We prove that the grand canonical Gibbs state of an interacting two-dimensional quantum Bose gas confined by a trapping potential converges to the complex Euclidean field theory with local quartic self-interaction, when the density of the gas becomes large and the range of the interaction becomes small. We obtain convergence of the relative partition function and convergence in $L^1 \cap L^\infty$ of the renormalised reduced density matrices. The field theory is supported on distributions of negative regularity, which requires a renormalisation by divergent mass and energy counterterms. Unlike previous results in the homogeneous setting of the torus without a trapping potential, the counterterms are not given by a finite collection of scalars but by diverging counterterm functions. This leads to significant new mathematical challenges. For our proof, we also derive quantitative bounds on the Green function of Schrödinger operators and of its gradient, which might be of independent interest.

We present STAMP (Selective Task-Aware Mechanism for Text Privacy), a new framework for task-aware text privatization that achieves an improved privacy-utility trade-off. STAMP selectively allocates privacy budgets across tokens by jointly considering (i) each token's importance to the downstream task (as measured via a task- or query-specific representation), and (ii) its privacy sensitivity (e.g., names, dates, identifiers). This token-level partitioning enables fine-grained, group-wise control over the level of noise applied to different parts of the input, balancing privacy protection with task relevance. To privatize individual token embeddings, we introduce the polar mechanism, which perturbs only the direction of embeddings on the unit sphere while preserving their magnitude. Decoding is performed via cosine nearest-neighbor search, aligning the perturbation geometry with the decoding geometry. Unlike isotropic noise mechanisms, the polar mechanism maintains semantic neighborhoods in the embedding space and better preserves downstream utility. Experimental evaluations on SQuAD, Yelp, and AG News datasets demonstrate that STAMP, when combined with the normalized polar mechanism, consistently achieves superior privacy-utility trade-offs across varying per-token privacy budgets.

A game $G$ is said to have the evil twin property if there exists $G^* \in \{G,G+*\}$ such that $o^+(G) = o^-(G^*)$ and $o^+(G^*) = o^-(G)$. We study sums of wildflowers, games of form $G:H$. We find that a large closed set of sums of wildflowers has the evil twin property, extending work of McKay--Milley--Nowakowski and Lo. Our argument partially generalizes the misère genus theory of Conway to partizan games, and requires proving several general theorems on ways to extend sets with the evil twin property. Many sums of mutant flowers of the form $\{*x_1,\dots,*x_n\}:a$, where $a$ is a number, also have the evil twin property. We also prove that this set of mutant flowers is the largest such closed set with the evil twin property, and that it is $\mathsf{NP\text{-}hard}$ to compute the outcome class of a sum of mutant flowers under either play convention via a reduction from \textsc{3-Sat}. Previous work on this topic was done by McKay, Milley, and Nowakowski, and later Lo.

This paper develops a general theory for first-order descent methods whose search directions are restricted to a prescribed dictionary in a reflexive Banach space. Instead of assuming that the linear span of the dictionary is dense, as in the classical Proper Generalized Decomposition framework of Falcó and Nouy or in the universality approach of Berná and Falcó, we introduce a geometric condition based on norming sets that guarantees density through a duality argument. This makes it possible to treat dictionaries arising from tensor formats, neural network units, and other nonlinear or parameterized approximation families within a unified setting. On the algorithmic side, we analyze a simple greedy update rule in which each iterate is obtained by minimizing the energy functional along one direction from the dictionary. Under mild differentiability, Lipschitz continuity, and ellipticity assumptions on the objective, we derive explicit quantitative descent bounds and sharp convergence rates. These include algebraic rates that improve those of classical steepest-descent schemes in Banach spaces, as well as arbitrarily high polynomial rates and exponential convergence in a critical regime. The results apply broadly to convex variational problems, high-dimensional approximation, and structured optimization methods that rely on restricted or compressed search directions.

We propose a unified iterative framework for the solution of frictionless mechanical contact problems, which relies exclusively on the solution of standard stiffness systems. The framework is built upon a two-step fixed-point algorithm: first, the displacement is computed for given contact forces; second, the contact forces are updated based on the displacement solution. The choice of the dual update scheme depends on the numerical contact formulation under consideration. Specifically, the Uzawa iterative scheme is obtained for the Lagrange multiplier formulation, while a penalty-based operator-splitting strategy is proposed for the penalty contact formulation. The main interest of such displacement-force splitting strategy is to involve only standard rigidity matrices in the solving step: no saddle-point or penalized ill-conditionned coefficient matrices have to be handled. Moreover only the right-hand side of the system is updated throughout the iterations, which enables matrix factorization reuse or efficient iterative solvers initialization. The main limitation of such splitting iterative strategies lies in the inherently slow convergence of the underlying fixed-point iterations. Moreover, convergence is guaranteed only within a narrow range of numerical parameter values (i.e., the augmentation or penalty parameter). This work addresses both issues by applying the Crossed-Secant fixed-point acceleration strategy, which substantially improves the convergence rate and renders the iterative schemes effectively parameter-unconstrained. To the best of our knowledge, this contribution provides the first computational demonstration of efficient, parameter-unbounded convergence for such contact formulations. The substantial practical benefits of the proposed approach are illustrated through representative three-dimensional academic and industrial frictionless contact problems.

We consider a family $\mathscr{F}$ of meromorphic functions defined in a domain $D$, a holomorphic function $ψ$ and a homogeneous differential polynomial $ P[f] $ of degree $d$ with weight $w$. In this paper, we prove the normality of $\mathscr{F}$ under certain conditions such as $f\neq 0$, $P[f]\neq 0$ and all the zeros of the function $P[f] - ψ^d$ have multipicity at least $\displaystyle{\frac{w+1}{w-1}}$, for each $f \in \mathscr{F}$.

We establish a quantitative homogenization result for an interface moving through a field of sufficiently sparse but possibly impenetrable random obstacles. From a physical viewpoint, such problems arise e.g. in the context of the motion of dislocations or magnetic domain walls in a material with impurities. More precisely, given an interface moving by forced mean curvature flow -- with a positive global driving force plus a spatially fluctuating (negative) driving force modeling the obstacles -- , we prove that the effective large-scale behavior of the forward front is governed by a constant-speed effective motion. For typical values of the global forcing, on large scales of the order $\varepsilon^{-1}$ we obtain a (relative) error estimate for arrival times of the front of the order $\varepsilon^{1/9-}$. Previous stochastic homogenization results for forced mean curvature motion in the literature have required a positive pointwise lower bound on the combined forcing, which implies the absence of any actual obstacles capable of locally blocking the interface motion. In contrast, our results are valid even in the presence of islands with locally negative forcing, potentially allowing for locally pinned interfaces and eventually enclosures left behind the main front. Thus, our homogenization result applies to settings closer to (but still strictly away from) the pinning-depinning transition.

We establish polynomially improved $L^\infty$ bounds for eigenfunctions of magnetic Laplacians on hyperbolic surfaces in the critical energy regime. We also show that, below the critical energy, the Hörmander bound is saturated by explicit eigenstates, which we call \emph{magnetic zonal states}. These states resemble zonal harmonics on the sphere and equidistribute on Lagrangian tori in phase space.

De Morgan bisemilattices are expansions of distributive bisemilattices by an involution satisfying De Morgan properties. They have attracted interest both as algebraic models of analytic containment logics, and as a case study for a certain generalisation of the Płonka sum construction (De Morgan- Płonka sums). In this paper, we provide a complete description of the lattice of subvarieties of the variety DMBL of De Morgan bisemilattices. For each subvariety in the lattice, we identify a finite set of finite generators, a characterisation of the De Morgan-Płonka representations of its members, and a syntactic description of its valid identities. In many cases, we also give an axiomatisation relative to DMBL.

Continual post-training of generative models is widely used, yet a principled understanding of when and why forgetting occurs remains limited. We develop theoretical results under a two-mode mixture abstraction (representing old and new tasks), proposed by Chen et al. (2025) (arXiv:2510.18874), and formalize forgetting in two forms: (i) mass forgetting, where the old mixture weight collapses to zero, and (ii) old-component drift, where an already-correct old component shifts during training. For equal-covariance Gaussian modes, we prove that forward-KL objectives trained on data from the new distribution drive the old weight to zero, while reverse-KL objectives converge to the true target (thereby avoiding mass forgetting) and perturb the old mean only through overlap-gated misassignment probabilities controlled by the Bhattacharyya coefficient, yielding drift that decays exponentially with mode separation and a locally well-conditioned geometry with exponential convergence. We further quantify how replay interacts with these objectives. For forward-KL, replay must modify the training distribution to change the population optimum; for reverse-KL, replay leaves the population objective unchanged but prevents finite-batch old-mode starvation through bounded importance weighting. Finally, we analyze three recently proposed near-on-policy post-training methods, SDFT (arxiv:2601.19897), TTT-Discover (arxiv:2601.16175), and OAPL (arxiv:2602.19362), via the same lens and derive explicit conditions under which each retains old mass and exhibits overlap-controlled drift. Overall, our results show that forgetting can by precisely quantified based on the interaction between divergence direction, geometric behavioral overlap, sampling regime, and the visibility of past behavior during training.

In this paper, we investigate the distribution of values of the complete exponential sum $S_{p,χ}(θ)=\sum_{n=1}^p χ(n)e(nθ)$, where $p$ is a large prime, $χ$ is a Dirichlet character (mod $p$) of order $d\geq 2$, and $θ$ varies over certain subsets of $[0,1]$. When $d=2$, these sums correspond to the values of the Fekete polynomial associated with $p$ on the unit circle. Our first result gives precise estimates for the tail of the distribution of $|S_{p,χ}(θ)|$ in a large uniform range, when $θ$ varies over the set $\{(k+1/2)/p\}_{1\leq k\leq p}$. This improves upon a result of Conrey, Granville, Poonen, and Soundararajan. We also consider the distribution of the maximum of $|S_{p,χ}(θ)|$ for $θ\in I_k=[k/p,(k+1)/p]$, and obtain upper and lower bounds for the distribution of large values of this maximum, valid in a uniform range that is nearly optimal: we make this precise in the paper. Our results provide strong support for a conjecture of Montgomery on the maximum of Fekete polynomials on the unit circle. In particular, we show that the distribution function exhibits double-exponential decay, with a surprising difference in behavior between the cases of even and odd order $d$.

We study compactness and noncompactness phenomena for the CR Yamabe equation on compact strictly pseudoconvex CR manifolds. First, in dimension five we establish uniform \emph{a priori} estimates for families of positive solutions of subcritical equations for the conformal CR sub-Laplacian \[ L_{J}u = u^{p}, \] with $p$ bounded away from the critical exponent, assuming positivity of the CR Yamabe constant and positivity of the $p$-mass at every point. As a consequence, the corresponding set of solutions is precompact in Hölder topologies. Secondly, we consider the equivariant CR Yamabe problem for a compact subgroup $G$ of pseudo-Hermitian transformations. We construct a $G$-invariant CR structure on $S^{3}$, not equivalent to the standard one, for which the associated CR Yamabe equation admits a sequence of $G$-invariant solutions whose maxima diverge, thereby proving noncompactness in the equivariant setting. The arguments combine a Pohozaev-type identity in pseudohermitian normal coordinates with a blow-up analysis and Liouville-type classification results on the Heisenberg group.

Differential Privacy (DP) is widely adopted in data management systems to enable data sharing with formal disclosure guarantees. A central systems challenge is understanding how DP noise translates into effective protection against inference attacks, since this directly determines achievable utility. Most existing analyses focus only on membership inference -- capturing only a threat -- or rely on reconstruction robustness (ReRo). However, under realistic assumptions, we show that ReRo can yield misleading risk estimates and violate claimed bounds, limiting their usefulness for principled DP calibration and auditing. This paper introduces reconstruction advantage, a unified risk metric that consistently captures risk across membership inference, attribute inference, and data reconstruction. We derive tight bounds that relate DP noise to adversarial advantage and characterize optimal adversarial strategies for arbitrary DP mechanisms and attacker knowledge. These results enable risk-driven noise calibration and provide a foundation for systematic DP auditing. We show that reconstruction advantage improves the accuracy and scope of DP auditing and enables more effective utility-privacy trade-offs in DP-enabled data management systems.

For mixed-integer linear programming and linear programming it is well known that symmetries can have a negative impact on the performance of branch-and-bound and linear optimization algorithms. A common strategy to handle symmetries in linear programs is to reduce the dimension of the linear program by aggregating symmetric variables and solving a linear program of reduced dimension. In their work ``Dimension Reduction via Color Refinement'' (DRCR), Grohe, Kersting, Mladenov and Selman show that it is sufficient to run a fast color refinement algorithm to detect permutation symmetries and reduce the dimension of the linear program. We extend DRCR in two directions. First, we show that DRCR can be extended to reflection symmetries, which generalize permutation symmetries. Second, we show the folklore result that DRCR can be applied to the continuous columns of mixed-integer linear programs. In order to derive additional reductions on the integer variables we use affine totally unimodular decompositions to reformulate mixed-integer linear programs into mixed-integer linear programs with fewer integer variables. Computational experiments on MIPLIB 2017 collection set using SCIP 10 show that DRCR is an effective tool for handling symmetries. For the linear programming relaxations, DRCR with reflection symmetries yields a modest reduction in running time compared to the original DRCR procedure. For mixed-integer linear programming models, DRCR is very effective at reducing the solution time compared to the default configuration of SCIP. Moreover, the developed DRCR detection algorithms are fast and scale well to large problem instances.

Magnetic relaxation drives plasma toward lower-energy equilibria under helicity constraints. In ideal magnetohydrodynamics (MHD), helicity is locally conserved, while resistive theories such as Taylor relaxation preserve only global helicity. This distinction has important implications for structure-preserving numerical methods. We compare three finite element formulations: an unconstrained scheme that does not conserve helicity, a mixed method based on finite element exterior calculus that preserves all local helicities, and a Lagrange multiplier approach that enforces only global helicity conservation. Numerical experiments on braided and knotted magnetic fields show that local helicity preservation prevents spurious reconnection and maintains nontrivial topology in ideal MHD or magneto-friction, whereas enforcing only global helicity allows further relaxation through local reconnection. Numerical results on magnetic knots and braids are provided. These results clarify how different levels of discrete helicity constraints influence magnetic relaxation and equilibrium structure in numerical computation.

In this paper, we present a geometric approach to exponentially small splitting in zero-Hopf bifurcations of arbitrary co-dimension. In further details, we consider a family of problems that generalizes the third order Michelsen/Kuramoto-Sivashinsky-type equations $ε^{2(κ-1)} f'''+f'={Q}(f)$, where ${Q}$ is an arbitrary real polynomial with $κ=\operatorname{degree}Q\ge 2$ simple real roots. For $ε=0$, the system has $(κ-1)$-many heteroclinic connections and we describe the exponentially small splitting for each connection for all $0<ε\ll 1$ under a separate nondegeneracy condition. In particular, we find that the $j$th-splitting is of the form $ε^{-\frac{3κ}{2}}\exp\left({-ε^{1-κ}T^j}\right)(C^j+\mathcal O(ε))$, where $T^j>0$ can be calculated explicitly and be interpreted as the blowup time of special unbounded solutions of the $ε=0$-limiting system in imaginary time $f'=iQ(f)$. Our approach extends a similar geometric method developed by the present author for the generic zero-Hopf bifurcation of co-dimension two, which does not rely on explicit time-parametrizations of the unperturbed heteroclinic connections and their singularities in the complex plane. Instead, we work exclusively in the complexified phase space and relate the exponentially small splitting to the lack of analyticity of center-like invariant manifolds of associated generalized saddle-nodes.

Homotopy algebraic methods have become increasingly influential in studying field theories. We consider semi-holomorphic Chern-Simons theory and its relation with the principal chiral model. In particular, we establish an explicit quasi-isomorphism between the cyclic $L_\infty$-algebras governing both theories which directly gives the Lax connection. This provides a concrete example for studying integrability of a two-dimensional system through the homotopy algebraic lens.

Random walks are fundamental tools for analyzing complex networked systems, including social networks, biological systems, and communication infrastructures. While classical random walks focus on pairwise interactions, many real-world systems exhibit higher-order interactions naturally modeled by hypergraphs. Existing random walk models on hypergraphs often focus on undirected structures or do not incorporate entropy-based inference, limiting their ability to capture directional flows, uncertainty, or information diffusion in complex systems. In this article, we develop a maximum-entropy random walk framework on directed hypergraphs with two interaction mechanisms: broadcasting where a pivot node activates multiple receiver nodes and merging where multiple pivot nodes jointly influence a receiver node. We infer a transition kernel via a Kullback--Leibler divergence projection onto constraints enforcing stochasticity and stationarity. The resulting optimality conditions yield a multiplicative scaling form, implemented using Sinkhorn--Schrödinger-type iterations with tensor contractions. We further analyze ergodicity, including projected linear kernels for broadcasting and tensor spectral criteria for polynomial dynamics in merging. The effectiveness of our framework is demonstrated with both synthetic and real-world examples.

We construct Grothendieck pairs witnessing that the following are not profinite invariants: stable commutator length, quasimorphisms (answering a question of Echtler and Kammeyer), property NL (which obstructs actions on hyperbolic spaces), and property FW$_\infty$ (which obstructs actions on finite-dimensional CAT(0) cube complexes). We also recover that property FA and non-abelian free subgroups are not profinite invariants. The method combines Rips constructions with iterated group-theoretic Dehn filling on hyperbolic virtually special groups.

This paper extends graphic statics by describing the forces and moments in any 3D rigid-jointed frame structure in terms of cell complexes using homology theory of algebraic topology. Graphic statics provides a highly geometric way to represent the equilibrium in bar structures. Unlike traditional matrix-based linear structural analysis which represents a structure as a set of nodes connected by bars, graphic statics imagines that the bar network defines a variety of higher-dimensional objects (polygonal faces, polyhedral cells, polytopes). These objects are related to piecewise-linear stress functions, the liftings of Maxwell, Rankine or Cremona. The requirement for such stress-functions to be plane-faced places a major limitation on the set of structures that can be analysed, as in many structures the spaces between bars do not correspond to flat polygonal regions. The CW-complexes of cellular homology provide a far-reaching generalisation of geometric notions such as polygons, polyhedra and polytopes, and their use here removes the requirement that spaces between bars must be flat. Here we demonstrate how any frame structure with bar-like members can be decomposed into a union of closed loops, each consisting of a closed circuit of bars. For general structures these loops are general closed space curves which cannot be spanned by flat polygons. Using chains of CW-complexes makes the new theory applicable to a much richer set of structural geometries. Unlike most descriptions of graphic statics, this approach is not restricted to purely axial forces. Shear forces, bending moments and torsional moments are included naturally, as described in Part 1 of this sequence of papers. Later papers will extend the approach to displacements, rotations and Virtual Work, and will give greater detail on how the loop formalism may be lifted toinvolve higher dimensional CW-complexes.

Accumulation at boundaries represents a widely observed phenomenon in active systems with implications for microbial ecology and engineering applications. To rationalize the underlying physics, we provide analytical predictions for the first-passage properties and spatial distributions of a confined active Brownian particle (ABP). We show that ABPs with absorbing and hard-wall boundary conditions are Siegmund duals, yielding a direct mapping between the propagators of the two problems. We analyze the system across low and high activity regimes -- quantifying persistent motion relative to diffusion -- and show that active motion, together with a favorable initial orientation, typically lowers the mean first-passage time relative to passive diffusion. Notably, the full time-dependent propagator between hard walls approaches a wall-accumulated stationary state given by the derivative of the splitting probability as a consequence of Siegmund duality.

The paper discusses several extensions of the recursive representation of the flow shop scheduling problem. It is shown that recursive functions make it possible to describe multiple extensions in a single problem. The paper considers altogether six extensions. The examples consider three types of recursive functions: functions associated with the machine, functions that adjust the procession time based on constraints, and functions that control the feasibility of the schedule. The structure of the superpositions of these functions is presented, and also descriptions of several objective functions by recursive functions are presented. Then the general requirements for a recursive function are formulated and its properties are described. Finally, a demonstration of the formulation of new problems is provided using examples of simple flow shop extensions and branch and bound optimization.

We mathematically prove that chemical reaction networks without hidden layers can solve tasks for which spiking neural networks require hidden layers. Our proof uses the deterministic mass-action kinetics formulation of chemical reaction networks. Specifically, we prove that a certain reaction network without hidden layers can learn a classification task previously proved to be achievable by a spiking neural network with hidden layers. We provide analytical regret bounds for the global behavior of the network and analyze its asymptotic behavior and Vapnik-Chervonenkis dimension. In a numerical experiment, we confirm the learning capacity of the proposed chemical reaction network for classifying handwritten digits in pixel images, and we show that it solves the task more accurately and efficiently than a spiking neural network with hidden layers. This provides a motivation for machine learning in chemical computers and a mathematical explanation for how biological cells might exhibit more efficient learning behavior within biochemical reaction networks than neuronal networks.

We show that the observable category of q-tame multiparameter persistence modules satisfies good metric and algebraic properties: it forms a complete metric space with respect to the interleaving distance, and it is Krull--Schmidt in the sense that every object admits an essentially unique decomposition into indecomposables. Moreover, we show that these metric and algebraic structures are compatible: two objects are at distance zero if and only if they are isomorphic. We argue that the observable category of q-tame multiparameter persistence modules is the right setup for multiparameter persistence by showing that many of the categories already considered in the literature form full subcategory of this category. We also characterize precompact sets in terms of finite representation type of certain discretizations, and show that the image of several of the main constructions in multiparameter persistence is precompact.

We consider the global optimization of a non-convex potential $U : \mathbb{R}^d \to \mathbb{R}$ and extend the controlled simulated annealing framework introduced by Molin et al. (2026) to the class of swarm gradient dynamics, a family of Langevin-type mean-field diffusions whose noise intensity depends locally on the marginal density of the process. Building on the time-homogeneous model of Huang and Malik (2025), we first analyze its invariant probability density and show that, as the inverse temperature parameter tends to infinity, it converges weakly to a probability measure supported on the set of global minimizers of $U$. This result justifies using this family of invariant measures as an annealing curve in a controlled swarm setting. Given an arbitrary non-decreasing cooling schedule, we then prove the existence of a velocity field solving the continuity equation associated with the curve of invariant densities. Superimposing this field onto the swarm gradient dynamics yields a well-posed controlled process whose marginal law follows exactly the prescribed annealing curve. As a consequence, the controlled swarm dynamics converges toward global minimizers with, in principle, arbitrarily fast convergence rates, entirely dictated by the choice of the cooling schedule. Finally, we discuss an algorithmic implementation of the controlled dynamics and compare its performance with controlled simulated annealing, highlighting some numerical limitations.

We show the existence of weak solutions to the fluid-structure interaction problem of a largely deforming viscoelastic bulk solid with a viscous fluid governed by the incompressible Navier-Stokes equations. In contrast to previous works, the fluid is allowed to slip along the solid boundary; namely, the so called Navier-slip boundary conditions are considered. Such boundary conditions naturally involve the time-changing outer normal of the fluid domain. Hence, their dependence on the varying geometry is one degree higher than in the previously considered no-slip case, which makes it necessary to adjust the concept of weak coupled solutions. Two classes of test functions are introduced: test functions that are continuous over the fluid-solid domain, and fluid-only test functions with nonzero tangential component at the boundary. The weak equations are established until the point of contact, and moreover, compatibility with the strong formulation is shown.

This paper studies the existence of solutions and, in particular, the well-posedness of a class of boundary control systems. Our main result provides explicit and verifiable conditions on the system data that guarantee continuous dependence of solutions on the initial data and $L^p$-inputs. The proof relies on a new boundedness estimate for the input/output maps of linear time-invariant infinite-dimensional systems with unbounded control and observation operators. The developed technique is applied to derive specific conditions for the exponential input-to-state stability of boundary-coupled heat equations with boundary disturbances and time-delays.

In this article, we discuss gradient robust discretizations for the simulation of non-linear incompressible Navier-Stokes problem and the optimal control of such flow. We consider several formulations of the flow problem that are equivalent for the continuous non-linear forward problem and compare their gradient robust discretization. We will then discuss the influence of the chosen formulation on the adjoint equations needed for gradient computation in the solution of the optimal control problem.

An anisotropic elastic material is referred to as exotic when, under specific loadings, its mechanical response exhibits a higher degree of symmetry than that prescribed by its intrinsic material symmetry. Such materials, which may be regarded as lying, conceptually and functionally, between two distinct symmetry classes, are of significant practical relevance. They enable the tailored design of metamaterials capable of reconciling otherwise incompatible mechanical requirements; for example, achieving directional isotropy of the Young's modulus in an intrinsically anisotropic medium. This work focuses on the systematic classification of exotic structures within the framework of three-dimensional linear elasticity. An exhaustive classification is carried out, leading to the enumeration of 18 exotic structures corresponding to symmetry classes higher than orthotropy. Representative examples of exotic elastic behaviours are analysed in detail.

Inspired by recent developments in the theory of stability results in the context of certain wave type phenomena, we discuss abstract damped hyperbolic type equations given in a block operator matrix form with regards to asymptotic behaviour of their solutions. Under mild conditions on the operators involved we provide criteria establishing strong or semi-uniform stability. In the particular case of Maxwell's equations, these criteria are implied under mild regularity conditions of the underlying domain causing spatial derivative operators satisfy certain compact embedding conditions and rather minimal assumptions on the damping conductivity. These assumptions improve on both regularity as well as on the structural requirements for the conductivity previously available in the literature.