The present study considers the operation of a laser that incorporates a photonic time crystal (PTC), the purpose of which is to generate a field characterised by multiple widely separated optical frequencies. This laser is the subject of both a proposal and theoretical investigation. The laser comprises an active medium and a PTC within a small cavity constructed from two photonic crystals that are positioned in an overlapping configuration. PTC is modulated by an external field. The spikes in the laser field spectrum are separated by the PTC modulation frequency. The development of a quantum model of the laser with PTC has been achieved, and the analysis of a lasing mode with multi-frequency spikes has been made. The investigation focused on the study of lasing conditions, output power, and the lasing field spectra. The experimental realization of the multi-frequency laser with PTC under realistic conditions is discussed.

In this article, we aim to further clarify certain subtle aspects of processes that exhibit long memory in the second-order sense. We construct a long-memory stochastic sequence, in the sense that the series of absolute autocovariances diverges, whose spectral density has an almost everywhere unboundedly divergent Fourier series. This suggests that the Fourier series of the spectral density of a generic long-range dependent process, one for which nothing is known except that its autocovariances are not absolutely summable, should be handled with great care. On the other hand, it is known that if one assumes regularly varying behavior for the autocovariances or the spectral density, along with suitable conditions on the associated slowly varying function, then the Fourier series of the spectral density converges everywhere, except possibly at 0. The process we construct can easily be simulated, and we compare its empirical and theoretical autocovariances.

This paper presents a new stochastic relay-based extremum-seeking controller (ESC) for multi-input-single-output (MISO) systems. The goal of this work was to create an algorithm that is much simpler to configure than alternative approaches making deployment to real-world problems easier. A solution is developed first for a static map and then adapted for a general class of dynamic systems. The number of configurable parameters is one per input channel for the static case and only one additional parameter is needed for the dynamic version. The problem of gradient identification is solved via the use of stochastic relay gains and a simple stability proof for the static case is presented. Simulation tests demonstrate the performance of the strategy for optimizing both static and dynamic systems.

We study charmonium properties at non-zero temperature in the temperature range 153 MeV $<T<$ 305 MeV using lattice QCD. We use HISQ action for dynamical quarks and Wilson clover action for valence charm quarks and calculate the correlation function of extended meson operators. Our lattice QCD results are consistent with the existence of all charmonium states below the open charm threshold in this temperature region. However, charmonium states acquire sizable thermal width, which increases with increasing temperature. The size of the thermal width follows the hierarchy of charmonium sizes, i.e. the smaller ground state charmonium has a smaller thermal width than the larger excited charmonia.

The design of physics-augmented neural networks (PANNs) for the purposes of constitutive modeling has received considerable attention as of late for a variety of material behaviors. Here, we revisit the classical framework of isotropic incompressible hyperelasticity in light of recent advances in the study of constitutive inequalities. We show that polyconvexity implies true-stress-true-strain monotonicity for a large class of incompressible strain-energy functions. The resulting elastic law obeys the physically reasonable Legendre-Hadamard (or ellipticity) condition as well as the notion of increasing stress with increasing strain. These results then inform the architecture of four distinct PANNs which are subsequently calibrated to three different sets of experimental data each. We show that different PANN parametrizations - satisfying the same constitutive constraints a priori - have varying approximation power for the description of material behavior. Moreover, even when distinct parametrizations perform comparatively well within the calibration regime, they show pronounced differences in extrapolation. This observation motivates a critical discussion about the predictive power of PANNs which also has implications for the modeling of more complex material behavior by virtue of neural networks.

In the search for new spin textures based on singular magnetic objects like Bloch-points or vortices, spinel compounds emerge as an interesting playground due to the interplay between magnetic anisotropy and complex interactions that extend well beyond first neighbors on a pyrochlore lattice. Based on an exploration of the exchange interaction phase diagrams of members of the Ge$B_2$O$_4$ family with $B$=Co and Ni, we show, using simultaneous modeling of inelastic neutron scattering measurements and single-crystal neutron diffraction data, that a 2-$k$ magnetic structure may be stabilized in these compounds. This leads to a short period spin vortex crystal, a variant induced by the magnetic anisotropy of the 3-$k$ Bloch-point structure predicted for isotropic spins. Our study rationalizes the formation of these multi-$k$ spin textures in frustrated antiferromagnets, as well as their anisotropy-dependent evolution.

Machine-learning methods are increasingly applied to astronomical surveys, providing powerful tools for detecting and studying galaxy clusters. We investigate the mass-redshift properties and completeness of the ComPACT galaxy cluster catalogue, constructed using a convolutional neural network applied to publicly available combined ACT+Planck maps. The ComPACT catalogue contains 2,962 SZ-selected galaxy cluster candidates. We confirm clusters by estimating redshifts using literature information and photometric techniques based on DESI Legacy Imaging Surveys data. Cluster masses are derived from ACT+Planck and Planck Compton-y maps via SZ scaling relations. The completeness is assessed using simulated cluster injections into real microwave maps. We confirm approximately $\sim$60 % of the ComPACT candidates as galaxy clusters. The redshifts span the range $0.007 < z < 1.7$, including approximately 116 new measurements. Masses are obtained for 56 % of the sample, covering the range $(0.25 - 13.1) \times 10^{14} ~M_\odot$ and including 158 new mass determinations. We identify five previously unreported massive clusters ($M_{500c} > 6 \times 10^{14}~M_\odot$) at $z > 0.7$, increasing the known population of such systems by approximately 10 %. The ComPACT catalogue expands the SZ-selected Planck-like cluster population, especially at high redshift and high mass, demonstrating the effectiveness of deep-learning approaches for cluster detection in microwave data.

We study local quasihelix and generalized quasihelix properties of several Gaussian Volterra processes with tempered, power-weighted, and logarithmic kernels, including tempered fractional Brownian motions and generalized fractional Brownian motion-type processes. These properties depend significantly on the values of the parameters involved, and we consider all possible cases in detail.

This study examines how parents of LGBTQ+ individuals in South Korea navigate the emotional rupture fueled by fear, isolation, and disorientation after learning their children's queer identity, encounter queer-related (mis)information as a way of coping with this emotional toll, and come to listen to queer realities relationally. Through this process, we highlight how parents reconstruct their identities as supportive parents, which reshapes their informating practices, making them more critical in assessing queer-related (mis)information, developing strategies to protect themselves from harmful narratives, and actively challenging misinformation to support others navigating similar experiences. This work contributes to CSCW by (1) foregrounding parents of LGBTQ+ individuals, an underrepresented yet critical stakeholder group in Queer HCI; (2) demonstrating how identity reconfiguration following a trauma-healing process could transform information practices; and (3) arguing that addressing misinformation requires attention beyond individual fact-based discerning to account for its relational, cultural, and emotional dimensions. Further, we invite CSCW scholars to reconsider the balance between abstracting and humanizing information, explore future design possibilities for parents of LGBTQ+ children, and reflect on the role of researchers as participants in collective research communities fueled by care.

Controllable multilevel resistance states are of interest for memory technologies like neuromorphic computing, but robust materials platforms toward such behavior remain limited. Here, we show that the non-centrosymmetric antiferromagnetic metal CeCoGe$_3$ suggests one such route through a kinetically hindered first-order magnetic transition. Cooling through the kinetically hindered first-order transition in an applied magnetic field produces a magnetic glass state in which high- and low-temperature magnetic phases coexist. The relative fraction of these phases can be controlled by the applied field in which the sample is cooled, and the electrical resistance is directly sensitive to that fraction. As a result, it is demonstrated that CeCoGe$_3$ supports stable multilevel resistive states. These results identify kinetically hindered first-order phase transitions as a promising route towards controllable multilevel magnetoresistive states.

We study a time-dependent non-Hermitian extension of the Schütte-Da~Providência spin-boson Hamiltonian with complex couplings. A time-dependent Dyson map containing a squeezing transformation maps the model, in an admissible bounded regime, to a Hermitian Hamiltonian with real instantaneous energy spectrum. The squeezing contribution generates a dilatation term allowing the Hermitian partner to be interpreted as a fixed-domain representation of a system with moving boundaries. While the fixed-boundary Hermitian model conserves $Q=N-S_0$ and forbids transitions between sectors differing by two bosonic quanta, the boundary motion opens such channels. For closed boundary protocols with constant background parameters the first-order integrated transition amplitude vanishes, reflecting the unitary nature of constant squeezing. Nontrivial transition control arises when the non-Hermitian parameter varies during the boundary motion, changing the dressed basis and allowing boundary-induced transitions to be suppressed or enhanced by coherent interference.

A version of the Law of the Iterated Logarithm for smooth functions in the upper-half space is proved. As a consequence, we show that certain size conditions on the gradient and the gradient of the laplacian of a smooth function, lead to self-improvement growth properties. The results are applied in situations where harmonicity is not present.

The interaction between neighboring cracks has been shown to strongly influence the fracture behavior of graphene. While previous studies focused primarily on crack spacing, the role of crack width remains poorly understood. Here, computational simulations are performed to investigate the coupled effects of crack width and inter-crack spacing $(W_\text{gap})$ on the tensile response of graphene containing parallel cracks. The results show that increasing crack width amplifies the sensitivity of mechanical properties to crack spacing, leading to significant enhancement of peak stress, fracture strain, and toughness at sufficiently large $W_\text{gap}$. For narrow cracks, crack coalescence dominates and causes brittle failure. In contrast, wider cracks promote delayed ligament rupture, increased energy absorption and ductile-like fracture behavior. The normalized toughness and fracture strain exceed those of equivalent single-crack systems by more than twofold. A crack-geometry design map is proposed to identify regimes of crack coalescence, independent propagation, and enhanced toughness.

Soft unclustered energy patterns (SUEPs) refer to high-multiplicity, isotropic distributions of low-momentum particles that could arise in strongly-coupled hidden sector theories. A search for SUEPs whose decay products contain muons in the final state is presented using 140 fb$^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the ATLAS detector at the Large Hadron Collider during 2015-2018. The analysis targets SUEP signatures via gluon-gluon fusion production of a scalar mediator in Hidden Valley scenarios. No significant excess over the Standard Model expectation is observed. Exclusion limits are set on the product of the mediator production cross section and the branching fraction for its decay into a SUEP, down to 0.05 fb for a mediator mass of $m_S$ = 750 GeV, 0.4 fb for $m_S$ = 400 GeV, and 70 fb for $m_S$ = 125 GeV; the last value, when identifying the mediator with the Standard Model Higgs boson, translates to an upper limit on the branching fraction of around 0.2%.

Many approaches to quantum gravity require replacing the traditional black hole geometry with an Exotic Compact Object (ECO), which has a large but not infinite redshift at its surface. We argue that near the ECO surface, the vacuum Einstein equations imply a metric that is chaotic, with increasingly large oscillations as we approach the surface. This behavior is analogous to the `cosmic billiards' found in the BKL analysis of cosmology near the big bang. For the ECO, some of the potential walls of this billiards change sign to become `cliffs', resulting in a runaway behavior where some compact directions squeeze to zero size. In string theory such squeezing yields a natural continuation to the interior geometry of fuzzballs, where compact directions collapse to create monopoles.

In this paper, we propose a novel approach to detect heteroskedasticity in regression models with regressors contaminated by measurement error. Specifically, inspired by the integrated conditional moment (ICM) approach, we construct test statistics based on a deconvolved residual-marked empirical process and establish their asymptotic properties in both ordinary smooth and supersmooth cases, assuming the measurement error distribution is known. The issue of an unknown measurement error distribution is addressed by employing estimators of the measurement error characteristic function based on repeated measurements. Furthermore, depending on whether the measurement error distribution is known or not, to obtain critical values from the case-dependent limiting null distributions, we propose two computationally attractive multiplier bootstrap methods where the "parameter estimation effect" is successfully addressed. Finally, simulation results and empirical studies about corn yields and household budget shares confirm the favorable properties of the proposed tests.

Ferroelectric domain variants that are energetically equivalent are expected to remain preserved during polarization reversal under a symmetry-preserving electric field. However, recent experiments on relaxor-ferroelectric crystals have revealed irreversible elimination of inclined domain walls during AC poling, while the underlying mesoscale mechanism remains unclear. Here, we investigate the domain-wall motion during AC poling of rhombohedral Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_3$--PbTiO$_3$ single crystals containing both 71$^\circ$ and 109$^\circ$ domain walls within a quasi-two-dimensional laminated geometry using phase-field simulations. The simulations reveal that the domain-wall behavior during polarization reversal depends on the spacing ratio between the 71$^\circ$ and 109$^\circ$ domain walls. Closely spaced 71$^\circ$ domain walls undergo irreversible elimination, whereas more widely separated walls are preserved, while the 109$^\circ$ domain walls remain intact. A threshold ratio for domain-wall elimination is identified and found to depend on the mechanical boundary conditions. By tracking the domain-wall trajectories during the switching process, we attribute this behavior to unsynchronized motion of neighboring 71$^\circ$ domain walls arising from long-range elastic interactions when the walls become strongly coupled. This collective motion breaks the symmetry between energetically equivalent domain variants and leads to irreversible domain-wall elimination during polarization reversal. These findings provide mechanistic insight into collective domain-wall evolution during polarization reversal and suggest that proximity-driven symmetry breaking may provide a mesoscale mechanism for domain engineering in ferroelectric materials with high domain-wall densities.

Extending Enriques' characterization to algebraically closed fields of characteristic $p \geq 7$, we show that every smooth projective surface $X$ with $h^1(X, \mathcal{O}_X) = 2$ and $p_1(X) = p_2(X) = 1$ is birational to an Abelian surface. This characterization fails if $p \leq 5$, and we give a sharp alternative.

Existing identification results in proximal causal inference often focus on marginal interventional distributions using standard outcome or treatment bridge functions. These methods do not generally identify joint interventional distributions that contain all proxy variables that were used to define the corresponding bridge functions. In many applications, however, these joint interventional distributions are a natural target of interest. We introduce extended bridge functions and derive new identification results for joint interventional distributions that may retain all relevant proxy variables. We then apply these results to proximal identification algorithms, where interventional kernels naturally arise as intermediate objects, yielding a generalized framework based on kernel operations.

In this work, we study the estimation of treatment duration effects in observational survival data, where treatment and covariate histories evolve over time and longer observed durations are only attainable among individuals who remain event-free and under follow-up, leading to immortal time bias under naive analyses. The cloning-censoring-weighting (CCW) framework provides a practical approach to emulate target trials of treatment duration strategies, but several methodological aspects remain insufficiently understood. We focus on static treatment duration strategies under two settings of increasing complexity: baseline confounding only, and confounding with time-varying covariates. We formalize the assumptions underlying CCW, with particular emphasis on treatment admissibility, relaxed intervention rules, and the distinction between artificial and natural censoring. We then compare several estimation approaches after cloning and censoring, including inverse probability of censoring weighting (IPCW), the G-formula, and doubly robust estimators, through simulation studies assessing robustness, variability, and sensitivity to censoring model misspecification. Finally, we apply the framework to a Breast Cancer cohort to emulate a target trial comparing 2 versus 5 years of adjuvant tamoxifen in early stage breast cancer. Due to the small number of events and limited support for the 2-year strategy, estimates are associated with substantial uncertainty. These findings highlight both the practical relevance and the limitations of CCW, and underscore the importance of sensitivity analyses in complex longitudinal observational settings.

We study $\ell$-colourings of $(v,k,λ)$-BIBDs (balanced incomplete block designs) where, within each block, one colour is absent and each of the $\ell-1$ other colours appears exactly $\frac{k}{\ell-1}$ times. We establish several necessary conditions for such colourings to exist. We also use these coloured BIBDs to provide new necessary conditions for the existence of Hadamard matrices, affine planes, and twin prime powers.

We numerically approximate the Tomita-Takesaki modular operator for local subalgebras of the 1+1-dimensional massive Majorana field. Our method works at the one-particle level with a discretisation of time-0 data in position space. The local subspaces we consider are associated with one double cone and with the disjoint union of two double cones. In order to avoid boundary effects, we primarily choose the overall spacetime to be a cylinder; different choices of boundary conditions (antiperiodic and periodic) are considered. We compare our numerical results to known analytic expressions in the massless case. It turns out that the modular operator has a non-trivial dependence on the mass. In the case of two double cones, the modular generator does not only have ''local'' contributions (supported on the diagonal in configuration space) but also ''bilocal'' terms (connecting the two double cone regions); we find the latter to be less prominent at higher masses, in line with expectations.

We study $3$-dimensional trans-Sasakian manifolds using the Newman--Penrose formalism. In this framework, the geometry of the structure vector field is encoded by scalar spin coefficients: acceleration, shear, expansion, and twist. A central observation is that, in dimension $3$, the trans-Sasakian condition is equivalent to the characteristic vector field defining a shear-free geodesic congruence, or equivalently a conformal foliation by geodesics. Thus, the Newman--Penrose equations provide a direct scalar formulation of the conformal foliations studied by Baird and Wood in the theory of harmonic morphisms. Within this framework, we derive curvature and Laplacian identities for trans-Sasakian manifolds and their main subclasses, including formulae for the Ricci tensor, scalar curvature, Einstein condition, rough Laplacian, divergence and harmonicity of the characteristic vector field, together with several illustrative examples. As an application, we consider trans-Sasakian structures compatible with fixed homogeneous metrics of type ${\Bbb E}(κ,τ)$. We prove a rigidity result: in the non-space-form cases, the Newman--Penrose equations force the characteristic vector field to be vertical. Hence, for $τ\neq0$ and $κ\neq4τ^2$, every compatible trans-Sasakian structure is the canonical vertical $α$-Sasakian structure, while for $τ=0$ and $κ\neq0$, it is vertical and cosymplectic. In particular, these non-space-form homogeneous metrics admit no proper compatible trans-Sasakian structures.

When a magnetic material hosts spin-wave excitations, or magnons, the local magnetization can rotate in circular or elliptical orbits, the latter arising naturally in the presence of magnetic anisotropies transverse to the equilibrium magnetization. This article investigates the diffusive transport of elliptical magnons in easy-plane ferromagnets. Our analysis starts with the derivation of the magnon dispersion relation and magnon spin from the Landau-Lifshitz-Gilbert equation with a perpendicular magnetic anisotropy. Then, using the Boltzmann transport equation in the relaxation time approximation and perturbation analysis, the magnon-spin and magnon thermal conductivities are obtained, quantifying the magnon transport in the insulator. Our calculations demonstrate that, in both three- and two-dimensional systems, the effects of ellipticity on magnon transport coefficients result in an enhancement or a decrease, depending on whether magnets with a easy or hard perpendicular-to-plane axis are considered, respectively. On the other hand, our results predict an enhancement of the magnon heat transport for both easy- and hard-axis magnetic systems. Our study supports previous works on magnon ellipticity and makes a step towards clarifying its effect on magnon transport properties.

This paper proposes CAT-MoEformer, a context-aware transformer with scene-conditioned mixture-of-experts (MoE) feed-forward networks, for proactive mmWave beam prediction from compressed uplink pilot observations. The spatial encoder comprises a three-layer asymmetric convolutional network followed by a squeeze-and-excitation recalibration block, which extracts frequency-beam correlation features from pilot tensors without explicit channel reconstruction. A truncated pretrained GPT-2 backbone models the temporal evolution of beam sequences, with the feed-forward networks in the upper three transformer layers replaced by scene-conditioned MoE-FFN modules. A lightweight gating network maps the scenario label and normalized user equipment speed to expert mixing weights, conditioning the routing decision on physical propagation descriptors rather than on latent hidden states. This design yields interpretable expert assignments and eliminates the load imbalance associated with token-level routing. To prevent expert collapse under soft routing, a three-stage training strategy is introduced: hard expert assignment in the first stage establishes scene-specific specialization, isolated gating network training in the second stage aligns the soft routing distribution with the hard partition, and top-1 hard inference in the third stage fine-tunes the model under deterministic single-expert activation to maximize scene-specific precision. Simulation results on 3GPP TR 38.901 Urban Macro channel simulations with $64{,}000$ user samples demonstrate that CAT-MoEformer achieves a Top-1 beam prediction accuracy of $94.88\%$ and a beam switching instant accuracy of $80.62\%$, representing gains of $2.33\%$ and $9.55\%$ respectively over a CNN+GPT-2 baseline, with an inference latency of $0.52$~ms.

High-power structured light has a wide range of applications, from material processing and high-capacity optical communications to programmable electron beams, plasmas, and nuclear states. On-demand generation of structured light and adaptive control of beam profiles are essential for many practical applications, but are difficult to achieve at high power. Here, we demonstrate reconfigurable generation of structured light from a high-power multimode-fiber laser amplifier through full-field control of a low-power seed. An efficient nonlinear beam shaping scheme based on a local linear approximation of the complex nonlinear input--output relation is developed and realized in situ. Diverse structured beams such as Gaussian, Bessel, vector and orbital angular momentum beams are directly generated from the fiber amplifier at powers exceeding 500 W. Our scheme enables real-time programmability of structured light and is readily scalable to even higher power levels. This work provides a general framework for controlling high-dimensional nonlinear systems without accurate knowledge or tractable model.

This study has presented a comprehensive computational fluid dynamics (CFD) analysis of combustion flow in a realistic can combustor, evaluating the influence of various turbulence models on flow, thermal, and species fields. The non-premixed combustion modeling is performed using a presumed (beta) PDF approach in conjunction with a steady laminar flamelet model employing the San Diego reaction mechanism, and the turbulence is modeled using the RANS approach. The influence of turbulence models (standard $k-ε$, realizable $k-ε$, SST $k-ω$, LPS-RSM) on the velocity field, such as the mean axial velocity, mean transverse velocity, turbulent kinetic energy (TKE) and shear stress, is analyzed, besides their influence on temperature and species (\ce{C3H8}, \ce{CO2}, and \ce{CO}) concentration. Analysis showed that despite the shortcomings of the isotropic turbulent viscosity formulation of the SST $k-ω$ model being evident, it predicted the mean axial velocity, mean transverse velocity, turbulent kinetic energy and shear stress more accurately. Additionally, it predicted the flow features expected in a can combustor, such as the central recirculation zone (CRZ) and central vortex core (CVC), more accurately than other models. Besides, the model predicted a higher temperature in the primary zone, which is supported by a lower prediction of \ce{C3H8}, and elevated TKE, both of which support strong mixing and efficient heat release. Furthermore, the SST $k-ω$ model predicted the most compact stoichiometric mixture fraction bubble, encompassing CRZ and shear layers, indicating that the majority of the combustion occurs in the primary zone. The corresponding progress variables also indicated high values in the primary zone and shear layers, confirming near completion of the reaction, supported by negligible prediction of \ce{C3H8} and \ce{CO} at the outlet.

The constitutive behavior of materials is modeled through relationships between stress, strain, and possibly additional internal variables. This results in relatively high-dimensional feature spaces for machine learning models rendering the efficient generation of informative datasets essential as brute force methods suffer from the curse of dimensionality. This work introduces a diversity-aware batch-mode query-by-committee active-learning strategy to generate datasets of maximum information content at minimum cost. In contrast to existing methods, this novel method selects multiple informative, non-redundant queries per iteration, enabling concurrent generation of informative datasets and reducing the number of machine-learning retraining cycles. A central component of this method is a cosine-similarity-based metric that complements the uncertainty criterion based on committee variance by promoting within-batch diversity. The query selection is guided by committee variance and a diversity-promoting criterion. The approach is benchmarked for efficient stress-space sampling in data-driven constitutive modeling. In this setting, a committee of support vector classifiers approximates the so-called yield surface, which is a manifold dividing the six-dimensional stress space into an elastic and plastic domain. We demonstrate that the method handles different batch sizes robustly, maintains high within batch diversity, and rapidly reduces committee uncertainty. The resulting machine learning yield surfaces achieve predictive accuracy comparable to sequential active learning, while requiring substantially fewer retraining cycles. This makes the proposed approach an efficient strategy for stress space sampling in data driven constitutive modeling and for reducing time to solution via concurrent data collection in each iteration.

This paper investigates robust synchronization for multi-agent systems (MASs) governed by parabolic partial differential equations in the presence of both observable and unobservable disturbances. Using only boundary output measurements, a disturbance observer is designed to estimate observable Dirichlet boundary disturbances while ensuring robustness of the observer error system with unobservable disturbances occurring in the domain. Using only the reference signal and local output information, distributed synchronization controllers are then constructed to enable all agents to track the reference trajectory. In particular, exponential tracking is achieved in the absence of unobservable disturbances, while robustness is preserved when additional unobservable disturbances occur during controller implementation. We further analyze the impact of unobservable Dirichlet-Robin boundary disturbances on synchronization performance by proving the boundedness of solutions to the synchronization error system. Moreover, to characterize the influence of all disturbances, input-to-state stability (ISS) is established for the closed-loop system. For the involved systems, the generalized Lyapunov method and the recursion technique are extensively employed in the stability analysis, and the lifting technique and semigroup theory are used to prove the well-posedness. Simulation results validate the proposed control scheme, demonstrating effective disturbance estimation and rejection, robust synchronization, and the ISS properties under various scenarios.

For the information transmission over a binary symmetric channel the random coding is used. The transmission of exponential number of messages is considered. The exact decoding error probability exponent is derived. The proof is based on the new results on the distribution of a certain sum of random variables.