Papers

Kalman-type filters are widely used for tracking dynamic systems, yet the confidence regions commonly derived from their estimated covariances can become unreliable under nonlinearities, non-Gaussian disturbances, and model mismatch. In this work, we develop a conformal prediction (CP) framework for equipping Kalman-type filters with statistically reliable confidence regions. Unlike CP applied to black-box estimators, our approach exploits the recursively estimated first- and second-order moments of the state posterior, which capture the time-varying uncertainty induced by the underlying dynamics. Based on these statistical features, we propose three complementary constructions. The first conformally calibrates Gaussian confidence regions induced by the filter moments. The second employs quantile regression to map the estimated moments into the boundaries of adaptive convex regions, which are subsequently calibrated. The third learns a Gaussian-mixture representation of the posterior and conformalizes the resulting density-based regions, enabling the characterization of multimodal and non-convex uncertainty sets. We establish finite- sample coverage guarantees for both sample-wise confidence, which controls miscoverage at individual time instances, and trajectory- wise confidence, which jointly covers the state sequence over a prescribed horizon. Numerical experiments across diverse linear and nonlinear dynamic systems demonstrate that the proposed methods attain the prescribed coverage while producing tight and informative confidence regions, and highlight the relative merits of the three constructions under different posterior characteristics.

Downlink multi-user multiple-input multiple-output (MIMO) precoding with limited channel state information (CSI) feedback in multi-cell systems is studied. Conventional codebook-based CSI feedback compresses the UE-specific physical channels, which leaves an inherent mismatch between the base-station (BS) precoders and the interference-aware UE combiners. To address this limitation, an effective CSI (ECSI) feedback framework is proposed in which UEs compute their linear combiners from precoded downlink pilots, construct corresponding post-combining effective channels, and report compact quantized representations using the same payload structure as in conventional schemes. The BS reconstructs the effective CSI and iteratively refines its precoders through over-the-air signaling without incurring additional downlink overhead. Analytical expressions are derived to characterize the effective-channel estimation error under both conventional CSI and ECSI feedback, explicitly capturing the impact of beam selection and rank truncation. Simulations demonstrate fast convergence within a few iterations and up to 30% average sum-rate improvement over conventional CSI-based precoding, with gains reaching 100% at the 10th percentile of per-stream rates in interference-limited conditions.

In this paper, we consider a nonlocal elliptic equation involving a nonnegative parameter $a$ that quantifies the strength of the nonlocal term, posed in a smooth bounded domain with homogeneous Dirichlet boundary conditions and a given nonnegative source term $f$. This class of problems arises in several applications, including the modeling of thermistor behaviour and population dynamics with crowding effects. We focus on the breakdown of the maximum principle as the parameter $a$ increases. We characterize the two types of degeneracy that may occur, possibly simultaneously, at the critical parameter $a^*$: the solution may vanish at an interior point of the domain, possibly forming a dead-core region, or its normal derivative may vanish on the boundary. In particular, we obtain sufficient conditions for the emergence of dead-core solutions, thereby answering an open question raised in the recent literature. Several one- and two-dimensional examples are constructed to illustrate each possible scenario. Additionally, we study an optimization problem motivated by biological considerations, where the goal is to maximize the critical threshold $a^*$ over an admissible class of resource distributions. For sources with prescribed total mass, a uniform upper bound, and an interior-contact condition, we show that the critical threshold is unbounded and that the corresponding total population can be arbitrarily small. We also establish the existence of a maximizer in a class with a prescribed positive lower bound on the total population, a uniform bound on the sources, and the same interior-contact condition.

For positive integers $n,r,t$, let $\delta(n,r,t)$ denote the maximum possible minimum degree of a balanced $r$-partite graph with parts of size $n$ and chromatic number at most $t$. Lo, Treglown and Zhao established a general upper bound for this parameter and used it, together with explicit constructions, to determine the corresponding multipartite clique threshold up to an additive constant in a broad parameter range. I determine the chromatic parameter throughout the range $r=mt-a$, $m\ge2$, $t\ge3$, $2\le a\le \min\{m,t-1\}$. The answer differs from the Lo–Treglown–Zhao upper bound by at most one. I give an explicit arithmetic criterion deciding when this one-unit correction occurs. The proof reduces the problem to an integer matrix extremum. In the boundary case, equality forces the supports of all mixed rows to form a spanning star, after which the only remaining obstruction is a divisibility condition. Combining this formula with the Andrasfai–Erdos–Sos theorem sharpens the known equality range for $f(n,r,t+1)=\delta(n,r,t)$. In particular, for $t=3$ it removes the remaining size restrictions at $r=10$ and $r=13$. Together with the $r=7$ result in arXiv:2609.19177, the classical $r=4$ case, and the known congruence classes, this gives a formula for the multipartite $K_4$-free problem for every admissible $r\ge4$ and every $n\ge1$.

We investigate the optimal damping design and exponential stabilization for a class of higher-dimensional weakly degenerate damped wave equations. In weighted Sobolev spaces, we establish well-posedness and uniform exponential energy decay, and verify the existence of long-time optimal damping potentials. To overcome analytical difficulties arising from system non-self-adjointness, we use finite-time approximation via semigroup operator norms. Through linearization and adjoint-state analysis, we derive first-order necessary optimality conditions and show finite-time optimal dampings possess a bang-bang structure.

The paper presents a 3D numerical model of plasma in which a fully implicit PIC method with exact conservation of global energy and local charge is generalized to the electromagnetic case. This opens the possibility of simulating plasma equilibria with a high (up to an extreme) ratio of plasma pressure to magnetic field pressure, which are formed in open magnetic traps. The main goal of this work is to find out whether a fully implicit model, which usually performs numerous nonlinear iterations when solving the coupled Vlasov–Maxwell system, can compete in performance with semi-implicit models that achieve the same conservative properties at the cost of only a single particle push per time step. It turns out that in 3D geometry such competition is quite possible due to the growing computational cost of evaluating the mass matrices in the semi-implicit approach. The software implementation of the proposed numerical model is written in C++ within the parallel xpic code. Testing the code on problems of the development of the Weibel instability and the formation of plasma with extreme pressure showed good agreement between the semi-implicit and fully implicit approaches and made it possible to establish their relative speed.

Context. MWC 656 is a Be/X-ray binary identified as an emission-line object, X-ray and radio source and might be a weak gamma-ray source, harbouring an enigmatic secondary component. Aims. Our aim here is to study the orbital modulation of the H-alpha emission line, disc truncation and to evaluate the binary parameters. Methods. During the period 2021-2026, we obtained high resolution (30000) optical spectra of MWC 656 and analysed them together with the published data. Results. We find an orbital modulation of the H_alpha emission line with period P orb = 60.43 +/- 0.03 d. By assuming that the Be circumstellar disc is truncated by the companion, we estimate orbital eccentricity e = 0.11 +/- 0.01, semimajor axis a=160 R_sun, and mass of the binary M_1 + M_2 = 15.1 M_sun. Conclusions. The orbital modulation of the H_alpha emission suggests that (1) in this object we have a new type of cyclic variability of a Be disc; (2) the orbit is mildly eccentric; and (3) the secondary component of MWC 656 is a massive object 5 M_sun, more massive than the neutron stars - a stellar-mass black hole or a massive stripped star.

Algorithms in multi-agent systems such as federated learning, mobile robotic swarming, and consensus control can be designed and analyzed as distributed stochastic approximation algorithms. Such algorithms involve information exchanges between agents for various computations. The freshness of the information can be quantified using the Age of Information (AoI) metric. Consider robotic teams operating in highly obstructed geographical settings, such as subterranean or dense urban environments. Because of spatial disconnections, AoI has empirically been observed to be heavy-tailed with unbounded moments. However, most analyses assume AoI with bounded moments, creating a gap between theory and practice. To the best of our knowledge, ours is the first analysis under general heavy-tailed AoI with potentially infinite mean. We study the stability (almost sure boundedness of the distributed iterates) and convergence of multi-agent systems that are strictly dissipative in the scaling limit (system at “infinity”). Examples include most gradient-based and consensus algorithms under the Robbins-Monro step-size regime.

The ability to recover weak signals without sacrificing their spectral information is central to precision spectroscopy, yet conventional lock-in detection achieves noise rejection at the expense of spectral dimensionality and ultimately imposes a trade-off between detection bandwidth and sensitivity. Here, we introduce spectral lock-in detection, a versatile framework that extends lock-in noise rejection independently to every resolved component of a broadband spectrum. By separating the fast-time coordinate encoding spectral information from the slow-time coordinate carrying temporal modulation, the measured waveform is spectrally resolved before demodulation, enabling each frequency channel to be independently detected and integrated. We show analytically that, for spectrally stable signals, the signal power in each spectral channel remains invariant, while the noise power ideally decreases by 10 dB per decade of integration time, enabling spectral features buried beneath the instantaneous noise floor to emerge without loss of frequency information. We experimentally validate this framework in both phase-incoherent heterodyne terahertz spectroscopy and phase-coherent terahertz time-domain spectroscopy, demonstrating more than six orders of magnitude of sensitivity enhancement across the spectrally resolved channels. Because spectral discrimination is performed computationally on the acquired waveform, the approach requires neither sequential spectral scanning nor additional spectral-selection, multichannel-detection, or interferometric hardware. Spectral lock-in detection therefore provides a broadly applicable route to enhancing sensitivity across diverse spectroscopic platforms and frequency regimes, opening new opportunities for high-sensitivity, information-rich measurements across the electromagnetic spectrum.

Local quantum interactions generate dynamics in an exponentially large Hilbert space, yet locality and entanglement restrict the information that can spread and accumulate. Bounds on propagation and entanglement growth, together with tensor networks, exploit these restrictions to discard information unnecessary for describing the evolution. This leads to a sharper question: how much information must any low-rank representation retain? Here we determine these limits, up to logarithmic factors, for short-range interactions. For time-independent evolution, the optimal rank obeys $\log D=\widetilde O(t+\sqrt{\log(1/\epsilon)})$, with matching lower bounds fixing the accuracy exponent $1/2$; for arbitrary driving, matching fixed-time bounds instead give $2/3$. Correspondingly, the corresponding dynamical entanglement spectra exhibit distinct small-$\alpha$ Rényi laws, $\alpha^{-1}$ and $\alpha^{-2}$. In one dimension, the static limit is constructively attained by an explicit MPO algorithm, with an analogous extension to Liouvillian dynamics. Together, these results determine the irreducible information required to represent local quantum evolution and uncover distinct entanglement structures in static and driven dynamics.

The spectra of gamma-ray pulsar halos exhibit a clear cutoff feature at tens of TeV. This work investigates the origin of the spectral cutoff by interpreting the HAWC data of the Geminga halo. The most straightforward interpretation is that the cutoff reflects the maximum electron acceleration capability of the central PWN. We model this scenario using spherically symmetric diffusive shock acceleration, where the upstream scale of the PWN termination shock limits the maximum energy. We also propose an alternative interpretation of the cutoff: if the electron diffusion coefficient in the surrounding interstellar medium rises rapidly at high energies, a substantial fraction of high-energy gamma-ray flux from the target source can leak outside the analysis region, producing an observed spectral cutoff effect. Both explanations successfully reproduce the spectral cutoff of the Geminga halo. Meanwhile, the two scenarios make distinct predictions on the statistical properties of pulsar halo spectral cutoffs and the X-ray spectral features of the corresponding PWNe, which may be tested through further observations.

We prove that the Turán density of the tetrahedron $K_4^{(3)}$ satisfies $\pi(K_4^{(3)}) \le 14993367693127837/26880000000000000 < 0.557789$, improving Baber's upper bound of $0.5615$ and closing about $62\%$ of the gap to the conjectured value $5/9$. The proof uses an exact seven-vertex flag-algebra certificate incorporating degree-stationarity from Razborov's differential method. To find the certificate, we combine the established techniques of cutting planes and column generation to optimize jointly over flag families whose types have at most five vertices. We give a complete formal proof of this Turán density bound in Lean 4.

We establish a quantitative sound-soft scattering limit for a finite bubbly crystal near the upper edge of the first Bloch band of the corresponding infinite crystal. The inclusions form a dense periodic array of period $\varepsilon$ in a bounded Lipschitz domain, and their density contrast is $\delta=\varepsilon^2$, with fixed positive wave speeds. Under coordinate-reflection symmetry, we prove that the normalized capacitance symbol has a unique nondegenerate maximum on the Brillouin torus. Its Hessian defines a positive Dirichlet elliptic operator governing the limiting spectral detunings. A mean-constrained variational formulation allows us to compare the actual finite-array capacitance matrix with the truncated infinite-lattice operator and to prove exponential localization of their difference near the sample boundary. We obtain an $O(\varepsilon)$ norm-resolvent approximation and connect it to the full acoustic scattering problem, retaining the second-order Bloch correction required by the frequency scaling. For rescaled detunings outside the effective Dirichlet spectrum, the exterior $L^2$ and far-field discrepancies are $O(\varepsilon)$, while the interior $L^2$ field is $O(\varepsilon^{1/2})$. Numerical experiments illustrate the far-field convergence and the effective spectral modes. Explicit one-dimensional calculations describe finer Fabry–Pérot transmission windows and show that a fixed frequency strictly inside the first band need not have a unique scattering limit.

Under the AI Flow framework, communication networks distribute intelligence across devices, edge servers, and clouds, and computation at the receiver becomes a resource that can substitute for transmitted bits. Generative video compression (GVC) embodies this exchange by sending compact tokens with ultra-low bitrate and letting a generative decoder synthesize the video, yet how much bandwidth savings a unit of decoder compute actually achieves has never been quantified. To fill this vacancy, we model reconstruction quality as a two-factor power law in data rate and decoder compute, which fits measured DISTS of two GVC decoders with a mean error below 3%, and define the information capacity (IC) as the negative logarithmic slope along an iso-quality contour, namely the fraction of rate saved per fractional increase in compute at identical quality. IC is dimensionless and unit-invariant, thus enabling an architecture-agnostic comparison. It forms a field over the operating plane, locating where additional denoising steps are worth their cost. Across five datasets, the 14B decoder trades more compute for fewer rate about ten times more efficiently than the 1.3B decoder. IC also varies significantly across datasets, indicating imbalanced performance on the rate-compute trade-off in GVC methods.

Observations of the Milky Way show that galaxies have binary stars in their centres. Using Monte Carlo simulations, we model the population statistics of encounters of such binaries with galactic central black holes (BHs) of mass 10^5-10^{10} Msun (hypermassive BHs >= 10^8 Msun HMBHs). Whereas main-sequence single stars cannot undergo tidal disruption events around HMBHs, stellar collisions of main-sequence binary stars may produce observable transients. We use the post-Newtonian Einstein-Infeld-Hoffmann (EIH) equations as implemented in the three-body code Multistar. We simulate 100,000 models each for six BH masses and 10 different binary parameter distributions. We find that stellar collisions occur in all models, with collision fractions ranging from ~7% for circular, equal-mass binaries to ~0.2% for the observationally motivated Moe2017 binary distribution. Most collisions occur for prograde, tight binaries at low impact parameters beta = r_t/r_p, where the tidal force of the BH drives up the binary eccentricity during pericentre passage. Collision velocities are close to the binary escape velocity for lower-mass BHs (<= 10^8 Msun), but span a wider range for higher-mass BHs, implying an increasing fraction of stellar mergers. Using empirical loss-cone rates and the local BH mass function, we estimate detectable LSST collision rates of ~8,600 and ~3,000 events per year for our Kroupa mass function, Opik's law, inclined orbit model and our MS17 model, respectively, around 10^6 Msun BHs; ~330 and ~150 events per year around 10^8 Msun BHs; and ~3.5 and ~2.8 events per year around 10^9 Msun BHs. These results suggest that binary stellar collisions around HMBHs represent a potentially observable population of nuclear transients that may contribute to the growing sample of ambiguous nuclear transients detected by wide-field optical surveys.

Biometrical sciences and disease diagnosis in particular, are often concerned with the analysis of associations for cross-classified data, for which distance association models give us a graphical interpretation for non-sparse matrices with a low number of categories. In this framework, usually binary exploratory and response variables are present, with analysis based on individual profiles being of great interest. For saturated models, we show the usual linear relationship for log-linear models is preserved in full dimension for the distance association parameterization. This enables a two-step procedure to facilitate the analysis and the interpretation of associations in terms of unfolding after the overall and main effects are removed. The proposed procedure can deal with cross-classified data for profiles by binary variables, and it is easy to implement using traditional statistical software. For disease diagnosis, the problems of a degenerate solution in the unfolding representation, and that of determining significant differences between the profile locations are addressed. A hypothesis test of independence based on odds ratio is considered. Furthermore, a procedure is proposed to determine the causes of the significance of the test, avoiding the problem of error propagation. The equivalence between a test for equality of odds ratio pairs and the test for equality of location for two profiles in the unfolding representation in the disease diagnosis is shown. The results have been applied to a real example on the diagnosis of coronary disease, relating the odds ratios with performance parameters of the diagnostic test.

AI research agents must predict the effects of computational changes after budgeted experiments. WhatWorkedBench evaluates this experimental understanding through a delivered response surface of configuration scores. Agents inspect workflow code and buy measurements; exhaustive CPU references score conditional component effects, mean pair interactions, configuration choice, and delivery. The catalog spans 36 task conditions, 30 sources, 8 workflow families, and 1248 indexed configuration records, with 4,206 numerical controls. At eight purchased measurements plus two free anchors, pair-effect ridge selects an exact optimum on 15 of 22 sources; 13 of these cases have at least one conditional-effect error exceeding 10% of the task utility range. Shared-estimator comparisons measure acquisition and reconstruction on common observations. In a prospective typed study on 12 four-factor sources, DeepSeek Flash submits 12/12 direct tables and gains 0.147 recovery over a Gaussian process (GP) fitted to the same observations. Pro delivers 11/12 artifacts, with an all-attempt GP difference of -0.001 and a delivered-only difference of +0.063. On six prespecified new agent-evaluation sources, Flash and Pro gains are 0.149 and 0.074. In eight typed six-factor episodes, seven final tables satisfy verified code equivalences. Four fresh agents pass all six registered rules through named estimators and deliver consistent tables at 0.682 recovery versus 0.710 for separate direct-table runs. WhatWorkedBench links acquisition, inference, program structure, and delivery.

This paper introduces Passing, an interactive audiovisual installation that generates an endless journey from a single continuous monorail-window recording by reconstructing it as a spatiotemporal volume. Rather than replaying the footage linearly, the work resamples its spatial and temporal structure along nonlinear trajectories, producing a continuously passing landscape whose depth, speed, and temporal order become unstable. A camera-based viewer-presence detection system estimates whether a viewer is present in the viewing zone and uses this presence state to influence transitions among rendered video sequences. The resulting video stream is fed into SpecMaskFoley, a real-time video-to-audio synthesis model that generates a synchronized soundscape for the reconfigured image. The model is not used to reconstruct an objectively correct soundtrack, but functions as a speculative listener, proposing a possible auditory interpretation of a world whose conventional spatial and temporal premises have been disrupted. Passing distributes creative agency across the artist, who defines the rules of spacetime reconstruction; the AI model, which interprets the emergent visual flow as sound; and the audience, whose embodied presence influences the audiovisual trajectory. Through this structure, the work investigates how authorship and listening may be negotiated among human intention, machine inference, and audience interpretation. Artwork page: https://ryufurusawa.com/passing

The training efficiency of Variational Quantum Algorithms (VQAs) is dictated by the geometry of their loss landscapes, which can be formally analysed by mapping these functions to random fields on manifolds. Instead of VQAs, we can then directly study the corresponding random fields, in our case, the Wishart Hypertoroidal Random Fields (WHRFs). We are mostly interested in the distribution of critical points (especially local minima) of WHRFs. For this purpose, the Kac-Rice formula is presented, reformulated, and simulated. The findings identify a phase transition in the distribution of local minima. Beyond a specific threshold, local minima concentrate near the global minimum in function value, meaning that even local minima are good approximators of the global one. The threshold is governed by the ratio between the problem Hamiltonian degrees of freedom and by the number of independent parameters in the VQA. Since the degrees of freedom parameter scales exponentially, we propose symmetry reduction operations to lower the degrees of freedom. This mathematically reduces the dimension, scaling down the required parameter threshold and enabling to solve bigger problems.

Spin dynamics is conventionally treated as inertia-free. The inertial Landau-Lifshitz-Gilbert equation (iLLG) extends this with a second-order time derivative, predicting a high-frequency nutational mode that recent experiments have claimed to observe and interpreted as direct evidence for spin inertia. We show that when spin inertia is generated by eliminating additional dynamical degrees of freedom, the resulting exact spin-only description is generally non-Markovian. The iLLG is recovered as the low-frequency, second-order truncation of the underlying memory kernel. Using a minimal spin–cavity model, we show that the exact eigenfrequencies and those obtained via the iLLG differ and that the spin nutation mode predicted by the latter is a truncation-induced high-frequency artifact. This raises a broader question of the applicability of the iLLG obtained from analogous low-frequency truncations, which may likewise generate spurious high-frequency roots. Consequently, agreement of a high-frequency spectral feature with the iLLG nutation frequency does not, by itself, establish a physical nutation mode.

The deployment of unmanned aerial vehicles (UAVs) in low-altitude airspace requires accurate and timely radio maps for reliable communication and safe navigation. However, constructing such radio maps is challenging due to the prohibitive overhead of exhaustive measurements and the limited flight endurance of UAVs. To address this challenge, we propose an active learning framework based on flow matching for efficient low-altitude radio map construction from sparse measurements. We first analyze a plug-and-play (PnP) inference scheme with a flow-matching prior. By characterizing the late-stage refinement behavior through an ordinary differential equation (ODE), we theoretically show how the inference steps smoothly align with a continuous ODE flow to refine the map details. Recognizing that the early generative stages are largely noise-dominated, this insight motivates our proposed truncated flow matching plug-and-play (TFM-PnP) approach. TFM-PnP utilizes a spatial interpolation-based initialization to start the reconstruction from an intermediate flow time, thereby bypassing the inefficient early stages. We further use the generative diversity of flow matching to derive an uncertainty map to guide the UAV trajectory design. Specifically, we propose a weighted sampling approach to select a target location, followed by a Utility-Aware Path Search (UAPS) algorithm to design the corresponding UAV trajectories. Simulation results based on Sionna ray-tracing datasets show that the proposed framework outperforms the considered baselines, achieving more than 50% reduction in normalized mean squared error (NMSE).

We study ball-covering properties in Lipschitz-free spaces. We establish an extension criterion for proving that $\mathcal F(M)$ fails the ball-covering property and apply it to several classes of nonseparable metric spaces. In contrast, we construct a nonseparable uniformly discrete metric space $M$ such that $\mathcal F(M)$ has the uniform ball-covering property and is isomorphic to $\ell_1(2^\omega)$. More precisely, $\mathcal F(M)$ has the $\alpha$-ball-covering property for every $\alpha\in[-1,1)$. This example also shows that these quantitative ball-covering properties are not hereditary within the class of Lipschitz-free spaces. Finally, we prove some stability results under sufficiently small bi-Lipschitz perturbations of the metric.

Large coupled systems may be chaotic at the microscopic level while exhibiting stable collective behaviour at the macroscopic level. Distinguishing between these two forms of instability has been a problem in the physics literature, and several approaches have been proposed. In this paper, we address this problem by introducing and studying observable Lyapunov exponents, which measure the rate at which perturbations of initial conditions grow or decay when viewed through a chosen observable, rather than in the full phase space. For globally coupled maps, we consider finite-time observable Lyapunov exponents and define their mean-field counterpart by first taking the infinite-system limit and then the long-time limit. Our main result shows that, for a broad class of symmetric macroscopic observables, these exponents turn out to be determined by the linearisation of the self-consistent transfer operator, which is the nonlinear operator governing the evolution of the population distribution. We then apply this result to weakly coupled uniformly expanding maps and prove that their mean-field Lyapunov exponents are negative near a stationary mean-field state. Thus, although the microscopic dynamics is chaotic, perturbations decay at the macroscopic level. Our results provide a rigorous framework for distinguishing microscopic from macroscopic chaos in large interacting systems.

We give snakes that are longer than the previous best known in dimensions 13 through 20 and improve the general lower bound for every dimension $d \geq 21$. Our explicit snakes reach 371,711 edges in dimension 20. Twenty compatible paths in that cube allow generalisation to give snakes of length at least $(17/48)2^d$ for every $d \geq 21$. Their controlled overlaps allow copies to be joined across the layers of a larger cube without creating shortcuts. Four additional paths give the same bound for coils. We explain the construction, prove the joining rule, and then count its length. The finite paths and their required intersections are independently verifiable.

Building executable brain models is essential for moving neuroscience from description to mechanism and prediction. Human-brain-scale spiking simulation is constrained by highly irregular communication, multithreaded spike delivery, and the memory cost of sparse connectivity. We present CerebroSim, a scalable framework for whole-brain simulation. CerebroSim combines Delay-aware Spike Broadcast (DSB) for aggregated delay-aware communication, Race-free Synaptic Dynamics Computation (RSDC) for lock/atomic-free multithreaded delivery with HBM-aware optimization, and Sparse Synapse Storage Compression (3SC) for compact indexing with deterministic synapse regeneration. Using a model derived from magnetic resonance imaging and diffusion-weighted imaging, CerebroSim simulates 86 billion neurons and 100 trillion synapses on 18,432 nodes across 11.2 million cores of the LineShine Supercomputer, sustaining 24.44 PFlop/s, 91% weak-scaling efficiency, and 94% strong-scaling efficiency. This capability makes biologically constrained human-brain models practical for mechanistic studies of brain disorders and controlled in silico testing of intervention hypotheses.

This feasibility study presents a Hidden Markov Model (HMM)-based methodology for the Remaining Useful Life (RUL) estimation of rolling element bearings when the training vibration signals differ significantly from those of the target bearing. An AutoRegressive (AR) model is first employed to capture the machinery dynamics using vibration acceleration measurements from an initial operating period where all components including the considered bearing are still under healthy condition. The AR model is subsequently used to filter a newly acquired vibration signal from the faulty machinery, and typical Envelope Analysis is performed on the residual signal to identify fault-related repetition frequencies. The amplitudes of these frequencies, combined with statistical features of the AR residuals are fused through Principal Component Analysis to construct a sensitive to bearing degradation Condition Indicator (CI). Based on training data from the healthy state, a threshold is established, and a fault is declared when the CI exceeds this threshold. Once a fault is detected, its progression is modelled as a sequence of consecutive, distinct states, which are identified using K-Means clustering. A left-right HMM with continuous observation densities is estimated to represent the fault progression and thus predict the RUL. The HMM-based RUL estimation methodology is trained using vibration measurements from a limited number of two run-to-failure experiments with two nominally identical bearings, while RUL estimation performance is assessed on a third bearing of the same type. Despite the significant differences between the vibration data used for training and the life cycles of the training bearings with respect to the target bearing, the RUL estimation results indicate an adequate but conservative performance of the postulated HMM-based methodology.

We prove that a stable noncompact hypersurface with constant anisotropic mean curvature in $\mathbb{R}^{n+1}$ has only one end for $n \le 6$, under a natural ellipticity condition on the anisotropy. This provides an anisotropic counterpart of the one-end theorem for stable constant mean curvature hypersurfaces. We remark that the result is also new in $\mathbb R^7 (n=6)$, in the case of anisotropic minimal hypersurfaces. The proof relies on the existence of a Sobolev-type inequality.

Let $\mathcal{H}$ be a separable infinite dimensional Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal{H}$. A subalgebra $\mathfrak{A}$ in $\mathcal{B}(\mathcal{H})$ has the left (resp.\ right) partial factorization property if for any invertible operator $S\in\mathcal{B}(\mathcal{H})$, there exists an isometry (resp.\ a co-isometry) $U\in\mathcal{B}(\mathcal{H})$ such that $U^*S, S^{-1}U\in\mathfrak{A}$. We show that if $\mathfrak{A}$ is weak operator topology closed with the left (resp.\ right) partial factorization property, then $\mathfrak{A}$ is the nest algebra associated with its invariant subspace lattice. In particular, if $\mathfrak{A}$ is transitive, then $\mathfrak{A}=\mathcal{B}(\mathcal{H})$. This gives a positive answer to Question 6.3 raised by B.V.R. Bhat and M. Kumar in Publ. Res. Inst. Math. Sci. 60(2024), 507–537.

We study strong measurability and adapted approximations for maps taking values in possibly nonseparable metric spaces. After recalling the metric-space Pettis criterion, we give conditions under which measurability implies strong measurability. Under the continuum hypothesis (CH), every measurable map from a countably generated measurable space into a metric space is strongly measurable for every measure on the domain. For finite or $\sigma$-finite measures, the same conclusion holds when the target density is strictly smaller than every real-valued measurable cardinal. Under CH this includes targets of density at most $\mathfrak c$; if no real-valued measurable cardinal exists, it holds for all metric targets. For function-valued maps, we show that pointwise measurability and continuity of the sections need not ensure measurability in the function-space topology. We provide a verification criterion using countably many evaluations and essential separability of the range. Further, we obtain elementary $L^p$-approximations of progressive or jointly measurable adapted processes under suitable filtration assumptions, Lipschitz functionals with path and Wasserstein variables, and smooth approximations based on finitely many observations of a process with left- or right-continuous paths. Finally, under CH and suitable assumptions, we apply these results to controlled stochastic differential equations in separable Hilbert spaces, allowing for jumps, random coefficients, path dependence, and state- and control-law dependence; we establish convergence of states and costs uniformly over admissible controls, convergence of optimal values, and transfer of near-optimal controls.

The exponential decay of weak solutions towards the constant steady state of general cross-diffusion systems in bounded domains with no-flux boundary conditions is investigated. The proof of quantitative decay rates is based on the relative entropy method and involves two parameters: the exponent determining the entropy density and the exponent in the entropy production integral. The key ingredient are novel convex Sobolev inequalities, which extend existing results in the literature to a broad range of values of the two parameters. These inequalities are established using convexity arguments and the Gagliardo-Nirenberg inequality.