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Governing equations provide compact descriptions of physical systems, yet the variables in which they are simple are often hidden in high-dimensional measurements. This challenge is sharper for forced systems, whose responses depend on both intrinsic dynamics and time-dependent inputs. Here we introduce FLARE, a forced latent autoencoder for response equations that learns compact response coordinates, identifies sparse input-dependent latent dynamics and decodes equation rollouts to full responses. By estimating latent dimension from data and separating state estimation from external forcing, FLARE enables forecasts to be initialized from past responses and driven by prescribed future inputs. Across known dynamical systems, application-scale forced responses and visual observations, FLARE recovers compact forced dynamics and predicts long-horizon high-dimensional responses under inputs not used for training. By turning learned coordinates into a dynamical interface, FLARE extends equation discovery to systems whose effective states are hidden within complex observations, providing a route for interpretable modelling and prediction of high-dimensional responses in forced dynamical s

The subpolar oceans are characterized by intense storm forcing and complex littoral topography. Submesoscale frontal instabilities are significant sources of turbulent kinetic energy (TKE) in these regions. However, criteria for identifying and parameterizing these instabilities in regional models have predominantly relied on a geostrophic framework that neglects generalized ageostrophic shear. We derive criteria for overturning instability that account for stabilizing and destabilizing effects of ageostrophic shear on mechanically forced boundaries, deviating from the geostrophically derived potential vorticity (PV) criterion, $qf < 0$. Ageostrophic forcing modifies stability from that implied by the vertical PV structure underlying bulk surface boundary layer diagnostics, which may limit the applicability of such bulk criteria in strongly forced regimes and motivate the need for layer-resolved measures. We demonstrate their application using a feature model of a wind-forced jet, as well as a 1-km Regional Ocean Modeling System (ROMS) hindcast of the high North Atlantic, and assess the importance of forced ageostrophic overturning instability (AOI) in intense frontal zones. In

We present a conservation-based feedback-circuit decomposition specifically for general linear forced systems. In a role parallel to that of eigenvalues and eigenvectors for initial-value problems, the complete set of independent intrinsic circuit gains and their associated forcing-transformation vectors provide a complete analytical representation of both transient and equilibrium forced solutions. The sign of intrinsic circuit gains determines whether successive feedback cycles exhibit monotonic or oscillatory convergence to transformed forcing, while the forcing-transformation vectors determine the structure of transformed forcing. The exact transient and equilibrium solutions are represented analytically through the convergence of the finite-cycle forcing-transformation kernel to the equilibrium forcing-transformation kernel, which is guaranteed regardless of whether the magnitudes of circuit gains exceed one or unstable modes exist in the system. The feedback-circuit decomposition provides a new generic foundational mathematical tool for understanding, predicting, and controlling forced responses in a broad range of coupled linear systems across science and engineering.

Many physical systems are forced by external inputs, which can sometimes take the form of chaotic variation. A particular example is found in applications related to weather and climate, where chaotic variation is prevalent across various timescales. If the system in question has multiple attracting solutions for a given range of forcing, rate-induced tipping can be triggered by the chaotic forcing, with the difference in timescales between the forcing and the system acting as a `rate' parameter. In this paper, we explore the interplay between these two timescales in a low-order model of ice age dynamics. The model exhibits bistability between two equilibria in one region of the parameter space and between an equilibrium and a periodic orbit in another region. When chaotic variation of the parameters is allowed within these bistable regions, the solutions of the forced system undergo rate-induced tipping from one attractor to another. Simulations of the forced system show that the timescale of the chaotic forcing induces a resonance-like behaviour, with an optimal timescale at which the likelihood of rate-induced tipping is at its maximum. We combine basin instability theory, finit

We study, through discrete element simulations, the discharge of granular materials through a circular orifice on the base of a cylindrical silo forced by a surcharge. At the beginning of the discharge, for a high granular column, the flow rate $Q_{\rm ini}$ scales as in the Beverloo equation for free discharge. However, we find that the flow rate $Q_{\rm end}$ attained at the end of the forced discharge scales as $\sqrt{ρ_b P}D_o^3/D_s$, with $ρ_b$ the bulk density, $P$ the pressure applied by the overweight, $D_o$ the orifice diameter and $D_s$ the silo diameter. We use the work$-$energy theorem to formulate an equation for the flow rate $Q_{\rm end}$ that predicts the scalings only in part. We discuss the new challenges offered by the phenomenology of strongly forced granular flows.

In this paper we study the forced instance spaces of model RB, where one or two arbitrary satisfying assignments have been imposed. We prove rigorously that the expected number of solutions of forced RB instances is asymptotically the same with those of unforced ones. Moreover, the distribution of forced RB instances in the corresponding forced instance space is asymptotically the same with that of unforced RB instances in the unforced instance space. These results imply that the hidden assignments will not lead to easily solvable formulas, and the hardness of solving forced RB instances will be the same with unforced RB instances.

Oscillations in a power system can be categorized into free oscillations and forced oscillations. Many algorithms have been developed to estimate the modes of free oscillations in a power system. Recently, forced oscillations caught many attentions. Techniques are proposed to detect forced oscillations and locate their sources. In addition, forced oscillations may have negative impact on the estimation of mode and mode-shape if they are not properly accounted for. To improve the power system reliability and dynamic properties, it is important to first distinguish forced oscillations from free oscillations and then locate the sources of forced oscillations in timely manner. The negative impact of forced oscillation can be mitigated when they are detected and located. This paper provides an overview on the analysis technique of forced oscillations in power systems. In addition, some future opportunities are discussed on forced oscillation studies.

The purpose of this work is twofold. First, we construct probabilistically strong solutions to the three-dimensional Euler equations perturbed by additive noise that are $\mathbb{P}$-almost surely continuous in time, Hölder in space, and satisfy the local energy inequality up to an arbitrarily large stopping time. Second, we prove several non-unique ergodicity results for the forced Euler equations with continuous-in-time external forcing. The solutions we construct are genuinely random and, almost surely, strictly dissipative and not steady states.

Tournament-based compensation schemes with forced distributions represent a widely adopted class of relative performance evaluation mechanisms in technology and corporate environments. These systems mandate within-team ranking and fixed distributional requirements (e.g., bottom 15% terminated, top 15% promoted), ostensibly to resolve principal-agent problems through mandatory differentiation. We demonstrate through agent-based simulation that this mechanism produces systematic classification errors independent of implementation quality. With 994 engineers across 142 teams of 7, random team assignment yields 32% error in termination and promotion decisions, misclassifying employees purely through composition variance. Under realistic conditions reflecting differential managerial capability, error rates reach 53%, with false positives and false negatives each exceeding correct classifications. Cross-team calibration (often proposed as remedy) transforms evaluation into influence contests where persuasive managers secure promotions independent of merit. Multi-period dynamics produce adverse selection as employees observe random outcomes, driving risk-averse behavior and high-performer

We study forced periodicity of two-dimensional configurations under certain constraints and use an algebraic approach to multidimensional symbolic dynamics in which $d$-dimensional configurations and finite patterns are presented as formal power series and Laurent polynomials, respectively, in $d$ variables. We consider perfect colorings that are configurations such that the number of points of a given color in the neighborhood of any point depends only on the color of the point for some fixed relative neighborhood, and we show that by choosing the alphabet suitably any perfect coloring has a non-trivial annihilator, that is, there exists a Laurent polynomial whose formal product with the power series presenting the perfect coloring is zero. Using known results we obtain a sufficient condition for forced periodicity of two-dimensional perfect colorings. As corollaries of this result we get simple new proofs for known results of forced periodicity on the square and the triangular grids. Moreover, we obtain a new result concerning forced periodicity of perfect colorings in the king grid. We also consider perfect colorings of a particularly simple type: configurations that have low ab

Datasets are essential for any machine learning task. Automatic Music Transcription (AMT) is one such task, where considerable amount of data is required depending on the way the solution is achieved. Considering the fact that a music dataset, complete with audio and its time-aligned transcriptions would require the effort of people with musical experience, it could be stated that the task becomes even more challenging. Musical experience is required in playing the musical instrument(s), and in annotating and verifying the transcriptions. We propose a method that would help in streamlining this process, making the task of obtaining a dataset from a particular instrument easy and efficient. We use predefined guitar exercises and hidden Markov model(HMM) based forced viterbi alignment to accomplish this. The guitar exercises are designed to be simple. Since the note sequence are already defined, HMM based forced viterbi alignment provides time-aligned transcriptions of these audio files. The onsets of the transcriptions are manually verified and the labels are accurate up to 10ms, averaging at 5ms. The contributions of the proposed work is two fold, i) a well streamlined and efficien

We introduce the problem of adapting a stable matching to forced and forbidden pairs. Specifically, given a stable matching $M_1$, a set $Q$ of forced pairs, and a set $P$ of forbidden pairs, we want to find a stable matching that includes all pairs from $Q$, no pair from $P$, and that is as close as possible to $M_1$. We study this problem in four classical stable matching settings: Stable Roommates (with Ties) and Stable Marriage (with Ties). As our main contribution, we employ the theory of rotations for Stable Roommates to develop a polynomial-time algorithm for adapting Stable Roommates matchings to forced pairs. In contrast to this, we show that the same problem for forbidden pairs is NP-hard. However, our polynomial-time algorithm for the case of only forced pairs can be extended to a fixed-parameter tractable algorithm with respect to the number of forbidden pairs when both forced and forbidden pairs are present. Moreover, we also study the setting where preferences contain ties. Here, depending on the chosen stability criterion, we show either that our algorithmic results can be extended or that formerly tractable problems become intractable.

We define a new, partizan, loopy combinatorial game, Forced-Capture Hnefatafl, similar to Hnefatafl, except that players are forced to make capturing moves when available. We show that this game is PSPACE-hard using a reduction from Constraint Logic, making progress towards classifying proper Hnefatafl.

We analyze the eccentric response of a low mass coplanar circumbinary disc to secular tidal forcing by a Keplerian eccentric orbit central binary. The disc acquires a forced eccentricity whose magnitude depends on the properties of the binary and disc. The largest eccentricities occur when there is a global apsidal resonance in the disc. The driving frequency by the binary is its apsidal frequency that is equal to zero. A global resonance occurs when the disc properties permit the existence of a zero apsidal frequency free eccentric mode. Resonances occur for different free eccentric modes that differ in the number of radial nodes. For a disc not at resonance, the eccentricity distribution has somewhat similar form to the eccentricity distributions in discs at resonance that have the closest matching disc aspect ratios. For higher disc aspect ratios, the forced eccentricity distribution in a 2D disc is similar to that of the fundamental free mode. The forced eccentricity distribution in a 3D disc is similar to that of higher order free modes, not the fundamental mode, unless the disc is very cool. For parameters close to resonance, large phase shifts occur between the disc and bina

We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while also trying to lock onto an external drive. Previous work on the forced Kuramoto model uncovered two main types of attractors, called forced entrainment and mutual entrainment, but the details of the bifurcations between them were unclear. Here we present a complete bifurcation analysis of the model for a special case in which the infinite-dimensional dynamics collapse to a two-dimensional system. Exact results are obtained for the locations of Hopf, saddle-node, and Takens-Bogdanov bifurcations. The resulting stability diagram bears a striking resemblance to that for the weakly nonlinear forced van der Pol oscillator.

This paper proposed a new method to locate the source of forced oscillation that involves resonance with natural oscillation modes. The new method is based on comparing the oscillation mode shape of the forced oscillation with that of the natural oscillation that the forced oscillation resonating with. The location that has the largest angle difference between the forced oscillation mode and the natural oscillation mode usually indicates the location of the driving force in forced oscillations. Some examples in actual U.S. EI system verified this approach.

For a degree sequence, we define the set of edges that appear in every labeled realization of that sequence as forced, while the edges that appear in none as forbidden. We examine structure of graphs whose degree sequences contain either forced or forbidden edges. Among the things we show, we determine the structure of the forced or forbidden edge sets, the relationship between the sizes of forced and forbidden sets for a sequence, and the resulting structural consequences to their realizations. This includes showing that the diameter of every realization of a degree sequence containing forced or forbidden edges is no greater than 3, and that these graphs are maximally edge-connected.