-luminosity polarised lepton collider. By contrast, certifying genuine multipartite entanglement is more challenging, with only limited sensitivity projected for a specific polarisation benchmark within the expected ILC luminosity. The study establishes $e^+e^-\to t \bar{t}Z$ as an attractive laboratory for probing multipartite entanglement in high-energy collisions and provides a general mixed state framework that applies to any tripartite spin system.

We develop a framework for conformal prediction in dyadic regression problems under complex missingness mechanisms. At the theoretical level, we develop general technical tools for establishing finite-sample validity of conformal prediction under distributional invariance conditions weaker than exchangeability. A key result handles the case where the sample itself is a random subset of the index set, a setting not covered by existing theory, via a novel bijection argument that constructs an explicit measure-preserving correspondence between events. In addition, we propose conformal prediction procedures for jointly exchangeable arrays, including full conformal, split conformal, a row-column approach exploiting similarities within rows and columns, and a selective conformal procedure achieving mask-conditional validity. For missing elements, we establish asymptotic validity of a weighted conformal procedure under a nonparametric graphon model for the missingness mechanism. We further establish conditional validity results for both continuous and discrete responses; to the best of our knowledge, this is the first formal proof of asymptotic conditional validity for weighted conformal prediction under a missing-not-at-random assumption. The proposed methods are illustrated on synthetic and real network data.

We construct a weighted Riemannian manifold $(\mathbb R^2,g,μ)$ satisfying $\mathrm{CD}(1/2,\infty)$, the curvature-dimension condition, with the following property: if $γ$ denotes a centered Gaussian measure on $\mathbb R^2$, then there is no Lipschitz map $T:(\mathbb R^2,\|\cdot\|) \to (\mathbb R^2,g)$ satisfying $T_\#γ=μ$. Building on this, we prove a Weyl-type asymptotic law for the eigenvalues of the weighted Laplacian $-Δ_{g,μ}$ and show that they are asymptotically negligible when compared to the eigenvalues of $-Δ_γ$. These results give strong counterexamples to two questions of E. Milman and complement the recent counterexample of Aryan.

We classify the distributional self-embeddings of the centered first limit Bourgain-Rosenthal-Schechtman space $R_ω^{p,0}$, $1<p<\infty$. Using a Boolean rigidity principle for its canonical independent-sum realization, we show that every such embedding is induced by a finite packing of Bernoulli factors. As a consequence, we also prove that $R_ω^{p,0}$ admits no proper non-zero internal compressions. Moreover, for $p\notin2\mathbb N$, we obtain a complete description of the linear isometric embeddings of the non-centered space $R_ω^p$, and, for $p\neq2$, we determine its group of surjective linear isometries.

Scaling superconducting quantum computers toward thousands of qubits remains a difficult control hardware problem. It requires hardware that reduces room-temperature to cryogenic wiring and cryogenic power while preserving in-fridge programmability for microwave pulse generation. This work develops a 4 K hybrid photonic/CMOS control architecture in which optical fibers distribute shared shaped pulse templates, while local cryogenic CMOS (Cryo-CMOS) circuits provide transmission control, amplitude programming, sample-and-hold envelope shaping, LO-tone and phase selection, and microwave upconversion, enabling both single-qubit and two-qubit gate generation within the same control path. Compared with fully Cryo-CMOS controllers, this architecture reduces per-channel active dissipation by moving high-speed sampled RF/IF waveform synthesis and waveform-memory access out of each cryogenic channel. Compared with purely photonic-link qubit-control approaches, it adds local 4 K programmability for pulse selection, amplitude scaling, timing updates, and LO-phase control, while remaining compatible with room-temperature real-time feedback and quantum error correction (QEC) workflows. We present architecture-level first-order models for 4 K power dissipation, waveform-memory scaling, and controller-induced fidelity limits, and cross-check the dominant fidelity terms using a three-level transmon simulation. The analysis shows that shared optical pulse template distribution with local 4 K envelope programming is a feasible path toward scalable superconducting qubit control.

We prove, to all orders, maximal transcendentality of the strongly coupled large-N Principal Chiral Model in the double-scaling regime introduced in our earlier work. We also prove that, after a natural shift of the coupling constant, the coefficients of the vacuum-energy expansion are expressed purely as polynomials in odd zeta values with rational coefficients. The first 35 explicitly computed orders reveal further number-theoretic regularities, pointing to hidden structure beyond maximal transcendentality.

The measurement of high energy diffuse gamma rays by various ground-based air shower detectors have opened a new chapter for high energy particle physics and astrophysics. The broad range of viable dark matter candidates motivates extending indirect searches to heavier dark matter masses, opening new opportunities to uncover the nature of dark matter. If dark matter is composite rather than point-like, then the thermal unitarity bound can be relaxed, opening up the possibility of dark matter masses far beyond the electroweak scale. We perform a model agnostic search for heavy annihilating dark matter using the gamma-ray measurements and upper limits from Tibet AS$_γ$, LHAASO, KASCADE-Grande, Pierre Auger Observatory, and Telescope Array. These highest energy datasets enable us to probe new regions of parameter space and set world-leading limits on the annihilation cross sections for dark matter masses $10^5$--$10^{12}$ GeV. Our work highlights the power of high energy gamma-ray datasets in discovering heavy dark matter signatures in the near future.

Boson clouds formed via superradiance around spinning black holes offer a novel probe of ultralight particles. We show that such gravitational atoms can undergo a self-stimulated avalanche: a coherent quadrupolar transition is seeded by external gravitational waves and amplified by self-generated radiation feedback. We formulate an effective two-level description, validated by numerical simulations, that captures the logistic population transfer and the resulting delayed gravitational-wave pulse with a characteristic envelope, and assess its detectability with future detectors. As a gravitational analogue of superfluorescence, this cooperative emission mechanism opens a new observational avenue into the ultralight dark sector.

We provide the cosmic-ray (CR) fluxes of antiprotons and antideuterons produced by the Galactic annihilation or decay of weak-scale dark matter (DM) particles of masses in the range from a few GeV to 100 TeV. We estimate these fluxes based on the updated models for the propagation of charged particles in the Galaxy and using the improved $\bar{p}$ and $\bar{d}$ spectra provided by $\texttt{CosmiXs}$. For the updated propagation models we consider the MIN/MED/MAX sets under the new SLIM/BIG/QUAINT schemes. We treat the Galactic propagation in a semi-analytic way including different possible effects such as spatial diffusion, energy-losses, convection and diffusive reacceleration. For the DM distribution in the Galactic halo we consider NFW, Einasto and Burkert profiles with the most updated parameters. Moreover, we also incorporate the latest models for the inelastic cross-sections of $\bar{p}$ and $\bar{d}$ based on ALICE data. We validate our calculations with those available in the literature or those obtained from other publicly available numerical packages. We compare the CR fluxes obtained in this work with those provided previously by $\texttt{PPPC4DMID}$ which were based on old propagation scenarios. We find that the CR fluxes obtained here with the new propagation models are much more robust (compared to the older ones) under the variation MIN - MAX. We also discuss the impact of this in the improvement of the discovery potential of a possible DM signal in the light of the present and upcoming CR observations. We provide all our results for the DM-induced interstellar CR fluxes in a tabulated format (for the kinetic energy range 0.1 GeV - 100 TeV) in the $\texttt{GitHub}$ repository of the newly created $\texttt{CosmiXsPPPC}$ project. The results are ready to be used for studies related to DM indirect searches.

We present the first Atacama Large Millimeter/submillimeter Array (ALMA) Band 3 (100 GHz) and Band 6 (243 GHz) continuum observations of the Arches cluster, one of the youngest and most massive stellar clusters in the Milky Way. We detect and characterise millimetre emission from 23 massive stars, including WN7-9h Wolf-Rayet stars, O-type supergiants and hypergiants. By combining our ALMA measurements with archival Very Large Array data spanning 5-22.5 GHz, we derive broadband radio-millimetre spectral indices and investigate the radial structure of stellar winds through frequency-dependent clumping diagnostics. The majority of Wolf-Rayet stars exhibit spectral indices clustered around $α\approx 0.7-0.8$, consistent with predominantly thermal free-free emission from dense, partially optically thick winds. In contrast, several O-type stars show flat or negative broadband spectral indices, indicative of non-thermal synchrotron emission likely associated with colliding-wind binaries. Using millimetre flux densities, we derive clumping-scaled mass-loss rates spanning $\log(\dot{M}/\mathrm{M}_{\odot}\,\text{yr}^{-1})\approx-4.1$ to $-4.9$ for the WN stars and $-4.9$ to $-5.4$ for the O super-/hypergiants, consistent with expectations for luminous massive stars in the Galactic Centre environment. We find significant evidence of structured wind clumping at millimetre wavelengths that generally decreases with increasing radius, supporting structured wind models with strong inner-wind inhomogeneities. These results demonstrate the power of combined radio-millimetre observations for constraining mass-loss and wind structure in massive stars, and provide new insight into stellar feedback in extreme cluster environments.

Michael Farber introduced a generalization of the Lusternik--Schnirelmann category for closed 1-forms. In this paper, we introduce and study a corresponding version of topological complexity for closed 1-forms. We establish analogues of the basic properties of ordinary topological complexity, including inequalities relating this invariant to the Lusternik--Schnirelmann category for closed 1-forms. We also prove a closed 1-form analogue of the navigation-function method: upper bounds for our invariant can be obtained from the dynamical properties of gradient-like flows of closed 1-forms.

We investigate the relationship between the analytical properties of functions of bounded variation and the statistical behavior of hyperuniform point processes. We establish several characterization formulas for the jump part of the gradient of a bounded variation function, extending and unifying previous results by Beretti--Gennaioli and Dávila. In particular, we provide new expressions for the $L^2$-jump of the gradient using both difference quotients and Fourier transform methods. Furthermore, we connect these analytic structures to the theory of hyperuniform point processes. By analyzing the variance of linear statistics associated with bounded variation functions, we provide asymptotic estimates that depend on the specific classification of the hyperuniformity of the point process. The results show how the regularity and jump discontinuities of a function dictate the growth rate of fluctuations in point processes. Finally, we introduce an averaged quadratic BMO-type oscillation functional over translated and rotated cube partitions, similar to the one recently studied by Ambrosio et al., and prove, using results from point process, that it converges to an explicit dimensional constant times the $L^2-$jump, giving in particular a further new characterization of the perimeter of a set.

This paper establishes for the first time the iterative and rigid theory of weak$^{*}$ slices within a non-metric framework, demonstrating that dual convex sets under the pure weak$^{*}$ topology can achieve localization, diameter control, and fine structural analysis. It fundamentally transforms the traditional understanding of the geometric properties of weak$^{*}$ topology and thereby pioneers a new direction in non-metric weak$^{*}$ slice geometry. By developing a new technique involving intricate manipulations of weak$^{*}$ slices and a carefully designed iterative selection process, we prove that if $M$ is a closed subspace of a G$\mathrm{\hat{a}}$teaux differentiability space $X$, then $M$ is a G$\mathrm{\hat{a}}$teaux differentiability space. As a Corollary, we get that if $X$ is a weak Asplund space and $M$ is a closed subspace of $X$, then $X$ is a G$\mathrm{\hat{a}}$teaux differentiability space. Thus, we definitively solve an open problem raised 46 years ago by D.G. Larman and R.R. Phelps (J. London Math. Soc., 20(1979), 115--127).

Hypercube graphs are fundamental model spaces of positive curvature in discrete comparison geometry. We establish the following spectral rigidity theorem. Let $G$ be a finite, connected, simple, unweighted graph with Bakry--Émery curvature bounded below by $K>0$. Denote by $Δ$ the maximum degree of $G$, and let $0=λ_0<λ_1\leq\cdots$ be the eigenvalues of the non-normalized Laplacian. Then $$ λ_{Δ-1}=K \quad\Longrightarrow\quad G\cong H_Δ, $$ where $H_Δ$ is the $Δ$-dimensional hypercube graph. Thus, in the unweighted setting, the multiplicity condition $λ_Δ=K$ appearing in the hypercube rigidity theorem of Liu, Münch, and Peyerimhoff can be weakened to $λ_{Δ-1}=K$. This improvement is optimal. The restriction to unweighted graphs is essential: the strengthened rigidity statement fails in the weighted setting. Our argument is built upon an interplay between the global spectral embedding induced by the first eigenspace and a local analysis of curvature matrices.

In this paper, we prove the local boundedness of solutions to systems of partial differential equations in divergence form. More specifically, we consider systems that include the first variations of functionals depending on the spatial variable and exhibiting nonstandard growth with respect to the gradient, such as $$\int_Ω \left( 1+ h(|Du|)\right) ^{α(x)} \, d x,$$ where the convex function $h=h(t)$ does not satisfy the so-called $Δ_2$ property and does not exhibit the conventional polynomial growth behavior.

Von Neumann's Hilbert-space formalism of quantum mechanics constitutes a logico-physical theory of observed or measured reality. Imposing the logical constraint of Booleanity, essential for objectively shareable descriptions among observers, reveals the physical meaning of classicality inherently embedded within the formalism itself. Starting from this consideration, the present work reformulates the quantum-classical transition via Hilbert-space classical mechanics (HCM), grounding classicality not in the dynamical limit ($\hbar \to 0$), but in the logical constraint of Booleanity (i.e., the mutual commutativity of preparable states). Within this state-centric framework, applying the Einstein-Podolsky-Rosen (EPR) criterion alongside locality and measurement independence reduces standard quantum mechanics to the HCM model. Thus, the EPR argument reveals not quantum incompleteness, but the implicit classical boundaries of its own premises. To resolve this impasse, we articulate a nuanced quantum ontology grounded in a fundamental structural bipartition between the observational environment and the observed object, which accommodates three categorical distinctions: ontic, processional, and tropos-existential. Building on this, we propose a criterion of objective reality wherein descriptive objectivity is treated as merely a sufficient condition for physical reality. This addresses the historical Bohr-Einstein ambiguity, enabling the quantum formalism to ontologically unify objective measured phenomena and non-objective observed interference within a context-dependent framework.

We develop a data-driven framework for estimating optimal linear response of nonlinear dynamical systems. Our approach is based on kernel-smoothed approximations of the transfer/Koopman operators of the system, built from possibly high-dimensional observations along trajectories. Combining these operator approximations with the theory developed in [Antown et al. (2018), J. Stat. Phys., 170(6), 1051-1087], we formulate a computationally tractable optimization problem for the optimal infinitesimal perturbation realising any desired manipulation of the spectrum. We also introduce a notion of optimal-response vector fields for visualising, and physically interpreting, the system's response to the optimal perturbation under arbitrary observations. Our focus is on finding perturbations that optimally increase the frequency or optimally suppress the decay of correlations of almost-cycles or almost-invariant sets associated with the eigenvalues of the kernel-smoothed transfer operator. We illustrate our approach with applications to low-dimensional periodic and chaotic systems, as well as a high-dimensional example involving the El Nino Southern Oscillation in a comprehensive Earth system model. In these examples our approach discovers nontrivial optimal perturbations of the system, which are post hoc natural and consistent with the desired dynamical objectives.

In the round $N$-sphere, we calculate the Morse index and nullity of all immersed minimal 2-spheres having constant Gauss curvature. We also obtain bounds on the stability index of the associative cone in $R^7$ whose link is the Boruvka sphere in $S^6$.

We study one-point functions of composites of charge $e$ operators in the presence of a monodromy defect for a $U(1)$ global symmetry with monodromy $β$. We first compute these in free massless and massive theories, recovering in the former case the known $\sin(eπβ)$ dependence and obtaining in the latter a $\sin^2(eπβ)$ dependence. We then turn to holography and compute 1-point functions for operators $O$ of charge $J=Δ$ in $\mathfrak{su}(N)$ $\mathcal{N}=4$ SYM in the presence of a monodromy defect for a $U(1)\in SO(6)_R$. From a WKB analysis in large $Δ$ we recover the structure of standard and anchored saddles previously found in the literature, finding that, to subleading order in $1/Δ$, the anchored regime is resolved by a boundary layer effect. Finally, using heat kernel methods, we determine the monodromy dependence of the induced 1-point function for the composite $O^{\dagger}O$, finding a smooth $\sin^2(Jπβ)$ behavior.

Several studies have associated globular clusters (GCs) with former Galactic accretion events by comparing their positions in the energy-angular momentum ($E$-$L_z$) plane, an approach further supported by similarities in their age-metallicity relations. However, recent merger simulations suggest that GCs initially associated with the Gaia-Sausage-Enceladus (GSE) disc may have lost their orbital energy and thus may not reliably trace this accretion event. We extend this framework by considering three N-body simulations of the Milky Way-GSE merger with different initial masses, mass ratios, and gas content. In addition to GCs belonging to the GSE disc progenitor, we accounted for GCs in its halo and, in gas-rich models, a population of GCs formed during the Milky Way-GSE merger. We confirm that most GCs originating in the disc have lost a significant part of their orbital energy during repeated passages through the dense disc medium, and we conjecture that associated tidal shocks may have destroyed many of them. In contrast, GCs from the halo and GCs formed during the merger have largely retained their orbital energy, which remains comparable to that of GSE stars even up to 9 Gyr after the completion of the merger. By using a more realistic GC population and GSE modelling, we find that most GCs linked to GSE can be associated with Milky Way accretion events in the $E$-$L_z$ plane, which supports previous observational associations based on a combination of energy-angular momentum and age-metallicity relations.

Ordinary, s-wave superconductors have been recognized as being topological phases of matter, in which the dynamical gauge field implies less understood global features. Using the tools of topological field theories and generalized symmetries, we provide an updated description of these systems. At very low energies, the Higgs model reduces to the BF theory, which exhibits topological order. Furthermore, the gauge field must be a spin$_c$ connection, to describe the spin of fermions forming Cooper pairs. Gauging implies that superconductors are inherently bosonic systems, yet they are endowed with a gravito-magnetic anomaly that is the remnant of their fermionic origin. We recognize that this anomaly is related to the Gaiotto-Kapustin-Thorngren bosonization, achieved via gauging fermion parity $(-1)^F$, now included in the gauge dynamics. This anomaly characterizes gauged electronic matter in great generality in three and four spacetime dimensions, forbidding trivial massive phases at low energy. It holds beyond the validity of the Higgs model, nd in other kinds of superconductors as well. It also appears in the nontrivial massless phase of three-dimensional electrodynamics, recently understood.

The open quantum Rabi model describes a two-level system coupled to a harmonic oscillator. A Gaussian phase transition for the nonequilibrium steady states has been predicted when the bosonic mode is soft and subject to damping. We show that oscillator dephasing is a relevant perturbation, which leads to a non-Gaussian phase transition and an intriguing cascade of instabilities for $k$-th order bosonic operators, as well as a jump in the steady-state qubit polarization. For the soft-mode limit, the equations of motion form a closed hierarchy and spectral properties can be efficiently studied. To this purpose, we establish a fruitful connection to non-Hermitian Hamiltonians. The results for the phase diagram, stability boundaries, and relevant observables are based on mean-field analysis, exact diagonalization, perturbation theory, and Keldysh field theory.

A novel numerical technique is presented to transform one random variable within a system toward statistical quasi-independence from any other random variable in the system. The method's applicability is demonstrated through a particle physics example where a classifier is rendered quasi-independent from an observable quantity.

Converting customer survey feedback data into usable insights has always been a great challenge for large software enterprises. Despite the improvements on this field, a major obstacle often remains when drawing the right conclusions out of the data and channeling them into the software development process. In this paper we present a practical end-to-end approach of how to extract useful information out of a data set and leverage the information to drive change. We describe how to choose the right metrics to measure, gather appropriate feedback from customer end-users, analyze the data by leveraging methods from inferential statistics, make the data transparent, and finally drive change with the results. Furthermore, we present an example of a UX prototype dashboard that can be used to communicate the analyses to stakeholders within the company.

We define and study two new classes of algebras, called higher-level affine wreath product algebras and higher-level affine Frobenius Hecke algebras. They depend on a Frobenius superalgebra and are defined, respectively, as path algebras of the higher-level affine wreath product category and higher-level affine Frobenius Hecke category. Our constructions produce a broad range of new higher-level algebras under a unified framework. Special cases include higher-level analogues of the degenerate affine Hecke algebra and affine Sergeev algebras, both of which appear to be new.