This article provides a simple trigonometric method for determining how many roots of a quintic equation are real and how many are complex, without solving the equation. The approach transforms a depressed quintic $t^5 + mt^3 + nt^2 + pt + q = 0$ with $m < 0$ into the trigonometric equation $f(θ) = α\cos^2\!θ+ β\cosθ+ \cos 5θ+ γ= 0$ via the Chebyshev identity $16\cos^5\!θ- 20\cos^3\!θ+ 5\cosθ= \cos 5θ$. The derivation is computationally light and conceptually natural, extending the quartic case to fifth-degree equations. As the Abel--Ruffini theorem forbids a general algebraic solution for the quintic, having a simple trigonometric criterion for the nature of its roots is especially appealing.

We consider a two-component semilinear reaction-diffusion system in a bounded spatial domain $Ω$ over a time interval $(0,T)$, which governs the water density $u(x,t)$ and the vegetation biomass density $v(x,t)$ for $x\inΩ$ and $0<t<T$. In this system, called the Klausmeier-Gray-Scott model, we assume that an unknown source depends only on the spatial variable and appears in the reaction-diffusion equation for $u$. The main subject is the inverse source problem of determining a source term from limited data on $(u,v)$. We establish two kinds of stability estimates by means of Carleman estimates. First, a Carleman estimate with a singular weight yields a Lipschitz stability estimate for the inverse source problem from data consisting of a snapshot $u(\cdot,t_0)$ in $Ω$ and $(u,v)$ in a subdomain $ω$ over a time interval. Second, without assuming boundary data, we prove a Hölder stability estimate in any interior subdomain $Ω_0$ satisfying $\overline{Ω_0}\subsetΩ$. We further study how much the observation data can be reduced while preserving uniqueness and stability in the inverse problem under suitable additional conditions.

We study the conditions under which Matrix Product States (MPS) or Matrix Product Operators are exact eigenvectors of an extensive local operator, such as a Hamiltonian. By suitably choosing the local operator, this covers a wide range of settings: Exact eigenstates of Hamiltonians, including scar states, exact MPS trajectories for driven quantum systems, steady states of local Lindbladians, generalized symmetries of either Hamiltonians or density matrices, and many more. Our key result is that that a local, fixed-size equation -- namely, how a single term in the operator acts on a block of tensors -- provides a necessary and sufficient condition for exact solutions. This allows to characterize the full space of solutions in all of the aforementioned problems, and to identify them both analytically and numerically. We elaborate on the concrete application of this characterization to all of the aforementioned settings, and in particular exemplify the power of our local characterization by using it to recover the quantum group symmetries of the XXZ model. We also discuss applications to numerical algorithms with MPS and the generalization of our results to 2D, i.e., projected entangled pair states (PEPS).

In this paper, we continue to study billiards inside cones $K\subset \mathbb{R}^n$ over strictly convex closed $C^3$ manifolds with non-degenerate second fundamental form. Recently we proved that the billiard is superintegrable, i.e., the billiard admits first integrals whose values uniquely determine all billiard trajectories. In this paper we prove that this billiard system admits $n-1$ independent first integrals in involution. Consequently, the system is completely integrable as a discrete-time Hamiltonian system. This provides an example of an integrable billiard where the billiard table is neither a quadric nor consists of pieces of quadrics.

We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. We implement a functional analysis of variance (FANOVA) to decompose high-dimensional functional time series, such as subnational age- and sex-specific mortality observed over years, into two distinct components: a deterministic mean structure and a residual process varying over time. Unlike purely statistical dimensionality-reduction techniques, the FANOVA decomposition provides a direct and interpretable framework by partitioning the series into effects attributable to data-specific factors, such as regional and sex-level variations, and a grand functional mean. From the residual process, we implement a functional factor model to capture the remaining stochastic trends. By combining the forecasts of the residual component with the estimated deterministic structure, we obtain the forecasted curves for high-dimensional functional time series. Illustrated by the age-specific Japanese subnational mortality rates from 1975 to 2023, we evaluate and compare the accuracy of the point and interval forecasts across various forecast horizons. The results demonstrate that leveraging these interpretable components not only clarifies the underlying drivers of the data but also improves forecast accuracy, providing more transparent insights for evidence-based policy decisions.

Catalytic carbon fixation to formic acid is important for studying the reduction of carbon footprint and the emergence of life. Can discrete quantum exhaustive search merged with other methods help reduce the carbon footprint? We suggest merging quantum, quantum inspired, and classical tools for a better simulation of various relevant processes. Quantum tools are often used for analyzing the electronic structure of molecules, sometimes because this problem is not scalable (in the number of orbitals) on classical computers while it is potentially approximately scalable on (future) quantum computers. It is potentially even solvable in the near future using variational quantum eigensolvers (VQE) yet a major obstacle to such analysis is the appearance of barren plateaus in the Hilbert space describing the problem. Here we make use of the basic (standard) tools while also including a novel one -- the discrete quantum exhaustive search, which relies on mutually unbiased bases, for analyzing the simplest non-catalytic process involving carbon dioxide, hydrogen and formic acid.

Classical eddy viscosity models of turbulence add an eddy viscosity term based on the Kolmogorov-Prandtl parameterization by a turbulent length scale $l$ and a turbulent kinetic energy $k^{\prime }$. Approximations of the unknowns $l,k^{\prime }$ are typically constructed by solving multi-parameter systems of nonlinear convection-diffusion-reaction equations. Often these over-diffuse so additional fixes are added. Alternately, one can solve an ensemble of NSE's with perturbed data and simply compute directly $k^{\prime }$(without modeling). The question then arises: Does this ensemble eddy viscosity approach over-diffuse solutions? We prove herein that for turbulence in a periodic box it does not.

Urban HCI investigates how digital technologies shape human behaviour within the social, spatial, temporal dynamics of public space. Meanwhile, robotic furniture research demonstrates how the purposeful animation of mundane utilitarian elements can influence human behaviour in everyday contexts. Taken together, these strands highlight an untapped opportunity to investigate how animated public furniture could mediate social interaction in urban environments. In this paper, we present the design process and in-the-wild study of mobile robotic benches that reconfigure with a semi-outdoor public space. Our findings show that the gestural performance of the benches manifested three affordances perceived by passersby, they activated engagement as robots, redistributed engagement as spatial elements, and settled engagement as infrastructure. We proposed an Affordance Transition Model (ATM) describing how robotic furniture could proactively facilitate transition between these affordances to engage passersby. Our study bridges robotic furniture and urban HCI to activate human experience with the built environment purposefully.

Adversarial training is a standard defense against malicious input perturbations in security-critical machine-learning systems. Its main burden is structural: before every parameter update, the current model must first be attacked to find a new adversarial perturbation, making training increasingly expensive and hard to sustain at large-model scale. Here we give an end-to-end quantum procedure for projected-gradient robust training under local stability and sparsity assumptions. The key step is to reformulate the coupled attacker--learner dynamics as a high-dimensional sparse linear system whose terminal block yields the final network-parameter state. In this formulation, the dominant query cost scales linearly with training time steps, up to logarithmic factors, and polylogarithmically with model size, while the full gate complexity records separate input-preparation and sparse-access overheads. This places core computational tasks for AI security on a concrete quantum footing and identifies a regime in which robust-training overhead can be reduced.

Emerging technologies introduce sociotechnical tensions that call for closer collaboration between technology design and policy. In this work, we introduce Design-Policy Adversarial Futuring, a scenario-based workshop method that supports design-policy engagement by structuring contestation between design and policy perspectives. We report on a workshop conducted in the autonomous mobility domain with 12 HCI researchers, used to explore and demonstrate the method in practice. The workshop illustrates how the adversarial futuring method can surface shifting harms, translate policy abstractions into situated use, and legitimise extreme ideas while maintaining grounded policy reasoning. This work contributes a reusable, exploratory method for supporting HCI-policy collaboration through contestation, which can be adapted across emerging technological domains.

Mechanisms of Mesogenesis generate the baryon asymmetry and dark matter of the Universe through late-time decays of Standard Model mesons into baryons and dark matter states. Utilizing the CP violation in the meson systems themselves, the resulting baryon asymmetry is directly controlled by collider observables, the CP asymmetry $A_{CP}$, and the branching fraction for the meson decays. Experimental probes of these decays place strong constraints on the amount of $CP$ violation required, placing it well above observed limits in meson mixing. Additionally, strong lower bounds on the proton lifetime seemingly rule out Mesogenesis mechanisms which use $D$ mesons. In this work, we propose to circumvent these constraints by ``morphing'' the mass of the dark sector particles using a late-time phase transition. The change in mass of the final decay products kinematically excludes meson and proton decays, relaxing the constraints on the model parameter space.

Federated Learning (FL) has emerged as a prominent paradigm for privacy-preserving distributed machine learning, yet two fundamental challenges hinder its large-scale adoption. First, gradient inversion attacks can reconstruct sensitive training data from uploaded model updates, so privacy risk persists even when raw data remain local. Second, without adequate monetary compensation, rational clients have little incentive to contribute high-quality gradients, limiting participation at scale. To address these challenges, a privacy trading market is developed in which clients sell their differential privacy budgets as a commodity and receive explicit economic compensation for privacy sacrifice. This market is formalized as a Privacy Auction Game (PAG), and the existence of a Bayesian Nash Equilibrium is established under dominant-strategy incentive compatibility (DSIC), individual rationality (IR), and budget feasibility. To overcome the NP-hard, high-dimensional Nash Equilibrium computation at scale, \textit{MFG-RegretNet} is introduced as a deep-learning-based auction mechanism that combines mean-field game (MFG) approximation with differentiable mechanism design. The MFG reduction lowers per-round computational complexity from $\mathcal{O}(N^2 \log N)$ to $\mathcal{O}(N)$ while incurring only an $\mathcal{O}(N^{-1/2})$ equilibrium approximation gap. Extensive experiments on MNIST and CIFAR-10 demonstrate that MFG-RegretNet outperforms state-of-the-art baselines in incentive compatibility, auction revenue, and social welfare, while maintaining competitive downstream FL model accuracy.

The Rust programming language is famous for its strong ownership regime: at each point, each value is either exclusively owned, exclusively borrowed through a mutable reference, or borrowed as read-only through one or more shared references. These rules, known as Rust's pointer-aliasing rules, are exploited by the Rust compiler to generate more efficient machine code, and enforced by Rust's static type system, except inside unsafe blocks. In this paper, we present our work in progress towards the first program logic for modularly verifying that Rust programs that use unsafe blocks comply with the pointer-aliasing rules.

We present a computationally tractable framework for real-time predictive control of multi-chiller plants that involve both discrete and continuous control decisions coupled through nonlinear dynamics, resulting in a mixed-integer optimal control problem. To address this challenge, we extend Differentiable Predictive Control (DPC) -- a self-supervised, model-based learning methodology for approximately solving parametric optimal control problems -- to accommodate mixed-integer control policies. We benchmark the proposed framework against a state-of-the-art Model Predictive Control (MPC) solver and a fast heuristic Rule-Based Controller (RBC). Simulation results demonstrate that our approach achieves significant energy savings over the RBC while maintaining orders-of-magnitude faster computation times than MPC, offering a scalable and practical alternative to conventional combinatorial mixed-integer control formulations.

Complex survey data are usually collected following complex sampling designs. Accounting for the sampling design is essential to obtain unbiased estimates and valid inferences when analyzing complex survey data. The area under the receiver operating characteristic curve (AUC) is routinely used to assess the discriminative ability of predictive models for binary outcomes. However, valid inference for the AUC under complex sampling designs remains challenging. Although bootstrap techniques are widely applied under simple random sampling for variance estimation in this framework, traditional implementations do not account for complex designs. In this work, we propose a design-based framework for AUC inference. In particular, replicate weights methods are used to construct confidence intervals and hypothesis tests. The performance of replicate weights methods and the traditional non-design-based bootstrap for this purpose has been analyzed through an extensive simulation study. Design-based methods achieve coverage probabilities close to nominal levels and appropriate rejection rates under the null hypothesis. In contrast, the traditional non-design-based bootstrap method tends to underestimate the variance, leading to undercoverage and inflated rejection rates. Differences between methods decrease as the number of selected clusters per stratum increases. An application to data from the National Health and Nutrition Examination Survey (NHANES) illustrates the practical relevance of the proposed framework. The methods have been incorporated into the svyROC R package.

We explore the combined lepton and hadron kinematic observables from the exclusive Valencia $2p2h$ model. We present variables of interest which are available due to the exclusive kinematics and compare them with the democratically distributed outgoing nucleon kinematics as currently treated in neutrino event generators. We also show the effect of nuclear re-scattering based on the NEUT semi classical cascade. We comment on the observability of these variables in current and future long baseline neutrino detectors.

Recently, a two-way RFID authentication protocol based on the AM-SUEO-DBLTKM variable matrix encryption algorithm was proposed for low-cost mobile RFID systems. Its design combines adaptive modulus selection, self-updating matrix ordering, and transpose/block-based matrix generation. In this paper, we show that the protocol has structural weaknesses. First, the underlying primitive remains a linear transformation modulo a session modulus, with no nonlinear confusion layer and no ciphertext chaining. Second, in the lightweight setting emphasized by the original paper, the update space is very small: there are only a few modulus choices, only four matrix-order choices when two secret matrices are used, and only a limited family of DBLTKM-generated matrices. Third, the correctness requirements of the protocol impose nontrivial constraints on the sizes of the modulus and plaintext coordinates, weakening the claimed entropy of the secret quantities. Building on these observations, we describe a multi-session algebraic attack path. Under repeated reuse of the same matrix and modulus -- an event plausible because of the small update space -- ciphertexts corresponding to $N_t$, $N_t+1$, $N_r$, and $N_r+1$ reveal a full column of the matrix. Across sessions, transpose-based matrix generation helps recover additional entries of the secret matrices, while the remaining entries can be obtained later from ordinary ciphertext equations. We then show that candidate factors of the session moduli can be tested by solving reduced equations for secret $S$ across many sessions and checking for mutually consistent solutions. This, in turn, enables recovery of candidate 64-bit moduli and the remaining protocol secrets. Taken together, our results indicate that the protocol is structurally insecure and admits a realistic route to full compromise in the lightweight parameter regime advocated for deployment.

We initiate the study of inverse source problems for quasilinear elliptic equations of the form \[ \left\{ \begin{array}{ll} \nabla \cdot (γ(x,u,\nabla u) \nabla u) = F & \text{in } Ω, \\ u = f & \text{on } \partialΩ, \end{array} \right. \] where $Ω\subset \mathbb{R}^n$, $n \geq 2$, is a simply connected bounded domain. We consider the specific nonlinearity $γ(x,u,\nabla u) = σ(x) + q(x) u$, with $q$ assumed to be known. By exploiting the nonlinearity to break the gauge invariance of the problem, we establish unique recovery of both $σ$ and $F$ from the associated Dirichlet-to-Neumann (DN) map under the structural conditions $q$ and $\nabla(σ/q)$ are nowhere vanishing in $\overlineΩ$. In the absence of these conditions, in particular in the linear case, we demonstrate that the inverse problem admits a gauge obstructing the uniqueness. We use higher order linearizations to obtain a complicated coupled system for the unknowns. The complexity of this system arises in part from the gauge freedom of the linearized equation, which is new in this context. We solve the system by constructing suitable complex geometric optics solutions and applying the unique continuation principle for nonlinear elliptic systems. We anticipate that the solution method developed here will prove useful in other inverse problems as well.

We demonstrate the first CV-QKD system featuring a custom-designed monolithic silicon photonic dual-polarisation transceiver. Leveraging PS-64-QAM, we achieved 1.9 Mbit/s secret key rate across 25 km of standard single-mode fibre, highlighting the potential of electronic-photonic integration for practical QKD.

Vulnerability detection in C programs is a critical challenge in software security. Although large language models (LLMs) achieve strong detection performance, their multi-billion-parameter scale makes them impractical for integration into development workflows requiring low latency and continuous analysis. We introduce VULNSCOUT-C, a compact transformer architecture with 693M total parameters (353M active during inference), derived from the Qwen model family and optimized for C code vulnerability detection. Alongside the model, we present VULNSCOUT, a new 33,565-sample curated dataset generated through a controlled multi-agent pipeline with formal verification, designed to fill coverage gaps in existing benchmarks across underrepresented CWE categories. Evaluated on a standardized C vulnerability detection benchmark, VULNSCOUT-C outperforms all evaluated baselines, including state-of-the-art reasoning LLMs and commercial static analysis tools, while offering a fraction of their inference cost. These results demonstrate that task-specialized compact architectures can match or even outperform the detection capability of models orders of magnitude larger, making continuous, low-latency vulnerability analysis practical within real-world development workflows.

Providing guaranteed quality of service for cell-edge users remains a longstanding challenge in wireless networks. While coordinated interference management was proposed decades ago, its potential has been limited by computational complexity and backhaul resource constraints. Distributed user scheduling and coordinated beamforming (D-USCB) offers a scalable solution but faces practical challenges in acquiring inter-cell channel state information (CSI), as base stations (BSs) are often restricted to signal strength measurements, and high-dimensional CSI exchange incurs substantial overhead. Inspired by integrated sensing and communication (ISAC), this paper proposes a sensing-assisted D-USCB (SD-USCB) framework to maximize the network throughput of multi-cell mmWave networks. Firstly, the framework leverages channel knowledge maps (CKMs) that map user locations to CSI estimates, where user locations are proactively sensed via ISAC echoes. Secondly, we employ a signal-to-average-leakage-plus-interference-plus-noise ratio (SALINR) metric for distributed ISAC beamforming optimization, in which BSs simultaneously communicate with users and sense their locations. These two components jointly enable distributed coordinated transmission with only user location information exchanged among BSs, thereby substantially reducing backhaul overhead. In addition, we devise efficient distributed user scheduling and ISAC beamforming algorithms to jointly optimize communication and sensing performance. Extensive numerical results demonstrate significant improvements in network throughput, validating the efficacy of the proposed framework.

In this paper, we answer the question posed by Goodwin and Röhrle for reductive groups and their parabolic subgroups. In addition, we consider an additive analogue of this problem. By studying this additive analogue, we identify similar properties between the Deligne-Lusztig character of a finite reductive group and the Harish-Chandra induction over the corresponding finite Lie algebra.

We study the blow-up behavior of solutions to the singular Liouville equation \[ Δ\tilde u+λe^{\tilde u}=4παδ_0 \quad\text{in }B,\quad \tilde u=0 \quad\text{on }\partial B, \] where $α>0$, $λ>0$ and $B\subset\mathbb R^2$ is the unit disk. Our main results give a complete classification of all blow-up solutions and determine the exact number of solutions to the above equation. More precisely, for fixed $α>0$ and $λ\in(0,λ_α)$, the singular Liouville equation has exactly $\lceil α\rceil+2$ solutions (up to rotation): a unique minimal energy solution; a unique singular sequence blowing up at the origin; and for each $1\le m\le\lceil α\rceil$, a unique $m$-peak sequence whose blow-up points are the vertices of a regular $m$-gon centered at the origin. This result answers the questions raised in Bartolucci-Montefusco \cite{Bartolucci-Montefusco06} and Bartolucci \cite{Bartolucci10}. We also prove the non-degeneracy of these solutions. Thus we provide a full description of the blow-up structure for the singular Liouville equation on the disk.

In this work we investigate Cauchy problem and initial boundary value problem for time-fractional Airy equation on the graphs with infinite and finite bonds. We studied properties of potentials for this equation and using these properties found the solutions of the considered problems. The uniqueness theorem is proved using the analogue of Grönwall-Bellman inequality and a-priory estimate.

In contrast to the complex $ϕ^4$ model, vortex-antivortex collisions in the complex $ϕ^6$ theory reveal a resonant structure due to the existence of a remarkably stable, long-lived, large amplitude oscillon in the broken vacuum. Surprisingly, it persists despite the absence of a mass gap associated with the flat direction in the broken vacuum. We demonstrate that its existence is related to a far-distance modification of the potential, namely, the appearance of an unbroken (false or true) vacuum.

A central objective of future collider experiments is to probe the structure of the Higgs potential, which requires access to trilinear scalar couplings, in particular the self-coupling of the observed Higgs boson. While this coupling is fixed in the Standard Model (SM), it can receive sizable modifications in many Beyond the SM (BSM) scenarios, often connected to solutions of open problems such as the origin of the matter-antimatter asymmetry of the Universe. In theories with extended scalar sectors, radiative corrections involving additional scalar states can significantly affect both the Higgs self-coupling and other trilinear scalar interactions, with important consequences for predictions of physical observables. Precise theoretical calculations are therefore essential for the interpretation of precision Higgs measurements and for identifying indirect signatures of new physics. This contribution presents the latest version of the public tool anyBSM, which provides automated calculations of all trilinear scalar couplings at full one-loop order in arbitrary renormalisable theories, including full momentum dependence and flexible renormalisation-scheme choices. In addition, the new module anyHH for di-Higgs production in gluon fusion is discussed in several exemplary BSM models, including scenarios with multiple resonances.

In this article, we prove the following results:\\ \noindent \text{(1).} Let $R$ be a smooth affine algebra of dimension $3$ over an algebraically closed field $K$ with $3!\in K$, then we show that $\Um_4(R)=e_1\Sp_4(R)$ and $\Um_4(R [X])=e_1\Sp_4(R[X])$. \noindent \text{(2).} We also show that if $R$ is a smooth affine algebra of dimension $4$ over an algebraically closed field $K$ with $4!\in K$, and assume that $\W_E(R)$ is divisible, then $\Um_3(R)=e_1\SL_3(R)$. As a consequence it is shown that if $R$ is a smooth affine algebra of dimension $4$ over an algebraically closed field $K$ with $4!\in K$, and assume that $\W_E(R)$ is divisible, then $\Um_4(R)=e_1\Sp_4(R)$. \noindent \text{(3).} We show that if $R$ is a local ring of dimension $3$ with $\frac{1}{3!}\in R$. Then $\Um_4(R[X])=e_1\Sp_4(R[X])$. \noindent \text{(4).} We also show that if $R=\oplus_{i\geq 0}R_i$ is a graded ring over a local ring of dimension $3$ with $\frac{1}{3!}\in R$. Then $\Um_4(R)=e_1\Sp_4(R)$.

We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally imposed randomness. Within the theory of moving manifolds, we establish a curvature-noise correspondence: fluctuations are governed by the inverse curvature tensor, while entropy production is controlled by curvature deformation. The invariant continuity law on a moving hypersurface yields a geometric Fokker-Planck equation, and curvature-velocity coupling generates a quadratic Onsager-Machlup functional determining path weights. The resulting entropy functional satisfies a curvature-driven monotonicity law, providing a geometric derivation of the Second Law. In two dimensions, the curvature invariant reduces to Gaussian curvature and encodes topology, so topological transitions produce discrete entropy jumps. When the ambient space carries a Minkowskian signature, the same curvature-kinetic quadratic form that generates dissipative thermal weights produces oscillatory phase weights, and the Laplace-Beltrami operator governing entropy evolution acquires a Schrödinger-type structure. This provides a geometric resolution of the apparent distinction between classical stochastic behaviour and quantum dynamics. These results show that stochastic behaviour, thermodynamic irreversibility, and quantum transition amplitudes are unified within the moving manifold framework. Geometry does not merely accommodate stochasticity; stochastic behaviour arises as a consequence of deterministic geometric evolution. The theory predicts curvature-controlled anisotropic diffusion, entropy jumps at topology-changing events, and a geometric thermal-quantum crossover in which classical stochastic weights and quantum amplitudes are generated by the same curvature-kinetic action.

The problem of electromagnetic scattering by cylinders is an old problem that has been studied in many configurations. The present publication provides a theoretical study on a not yet investigated general case: the set of finite metallic circular cylinders. A model which takes into account both the finiteness of the cylinders and their electromagnetic coupling is provided. The total field is written in a two dimensional problem in terms of cylindrical harmonics and is used to define current densities which are integrated in a three dimensional problem. The finiteness is taken into account assuming current densities that are identical from those of the two dimensional problem. Coupling effects are naturally taken into account via the matrix formulation of the boundary condition that binds together the cylindrical harmonic coefficients. The proposed closed-form is valid for great cylinder lengths and any cylinder radii. Numerical experiments are also provided in various configurations in order to evaluate the accuracy of the model. The model computational times happens to be 5 orders of magnitude shorter than a full-wave reference simulation, without significant loss of accuracy.

Mixed-halide perovskites (MHPs) offer good band gap tunability by stoichiometry changes, which is an essential property for the creation of multijunction solar cells. However, under illumination, halide ions in MHP segregate and create I- and Br-rich regions, which decreases the efficiency of potential solar cells. In this work, a method for a detailed investigation of the distribution of halide ions within the MHP during and after illumination is introduced. Calculations of the strain field created by the halide segregation were performed, and the obtained local displacement of atoms was used to calculate the x-ray diffuse scattering. By fitting the experimental data measured on the thin polycrystalline layer of FA0.83Cs0.17Pb(I0.6Br0.4)3 the distribution of Br- and I- ions within an illuminated MHP was determined and the subsequent relaxation process of the segregation in the dark was tracked. Creation of highly Br-rich regions within slightly I-rich volume during the illumination was observed.