In the early stages of development, Drosophila melanogaster embryos possess very fast and well-coordinated cell cycles. In the cell cycle, CDK activity is essentially regulated by binding CDK and CycB to form an active complex and by phosphorylating CDK via CDC25 and dephosphorylating it via Wee1. We develop a mathematical model for the embryonic cell cycle which is biochemically sound and which can be rigorously analysed after a model reduction. We show that there exists a region in the parameter space where the model describes oscillations. We then focus on the role of two parameters: the CycB synthesis and the activation coefficient of APC. Our main biological hypothesis is that the first one is responsible for the period lengthening over the first 14 cycles which can be experimentally observed and this hypothesis is supported by numerical simulations of our model: if the CycB synthesis is made time-dependent with a prescribed dynamics, then our simulations show qualitatively a very similar behavior to experimental data reported in the literature.

Recent advances in biomedical research have identified an increasing number of biomarkers associated with heterogeneity in patient responses to medical treatments. When a treatment is suspected to benefit certain patient subpopulations, adaptive enrichment designs may be more efficient and ethical. In such designs, an interim analysis is incorporated during the trial to select patient subpopulations for which the experimental treatment appears promising, according to predefined subpopulation selection rules. However, data-dependent selection can induce selection bias, causing conventional maximum likelihood estimators (MLEs) to overestimate the treatment effect in the selected patient subgroup. Existing inference methods for addressing this bias are typically rule-specific, highlighting the need for an estimation framework that accommodate a broader class of subpopulation selection rules. In this work, we define a general class of subpopulation selection rules based on the sample space partition condition and provide a systematic derivation that yields a unified formula for the Uniformly Minimum Variance Conditional Unbiased Estimator (UMVCUE). This generality allows our formulation to encompass a wide spectrum of adaptive enrichment designs, eliminating the necessity for case-specific derivations for each new design. Extensive simulations confirm the unbiasedness of the proposed UMVCUE, ensuring that therapeutic benefits are not overestimated. By bridging the gap between flexible interim subpopulation selection and rigorous statistical inference, our framework has the potential to facilitate the implementation of diverse subpopulation selection rules with greater ease in real-world trials and promote more efficient and ethical drug development.

We develop a classical well-posedness and regularity theory on a finite connected weighted graph for an extended mean field game system, its associated master equation, and a Hamilton-Jacobi- Bellman equation on the probability simplex, all in the presence of an individual noise operator. The geometric structure is inherited from the logarithmic-mean activation functional of discrete optimal transport, under which the entropic Fokker-Planck equation appears as a gradient flow on the graph and the individual noise operator is a bilinear form in the probability vector and the Wasserstein gradient. A central technical step is a quantitative preservation-of-positivity estimate for the discrete continuity equation, which rules out finite-time boundary degeneracy and yields a classical solution theory for the master equation on the open simplex without imposing any boundary condition. As an application, we recover a Nash equilibrium interpretation of the discrete system in terms of Markov chains on the graph. Our setup is inspired by the computational algorithms for optimal mass transport of [10, 11] and provides a rigorous well-posedness theory for several of the equations derived in [25].

The 3D mass distributions of galaxy clusters are generally triaxial, a geometry that is difficult to constrain from projected observations. In this work, we measure the projected halo shapes of clusters from their weak lensing signatures using the triaxiality functionality in the Cluster Lensing Mass Modeling software, a tool developed by the Dark Energy Science Collaboration to analyze data from NSF-DOE Rubin Observatory's Legacy Survey of Space and Time (LSST). We measure ensemble halo ellipticity on the plane of the sky via axis-aligned stacking and multipole expansion of the weak lensing data. We study a precursor dataset -- the redMaPPer cluster catalog, the metacalibration shape catalog, and the Directional Neighborhood Fitting photometric redshift catalog from the Dark Energy Survey Year 3 public data release. We select clusters that have a high centering probability (>90%) of the identified central galaxy, and use the satellite galaxy distribution to determine the major-axis orientation for stacking. We extend the analysis to the second order of ellipticity in the monopole and quadrupole measurement. The projected ellipticity of the cluster sample is found to be $0.310^{+0.017}_{-0.016}$ (axis ratio $0.527^{+0.018}_{-0.019}$). The projected cluster ellipticity shows no statistically significant dependence on mass and redshift. We further verify the accuracy of the cluster shape measurement using mock catalogs. This analysis is applicable to datasets from upcoming wide-area cosmic surveys such as LSST, Euclid, and the Roman Space Telescope, where larger sample sizes will lead to tighter constraints on the cluster ellipticities.

For decades, metrologists have debated heatedly whether a plane angle is a dimensional or dimensionless quantity; whether it is a base quantity in the International System of Units (SI) or a derived quantity. Two main points of view have emerged in the international metrology community. Those who hold the first view believe that a plane angle is a dimensionless derived quantity equal to the ratio of two lengths, and its unit, the radian, is the dimensionless number one (1 rad = 1 m/m = 1). Those who hold the second view believe that a plane angle is a dimensional quantity with its own independent dimension, and its unit, the radian, is not the dimensionless number one, as is currently accepted in the SI. This article demonstrates that, depending on the physical situation, a plane angle is described by either a dimensional or a dimensionless quantity. When measuring, expressing, and communicating an angle's size, physicists use the dimensional quantity plane angle. Its dimension and unit are independent of the dimensions of other quantities and their units. This quantity, plane angle, should be classified as a base quantity, and its unit, radian, should be included in the class of base SI units. In theoretical studies of physical systems with angular quantities, the latter always enter into equations as a dimensionless combination of dimensional plane angles. This dimensionless combination, in turn, is also a physical quantity characterizing the plane angle in question. This new quantity is a dimensionless derived quantity, which physicists also call an angle.

Existing conformal prediction methods for time-to-event outcomes leverage only baseline covariates, producing prediction intervals that are insufficiently informative to facilitate decision making. We propose History-Aware Prediction Sets (HAPS), a conformal framework that constructs prediction sets for individual event times using covariate histories observed up to a decision time, targeting coverage among individuals who have survived to this time. HAPS handles right censoring adjusted for time-varying confounders via inverse probability of censoring weighting. When the censoring weights are consistently estimated, it achieves PAAC (probably asymptotically approximately correct) coverage among survivors. We further propose two doubly robust extensions of HAPS to weaken reliance on consistent estimation of the censoring distribution. In simulations, HAPS and its extensions reduce median prediction interval length by up to 75\% relative to baseline comparators while maintaining close to nominal coverage. On two public benchmark data sets, HAPS reduces the median interval length by up to 60\% for predictions at year 5, compared to the baseline comparators.

Matrix product states provide efficient classical descriptions of quantum systems that may be useful as reference states for quantum algorithms such as quantum phase estimation and quantum-selected configuration interaction. Shallow circuit constructions for loading matrix product states onto quantum computers is necessary for this to be practical on near-term hardware. We present a decomposition of matrix product states to log-depth quantum circuits via a simple tree tensor network renormalisation procedure. Our method exposes an explicit parameter which can be used to trade a small amount of fidelity for large savings in circuit depth. We extend this decomposition to the case of matrix product operators allowing us to construct log-depth and ancilla-free circuits to calculate overlaps of the form $\left |\langleϕ|U|ψ\rangle\right |^2$. In particular, we demonstrate an interpretation of these circuits as \emph{verifier circuits} with application to circuit-level device calibration.

Accurate Channel State Information (CSI) prediction is essential for dynamic multiple-input multiple-output (MIMO) systems but remains computationally demanding. This letter proposes a resource-efficient predictor that combines a gated recurrent unit (GRU) encoder with Luong attention, a bottleneck gated fusion module, and a Dimension-wise Separable Linear Head (DSLH). The gated fusion module integrates local recurrent features with global attention context, while the DSLH reduces the cost of the output mapping. Evaluated on 3GPP TR 38.901-compliant channels, the proposed model achieves an average NMSE of -13.84 dB with 26% fewer parameters and approximately 2.3x higher inference throughput than a dimension-matched LinFormer baseline. The proposed model is best suited to LOS and mixed-condition scenarios, offering a practical accuracy-efficiency trade-off for short-horizon CSI prediction at moderate sequence lengths.

The Schrödinger--Newton (SN) equation provides a semiclassical framework for the evolution of self-gravitating of massive quantum systems. We propose a two-body Schrödinger--Newton model that separates local nonlinear self-localization from the nonseparable Newtonian pair potential. Analytically, we show that the nonlinear self-field preserves the Schmidt spectrum, whereas direct entanglement generation arises from the nonseparable pair potential. Using numerical simulations in a regularized one-dimensional geometry, we find that entanglement generation depends sensitively on the initial spatial configuration and on the mass ratio. Highly localized, self-bound wavepackets experience minimal entanglement growth during scattering. Spatial delocalization and kinetic dispersion broaden the interaction region, amplifying the entangling power of the pair potential and exciting higher-order spatial modes. For dispersive Gaussian initial states, mass asymmetry shatters the lighter particle, producing Wigner negativity and rapid entanglement growth, whereas stationary SN profiles strongly suppress this effect. Stationary SN profiles isolate the bare pair-potential contribution; dispersive Gaussian initial states inflate it.

In this study, large-scale molecular dynamics simulations with the Vashishta potential and the analytic bond-order potential (ABOP) were performed to investigate the effect of extended defects on the elastic properties of cubic silicon carbide (3C-SiC). Specifically, we focused on systems containing Shockley partial dislocations terminating stacking faults, along with double and triple dislocation complexes. The changes in the independent elastic stiffness constants C11, C12 and C44 upon varying the mentioned extended defects concentrations were quantified. Using the values of these constants, the effective bulk, shear, and Young's moduli were calculated for different defect types and concentrations. The moduli were calculated along particular crystallographic directions aligned with the mentioned defect configurations as well as evaluated using Voigt-Reuss-Hill averaging to provide overall orientation-independent characterization of the defect-altered lattice. The obtained results reveal a general trend of diminishing the material's stiffness with increasing densities of Shockley partial dislocations and dislocation complexes. Depending on the defect configuration, the average elastic moduli decrease by up to approximately 6 % with the Vashishta potential and up to about 4 % using the analytic bond-order potential. At this, triple dislocation complexes induce smaller perturbations. These findings demonstrate that extended defect networks can measurably modify the elastic response of 3C-SiC and should be considered in further scientific research and practical applications of this material.

We study common frequently hypercyclic vectors for countable families of weighted backward shifts acting on $\ell_p$ spaces, $1\leq p<\infty$. Using probabilistic techniques, we develop a general existence criterion, complemented by a non-existence result. These insights are then applied to the specific setting of countable families of polynomials of weighted backward shifts, providing conditions under which they share a common frequently hypercyclic vector.

We prove that the short-period eigenfunctions of quantum cat maps constructed by Kim and the author equidistribute on $\mathbb{T}^2$ in the sense of semiclassical measures. We also show that their logarithmically large $\ell^\infty$-norm is asymptotically concentrated on a bounded number of coordinates. Thus, for this explicit family, strong coordinate localization coexists with semiclassical equidistribution. These results confirm the behavior suggested by earlier numerical evidence of Kim and the author, and contrast with the scarring phenomena for short-period eigenfunctions observed by Faure, Nonnenmacher, and De Bièvre.

Since its introduction by Fisher, the method of hypothesis testing that relies on computing error probabilities has witnessed several developments. Perhaps the most significant development was the seminal contributions of Neyman and Pearson who brought in the concept of the alternative hypothesis with its corresponding error of the second kind. Significance tests have played a major role in various scientific and technological developments, but not without controversies. Although originally cast as frequentist approaches, Bayesian ideas have been incorporated into significance tests, widening access to them. The quantities central to computations of error probabilities are the sampling distributions, which can be computed even without thresholds or alternative hypotheses. Even though Fisher used the significance threshold of 0.05 in his calculations, he cautioned against prescribing any specific threshold. Recently, there have been calls for reformation in practice with regard to the almost standard use of the significance threshold of 0.05, prepublication confirmatory studies, the dichotomous consideration of the null and alternative hypothesis and abandoning significance tests altogether in favour of other approaches such as confidence intervals and Bayesian decision theory. In this paper, we examine these calls for reform and unearth their strengths and short comings.

In this paper we revisit, from a different perspective, a long-standing question: ``Is the systematic deficit observed in all branching ratios mediated by a $b\to s μμ$ transition due to New Physics, or to a hypothetical constant unknown universal hadronic contribution that mimics New Physics?'' The key observation that allows us to distinguish between these two possibilities is that non-perturbative contributions associated with $c\bar c$ loops affect inclusive $B\to X_s \ell\ell$ and exclusive $B\to K^{(*)}\ell\ell$ modes differently. In inclusive decays, factorizable contributions are exactly determined from data on $e^+e^-\to \mathrm{hadrons}$, while non-factorizable corrections are described by resolved-photon contributions at low $q^2$ and by local power corrections at high $q^2$. In exclusive decays, by contrast, hypothetical charming-penguin effects, beyond those already included in current uncertainty estimates, could appear, in a worst-case scenario, as a constant, universal contribution that it seems, in principle, indistinguishable from genuine New Physics. We identify two observables, constructed from ratios of exclusive to inclusive modes, that can discriminate between a New Physics contribution and a constant hadronic contribution. Moreover, these ratios can be measured directly by LHCb, as they do not require any normalisation to $J/ψK^{(*)}$ branching fractions from B factories. A preliminary evaluation of these observables with present data shows some preference for the New Physics interpretation. In a complementary test, a comparison between inclusive measurements and the corresponding sum of exclusive modes at high $q^2$ similarly disfavours an explanation based on a constant hadronic contribution. Finally, we provide projections for the new observables based on expected LHCb and Belle II measurements in the near future.

We study null homotopies of immersed spheres in $\mathbb{R}^3$ and the volume they sweep during contraction. For a smooth immersion with finitely many transverse self-intersections, we introduce a cable system that connects each bounded region of the complement to the exterior. From this construction we define the cable index and prove that it agrees with the Brouwer degree on each complementary region. Using this identification, we derive a degree-weighted lower bound for the swept volume of any Lipschitz null homotopy. We show that the bound is attained whenever the homotopy is sense-preserving, meaning the surface moves in a consistent direction, and the index evolves monotonically along the homotopy. In addition, in the case where the immersion arises as the boundary of an immersed ball, we construct an explicit homotopy that realizes this lower bound via a deformation of the ball. Finally, we present a linear-time algorithm that computes all cable indices from a finite cable system, providing a concrete and computable method for evaluating the lower bound.

We present a new set of lattice QCD ensembles with four flavors of smeared Möbius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{π^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

The singlet axial form factor of the nucleon provides essential input for a complete understanding of the nucleon axial structure. Together with the isovector and isoscalar octet channels, in the forward limit it forms the basis for a full flavor decomposition of the proton spin. In this work we present a lattice QCD determination of the singlet axial form factor $G^{u+d+s}_A(Q^2)$ and related strange contribution $G^{s}_A(Q^2)$ using a set of $N_f = 2 + 1$ CLS gauge ensembles with $O(a)$-improved Wilson fermions, with a full error budget for the extrapolation to the chiral, continuum and infinite-volume limits. Particular focus is placed on the treatment of the disconnected contributions, which constitute the crucial element for the extraction of the strange component. Together with determinations of the isovector and isoscalar octet axial form factors, this work provides a comprehensive lattice QCD determination of the nucleon axial structure across different flavor channels.

Apportionment assigns indivisible items among groups. By the Balinski-Young theorem, no method can satisfy both house monotonicity and the quota rule. This paper investigates quota violations caused by nonzero allocation constraints, and derives exact probability formulas for their frequency. Such violations occur in systems like the U.S. House of Representatives, where each state is guaranteed at least one seat. We analyze the three-state case, introduce the $τ$ statistic to parametrize population distributions, and prove an Asymptotic Quota Stabilization theorem: for fixed $τ$, quota behavior stabilizes as populations grow, yielding probability results for quota violations determined by the set of ultimately violatory $τ$ values. Applying this framework to the five classical divisor methods, we derive exact probability formulas. Additionally, we show that as the number of seats $M \to \infty$, these probabilities converge to method-specific constants. These results provide a precise, quantitative foundation for evaluating the fairness and frequency of quota violations in constrained apportionment systems.

We study two fundamental decremental dynamic graph problems. In both problems, we need to maintain a vertex-weighted forest of size $n$ under edge deletions, weight updates, and a certain information-retrieval query. Both problems can be solved in $O(\log n)$ time per update/query using standard dynamic forest data structures like top trees, even if additionally edge insertions are allowed. We investigate whether the deletion-only problem can be solved faster. First, we consider $\texttt{tree-sum}$ queries, where we ask for the sum of vertex weights in one of the connected components (i.e., trees) in the forest. We give a data structure with $O(n)$ preprocessing time and $O(\log^* n)$ time per operation, based on a micro-macro tree decomposition (Alstrup et al., 1997). If the forest is unweighted (i.e., all weights are 1 and cannot be changed), then the operation time can be improved to $O(1)$. Additionally, we give an asymptotically universally optimal algorithm. More specifically, our algorithm works in the group model, and processes $m$ operations on an initial forest $F$ in running time $O( \mathrm{OPT}(F, m) )$. Here $\mathrm{OPT}(F, m)$ is the number of weight additions and subtractions that a best possible algorithm performs to handle a worst-case instance for a fixed initial forest $F$ and a fixed number $m$ of operations. We achieve this with a combination of the aforementioned decomposition technique, precomputation of optimal data structures for very small instances, and some insights into the behavior of $\mathrm{OPT}$. Note that even the worst-case complexity of this algorithm remains unknown to us. Second, we consider $\texttt{subtree-sum}$ queries. Here, the forest is rooted, and a query $\texttt{subtree-sum}(v)$ returns the sum of weights in the subtree rooted at $v$. We show tight bounds for several variants of this problem. [...]

We develop a low-energy continuum model to describe the moiré physics of heterostructures, which is a generalization of the celebrated Bistritzer-MacDonald (BM) method [R. Bistritzer and A. H. MacDonald, Proc. Natl. Acad. Sci. U.S.A. 108, 12233 (2011)]. We take as an example the moiré physics of electrons in twisted bilayer kagomé (TBK) metals near $1/3$ filling where monolayer Dirac cones lie. We demonstrate the emergence of higher-order magic angles where significant local band flattening occurs as a high-order Van Hove singularity emerges and show how twisting alone can induce non-trivial topology. We, furthermore, show that while sublattice interference effects are present, their role is not as prominent as in monolayer kagome.

We continue the study of non-Abelian vortex string in 4D $\mathcal{N}=2$ supersymmetric QCD as critical superstring, and extend this analysis to $U(N)$ gauge theory with arbitrary even $N$ and $N_f=2N$ number of quarks. We introduce a special mass deformation and show that the SQCD hadron spectrum is still given by the string spectrum on the 2D $\mathcal{N}=2$ supersymmetric black hole. We perform a cross-check by computing the multiplicity of hadronic states of the high-energy part of the spectrum both from string and field theory pictures. We also clarify the spontaneous breaking of the global flavor symmetry by VEV of the massless baryon. We finally claim, that phase diagram of $\mathcal{N}=2$ SQCD with $N_f=2N$ consists of the Higgs phase at weak coupling and string/hadronic phase at strong coupling, separated by phase transition, and is seen as a conifold transition from string theory point of view.

We study stochastic zeroth-order optimization with decision-dependent distributions, where the sampling law depends on the current decision and only noisy function values are available. For the non-smooth non-convex setting, we establish an explicit convergence guarantee for finding a $(δ,ε)$-Goldstein stationary point with stochastic zeroth-order oracle (SZO) complexity of $\mathcal{O}(d^2δ^{-3}ε^{-3})$. In addition, we show that the above complexity can be achieved with single SZO feedback per iteration. We further extend the analysis to smooth and Hessian-Lipschitz objectives, obtaining complexities $\mathcal{O}(d^2ε^{-6})$ and $\mathcal{O}(d^2ε^{-9/2})$, respectively. In the Hessian-Lipschitz case, this improves the best-known dependence on $ε$ for decision-dependent zeroth-order methods by a factor of $ε^{-1/2}$.

The 1T polymorph of NbSe$_2$, long confined to the monolayer limit, has remained inaccessible in bulk. Here, we report the realization of bulk 1T-NbSe$_2$ via electrochemical Sn intercalation. Transmission electron microscopy directly reveals the formation of the 1T structure induced by Sn intercalation. The intercalated samples exhibit insulating transport behavior, in stark contrast to metallic 2H-NbSe$_2$. Density functional theory calculations, however, predict a metallic band structure, highlighting the crucial role of emergent electronic correlations in the observed insulating state. Raman spectroscopy further reveals vibrational modes associated with Sn intercalation and possible charge density wave order. Our results establish electrochemical intercalation as an effective route to stabilize otherwise inaccessible bulk polytypes, positioning bulk 1T-NbSe$_2$ as a new platform for investigating correlated electronic states.

Evaluative claims about LLM infrastructure -- ``workload X is fastest on hardware Y with software Z'' -- depend on a complex configuration space spanning hardware accelerators, interconnect bandwidth, software frameworks, parallelism plans, and communication libraries. Current infrastructure evaluation benchmarks publish a small set of end-to-end numbers that do not explain why one configuration outperforms another. We present CCL-Bench, a trace-based benchmark that addresses the limitations of existing benchmarks by recording reusable evidence for every ML workload. Each contributed data point in CCL-Bench packages an execution trace, a YAML workload card, and the launch scripts. We have developed a community-extensible toolkit to compute fine-grained compute, memory, and communication efficiency metrics from this evidence. Using CCL-Bench, we surface three claims that summary-statistic benchmarks cannot support: (i) higher compute-communication overlap can coincide with longer training step time and reveal inefficient parallelization choices, (ii) doubling TPU interconnect bandwidth yields a much higher end-to-end improvement in step time than doubling GPU interconnect bandwidth on small and medium workloads, and (iii) the best-tuned configuration on one training framework can run up to 3$\times$ slower than the best-tuned configuration on a peer framework on identical hardware.

Instabilities in thermodynamic systems are often undesirable, as they can lead to loss of control or even catastrophic behavior. Yet, the same mechanisms can also generate rich nonequilibrium behavior and may play a constructive role in living systems. We introduce a theoretical framework, inspired by Rayleigh's analysis of thermoacoustic instabilities, to study the emergence of mechanical activity. In particular, we derive Rayleigh-like criteria governing the onset of activity and the generation of rotational motion in a slow Newtonian probe coupled to driven chemical processes, described by Markov jump processes. These criteria are expressed in terms of the phase relation between entropic and frenetic contributions, providing a transparent condition for when chemical driving results in sustained rotational or active mechanical motion.

We present an explicit formula for the $n$-site chain graph contribution to the cosmological wavefunction for conformally coupled $ϕ^3$ theory in de Sitter space. Our result relies on the recent finding that the symbol of this function satisfies total compatibility with respect to the $A_{2n-2}$ cluster algebra, and that Rudenko's quadrangular polylogarithms provide, by construction, a complete basis for such functions. We prove our formula by directly relating a recursive set of differential equations satisfied by these wavefunction coefficients to a recursive coproduct formula for quadrangular polylogarithms.

Hydrogenated nanodiamonds may show a "transmission window" in infra-red spectra in the vicinity of diamond Raman frequency. This phenomenon is a manifestation of resonance coupling of incident photons with continuum states (Fano resonance). Hpwever, precise mechanism of appearence of the resonance and of related conductivity - surface hydrogenation or specific type of surface reconstruction - remains debatable. We present detailed analysis of infra-red spectra of nanodiamonds of different sizes (2.6-30 nm) possessing the "transmission window" and show that the C-H stretch vibrations of adsorbed functional groups cannot be responsible the the Fano resonance. At the same time, it is suggested that a bending mode of monohydride termination on nanodiamond (111) face may couple with diamond optical phonon, explaining the Fano resonance in some cases. The relative importance of the monohydride contribution and of the graphitic islets to the appearence of the "transmission window" and conductivity is likely dependent on dominating morphology and size distribution of nanodiamond grains.

Long propagation delays in underwater acoustic networks (UWANs) cause spatio-temporal uncertainty, constraining channel utilization in medium access control (MAC) protocols. Node mobility within autonomous underwater vehicle scenarios exacerbates these challenges by introducing dynamic propagation delays and varying spatial topologies. We present MobiU-MAC, a deep reinforcement learning (DRL)-based MAC protocol for mobile node access in UWANs that maximizes throughput via autonomous learning. MobiU-MAC incorporates CHILL-STER, a novel DRL algorithm optimized for UWANs that is both ranging-free and delay-robust. CHILL-STER employs a credit horizon-limited $λ$-return (CHILL-Return) mechanism to achieve stable learning under asynchronous delayed rewards, while the companion spatio-temporal experience replay (STER) mechanism addresses topological changes arising from node mobility. This work also demonstrates theoretically that DRL attains optimal policy learning equivalent to a standard Markov decision process under long propagation delays without requiring ranging. Performance evaluations indicate that MobiU-MAC outperforms existing DRL-based MAC protocols for UWANs by leveraging the maximum system delay boundary without ranging overhead, supporting the effectiveness of the proposed theory and algorithm in complex underwater dynamic environments.

The Kripke semantics of various logics arises via categorical dualities between a category of relational frames and their maps, and a category of algebras and logical homomorphisms. When the relational frames are considered as computational systems (e.g. the states of a machine), the corresponding algebra is one of logical predicates on these systems (e.g. predicates on these states, i.e. program logics). Our aim is to extend this phenomenon to relations, putting well-behaved relations between systems (e.g. bisimulations) in correspondence with relations between predicates. This is achieved by constructing particular relational extensions of Tarski duality (for infinitary classical propositional logic) and Thomason duality (for infinitary classical modal logic). We sketch how these dualities give rise to a proof system that relates formulae between different systems.

We present a statistics-aware compression strategy that processes photon timestamps directly from time-correlated single-photon counting (TCSPC) modules for time-domain fluorescence lifetime imaging (FLIM). Rather than storing or transmitting the full histogram per pixel, timestamps are projected onto sparse, non-uniform one-dimensional spline sketches, with knot positions optimally allocated based on Fisher information. This knot allocation concentrates sketch channels where the decay signal exhibits the greatest statistical discriminability, rather than using a uniform allocation. The proposed approach is extensively validated on synthetic mono- and bi-exponential decay data and on experimental fluorescent dye data, demonstrating comparable accuracy to full-histogram non-linear least-squares fitting (NLSF) and Poisson maximum-likelihood estimation (MLE) at compression ratios of up to 256x. We further validate the feasibility of integrating the timestamp-to-sketch projection directly into firmware via fixed-point (FXP) lookup-table (LUT) simulation, targeting high-spatial-resolution single-photon avalanche diode (SPAD) arrays subject to significant data-throughput constraints.