The four-body decay $Λ_b^0\to pK^-π^+π^-$ has led to the first observation of baryonic $CP$ violation. However, the underlying subprocesses $Λ_b^0\to N^* M$ and $Λ_b^0\to Λ^* M$, as well as the roles of excited nucleon ($N^*$) and hyperon ($Λ^*$) resonances, remain largely unexplored. Within the constituent quark model, we identify the relevant resonant states contributing to these underlying two-body transitions, including $N(1535)$, $N(1520)$, $Λ(1670)$, $Λ(1690)$, together with the remaining $1P$-wave baryon states. We obtain the resonant branching fraction ${\cal B}(Λ_b^0\to pK^-π^+π^-) =(30.0^{+2.8+4.0}_{-1.3-3.4}\pm1.8)\times10^{-6}$, while the resulting ${\cal A}_{CP}(Λ_b^0\to pK^-π^+π^-)=(3.18\pm0.11\pm0.13\pm0.11)\%$ provides a natural interpretation of the first observed baryonic $CP$ asymmetry. Our analysis establishes the first comprehensive framework for quantifying the impact of excited baryon resonances in multi-body beauty-baryon decays, with the associated mechanism generally applicable to baryonic $CP$ asymmetries.

Fine-mesh parabolic wave equation (PWE) simulations are high-fidelity but time-consuming, which limits real-time tunnel propagation analysis and motivates coarse-to-fine reconstruction. Existing machine learning (ML)-assisted tunnel models typically provide only one-dimensional (1-D) longitudinal refinement or two-dimensional (2-D) cross-sectional refinement, rather than joint 3-D enhancement. Motivated by this gap, this letter proposes a U-shaped gated spatio-sequential recurrent neural network (UG-SSRNN), a spatio-sequential reconstruction model for tunnel electromagnetic fields. UG-SSRNN jointly super-resolves transverse slices and models longitudinal evolution. It uses sliding-window context encoding and a K-layer convolutional recurrent backbone with a shared propagation-context state and diagonal feedback. A prediction-aware upsampling head leverages the previous prediction to improve slice-to-slice consistency. Experiments on four tunnel cross sections, unseen-material and unseen-frequency tests, and validation in the Massif Central tunnel show close agreement with fine-mesh PWE references. The proposed approach significantly reduces tunnel electromagnetic modeling time.

Swampland and compactification data tell us where EFT control can fail; stochastic cosmology asks which histories survive near that edge. We turn this question into a survival problem for fluctuating moduli over cosmological time scales. Hard loss surfaces, soft degradation profiles, finite horizons, and a stochastic generator define a survival probability, whose logarithm is the survival action. The Doob transform then converts this logarithmic survival cost into the drift of the ensemble conditioned to remain on the controlled side. Near a regular hard boundary with nonzero normal diffusion, the answer is universal: surviving histories develop an inward wall response fixed only by proper distance and normal diffusion. In this way, tower/species cutoffs, weak-coupling limits, string and Kaluza-Klein thresholds, and potential-based diagnostics acquire stochastic boundary layers without becoming microscopic forces. The inverse map tests when a conditioned drift is compatible with a scalar operational loss surface and reconstructs its boundary-normal Doob class. The construction therefore gives a stochastic survival interface between quantum-gravity control data and the histories that remain on the landscape side of control.

We investigate the mechanisms governing particle settling in turbidity currents using two-way coupled Eulerian-Lagrangian direct numerical simulations. The effective particle settling velocity is decomposed into a fluid velocity sampled at particle positions and a particle-fluid slip velocity. Their Eulerian mean profiles are obtained using a concentration-weighted average of the coarse-grained fields.The mean sampled fluid velocity is shown to be approximately equal to the ratio of the vertical turbulent flux of particles to their mean concentration. This velocity remains predominantly positive in both inertial-particle and passive-tracer cases, despite the zero Eulerian mean vertical fluid velocity. We therefore infer that this upward bias is inertia-independent and outweighs downward-directed biases associated with particle inertia. The passive-tracer cases further indicate that the upward bias arises from turbulent transport acting on an inhomogeneous concentration field, rather than from the so-called loitering effect (Nielsen, J. Sedim. Petrol., vol. 63, 1993, pp. 835-838).The mean slip velocity closely follows the terminal settling velocity predicted for a quiescent fluid with a correction for finite particle Reynolds number. This is consistent with a leading-order balance between buoyancy and drag in the slope-normal direction. Combining the two velocity components yields a simple model for the effective settling velocity across the entire flow depth, in good agreement with the simulation data.

This study develops a medical AI-assisted diagnosis system based on deep learning, which provides intelligent diagnostic solutions for epilepsy, a disease that seriously threatens the life and health of patients. Epilepsy has sudden and unpredictable seizures. Traditional diagnostic methods mainly rely on doctors' manual interpretation of EEG, which is time-consuming and dependent by experience. In response to the above challenges, this study designed a dual-system intelligent diagnosis framework, which includes two core components: the main discrimination system and the verification system. The main discrimination system uses a deep learning model that combines the innovative Mamba architecture with the Bi-LSTM structure to integrate and analyze heterogeneous data to achieve extremely high diagnostic accuracy; the verification system provides an explainable diagnostic basis through the SHAP method to enhance the credibility of the results. This system establishes a cross-modal database to realize intelligent analysis of multi-source heterogeneous data-fusion EEG signals and clinical text data for epilepsy. The system outputs results based on diagnostic consistency and confidence levels, and high-confidence predictions can also be used as automatic feedback sources to optimize the model. The experimental results show that the accuracy of the main discriminant model of the intelligent diagnosis system for epilepsy has increased from 92.6% to 98.7% and the F1 score has increased from 0.895 to 0.992, all of which have exceeded the existing optimal methods; the average processing time for verification system feedback integration is only 220 ms, which increases the overall diagnostic accuracy by 5.1%.

Quantum Hall isospin ferromagnetism in multilayer graphene offers a versatile playground for exploring flat band correlated physics, driven by the intricate coupling of spin, valley, orbital, and layer degrees of freedom. However, a nanoscale probe capable of simultaneously mapping local conductivity and chemical potential in these exotic phases has yet to be realized. Here, we introduce scanning conductivity and chemical potential microscopy (SCCM), a technique integrating scanning microwave impedance microscopy and Kelvin probe force microscopy. We demonstrate SCCM by probing the quantum Hall states and many-body Landau level energy spectrum in bilayer graphene. Applied to marginally twisted double bilayer graphene, SCCM then reveals a cascade of quantum Hall isospin ferromagnetic states with unexpected re-emergence behaviors. Significantly, experimental many-body Landau level energy spectrum further uncovers the intricate connections of these complex phenomena to inter-subband Landau level crossings and Landau level single-particle wavefunctions. These insights enable the construction of a comprehensive quantum Hall phase diagram. Our results demonstrate SCCM's capability in decoding complex quantum phenomena, establishing it as a versatile nanoscale probe for electron correlation and topology.

Topological states in antiferromagnets (AFMs) offer a promising platform for exploring novel physical phenomena and advancing the applications of AFM spintronics. The AFM topological insulator (TI) state stands out as one of the most representative and prominent cases. Unlike the previously proposed AFM-TI states in noninteracting systems, here we employ an extended Kane-Mele-Hubbard model to demonstrate that electron correlations can give rise to a $\mathcal{PT}$-symmetric AFM-TI state. This state breaks both spatial inversion symmetry $\mathcal{P}$ and time-reversal symmetry $\mathcal{T}$, and enables intrinsic topological nonlinear responses to dominate the leading-order dynamics of the system. The competition between electron correlations and spin-orbit coupling drives the system across a topological phase transition, where the closure of the bulk band gap induces singular behaviors in higher-order quantum geometric tensors. Such microscopic singular characteristics manifest macroscopically as pronounced enhancements in thermoelectric performance, charge conductivity, and thermal conductivity. These giant tunable transport signatures, which can be effectively modulated by mechanical strain and electrostatic gating, provide a feasible experimental route to probe and understand correlated topological materials.

This work presents a semi-analytical framework for analyzing spatially discrete traveling-wave modulated (SDTWM) loop networks, which exhibit cavity-like behavior and support discrete spatiotemporal modes. We introduce a computationally efficient method, based on the Interpath Relation, to analyze periodic networks using a single unit cell. This allows characterization of driven systems with single-tone, multi-tone, and multi-conductor loop configurations. The framework captures both multi-modal and multi-frequency harmonic interactions, and is extended to compute the spatial Green's functions of such loop networks using analytic array scanning. The analysis of example designs, such as an electrically small antenna and a non-magnetic circulator, is presented. These examples confirm that the proposed approach is computationally efficient and offers physical insight, making it well-suited for the optimization of multifunctional and nonreciprocal SDTWM electromagnetic systems.

This paper measures hour-of-day effects, filter precision, fragility, and realised yield in a 15-day paper-traded deployment of an autonomous memecoin trading system on Solana decentralised exchanges. The 190-trade sample (March 29 to April 12, 2026) shows a 40.5 percent win rate, mean per-trade return of +0.62 percent, cumulative +117.7 percent (net SOL +0.039), skewness -1.21, excess kurtosis 6.61. A Mann-Whitney U test of three poorest-performing UTC hours (2, 13, 23) against the others yields U = 1,274, p = 0.22; directional but not significant at n = 190. The three hours were selected in-sample, so the comparison is exploratory, not confirmatory. A parallel counterfactual rejection-tracking system collected 4,874 forward-sample observations across 184 distinct rejection events. Of those events, 17.9 percent reached a 50 percent drawdown from reference within 24 hours; 26.0 percent of forward samples recorded the rejected token below half-reference. The filter stack avoided these realised drawdowns: evidence that the rejection criteria are net-positive against forward-market outcomes. Fragility is the principal caveat. Removing the top three trades (1.6 percent of sample) flips cumulative return unprofitable. Profitability rests on a small number of large winners and is structurally fragile. The dataset and audit script are deposited under CC-BY-4.0 (Zenodo DOI 10.5281/zenodo.20043302).

The observed shift of the $Δ(1232)$ resonance peak in $π$-$p$ femtoscopic correlations challenges the conventional Breit-Wigner description of resonances in femtoscopy. We revisit the Koonin-Pratt framework by formulating femtoscopy in the momentum-space representation and employing the T-matrix approach to disentangle on-shell and off-shell contributions. By employing a Friedrichs-Lee model constrained by low-energy scattering data, we demonstrate that the finite spatial extent of the emission source induces sensitivity to off-shell dynamics, which leads to a peak shift accompanied by a dip on the high-momentum side of the peak. The resulting correlation strength, however, does not fully reproduce the measured amplitude, and a high-momentum side dip is not observed in experiments. The remaining discrepancies may be attributed to the structural complexity of the emission source beyond a simple spherical Gaussian approximation.

We introduce a notion of linkage for sheaves of modules on connected Noetherian schemes, extending classical linkage of modules. Linkage is defined for stable sheaves admitting finite free resolutions via the transpose and syzygy functors. We show that linkedness is a local property and that, on affine schemes, a coherent sheaf is linked if and only if its module of global sections is linked. We further show that linkage is preserved under restriction and, under suitable rank conditions, under gluing over connected schemes. We also obtain criteria for the existence of linked subsheaves when the structure sheaf is not a domain. In the projective setting, we compare invariants of linked sheaves, including graded cohomology modules, Castelnuovo-Mumford regularity, and Hilbert polynomials.

A well-known model in game theory, the Volunteer's Dilemma describes a group of $n$ players who decide whether to volunteer for a collective benefit at a personal cost, or to abstain and risk forfeiting the benefit altogether. A quantum version of this dilemma, developed within the Eisert-Wilkens-Lewenstein framework, allows each player to manipulate one qubit of a shared entangled state, leading to symmetric Nash equilibria with higher expected payoffs than in the classical game. Existing analyses, however, assume maximal entanglement. Within the same framework, we introduce a generalized Quantum Volunteer's Dilemma with a tunable entanglement parameter $γ$ and study the extent to which equilibrium behavior depends on the level of entanglement. We derive explicit conditions relating $γ$, the number of players, and the players' strategies under which symmetric Nash equilibria exist, focusing on two canonical strategy profiles: one for $2\leq n\leq 9$, and one for even $n$. We find that maximal entanglement is not required to sustain symmetric equilibria. Instead, equilibrium behavior persists above a threshold value, which we compute analytically in both cases. We also demonstrate that the threshold value directly depends on system size. This characterization is directly relevant for implementations on resource-constrained quantum devices, where entanglement is inherently limited.

Epileptic seizure prediction from scalp EEG is critical for closed-loop neurostimulation therapy. Existing deep-learning methods share two architectural limitations: they model EEG channels independently, neglecting inter-channel spatial synchrony, and process raw time-domain samples without frequency decomposition. A methodological limitation also affects the field: most studies use data splits that permit patient-level information leakage, yielding optimistic estimates that do not generalise to unseen patients. We present CG-MambaNet, a spatiotemporal seizure prediction framework addressing all three limitations. A depthwise separable CNN front-end decomposes each EEG patch into multi-scale spectro-temporal features, capturing delta-to-gamma band dynamics before sequence modelling. A two-layer graph convolutional network with a learnable adjacency matrix captures inter-channel functional synchrony without montage-specific coordinates, applicable to bipolar (CHB-MIT) and referential (SIENA) montages. A bidirectional Mamba encoder followed by a bidirectional LSTM models long- and short-range temporal dynamics, and a two-layer MLP produces the final seizure probability. This serial hierarchy ensures frequency decomposition precedes spatial mixing, which precedes temporal integration. Under strict leave-one-patient-out cross-validation with five independent random seeds, CG-MambaNet achieves AUC-ROC of 0.8152+/-0.0176 on CHB-MIT (n=22) and 0.7104+/-0.0261 on SIENA (n=6), surpassing all published cross-patient methods without domain adaptation. An event-level evaluation framework merging consecutive alarmed windows via a persistence filter reduces false predictions to 0.32 alarms/hour on CHB-MIT, demonstrating clinically meaningful alarm burden.

Sparse adaptive filters and impulsive noise robust algorithms have largely been developed along separate tracks, leaving a gap when both properties are needed simultaneously. This letter proposes the double proportionate sparse adaptive filter (DP-SAF), which closes this gap within a single $\mathcal{O}(M)$ update. Two independent diagonal gain matrices are introduced; one scales the adaptation step proportionately to coefficient magnitudes, and the other applies a magnitude-dependent zero-attraction that is strongest for inactive taps. A sign-error update provides robustness against impulsive corruptions. Both gain matrices are derived from a minimum-norm optimization framework. Simulations under a Bernoulli impulsive noise model show that DP-SAF consistently achieves a better steady-state MSD than the competing algorithms while matching or exceeding their convergence speeds.

The topology of Kähler manifolds is largely determined by the geometry due to its rigidity. In particular, the cohomology and Hodge theory of compact Kähler manifolds is quite restricted. We prove that within a certain threshold, the odd Betti numbers of any compact almost-hermitian manifold satisfying a degenerate Kähler condition are even, and the even Betti numbers are strictly positive. We call this new type of degenerated Kähler manifold acK. Our approach to proving these results makes use of a compactness theorem for acK manifolds, and a new version of Hodge theory for compact manifolds endowed with a Sobolev regular Kähler strucutre. In addition, we lay out a program to pursue the study of acK geometry that accommodates not only the classical viewpoint, but also constructive and finitary proofs, as well as formalization with proof assistants.

We investigate the collision dynamics of complex kink solutions in the complex sine-Gordon (CSG) model, focusing on the influence of the relative phase and initial velocity. The model's internal \( U(1) \) symmetry gives rise to a variety of solitary wave solutions, including complex kinks, radiative profiles, and Q-ball configurations. Through numerical simulations, we reveal rich and nontrivial phase-dependent behaviors such as the emergence of red and blue critical speeds, radiative emissions, bion and breather formations, and phase-sensitive oscillation modes. Moreover, we identify extreme values in energy and field quantities at the collision point, uncovering discontinuities that signify transition thresholds in the dynamical system. These findings underscore the complex interplay between internal degrees of freedom and dynamical variables in non-integrable soliton systems, offering new insights into field theories with internal symmetries.

We consider a family of pure Neumann $p$-Laplacian problems, including eigenvalue problems, Lane-Emden type equations, and extremal cases such as sign nonlinearities and the $1$-Laplacian. Using variational methods, we develop a unified framework that establishes existence of solutions and characterizes their asymptotic behavior as the parameters vary. This approach reveals a natural asymptotic connection between pure Neumann $p$-Laplacian equations and a relative isoperimetric problem known as the Neumann-Cheeger problem. We describe the shape of minimizers in domains with different geometries and obtain results on regularity, uniqueness, multiplicity, symmetry, and symmetry breaking phenomena.

Gravitational-waves from astrophysical sources are characterized by their extreme faintness, which remains a primary obstacle for both current and next generation detectors. While rotating black holes dressed in superradiant clouds of ultralight bosons are recognized as promising probes of physics beyond the Standard Model, their capacity to actively emit and modulate gravitational radiation remains largely unexamined. Here we demonstrate that these gravitational atoms can function as natural amplifiers of gravitational-waves via a stimulated emission mechanism analogous to astrophysical masers. By formalizing the interaction between the bosonic cloud and an ambient stochastic gravitational-wave background, we establish the rigorous selection rules and threshold conditions that govern this amplification. Our analysis reveals that the emission rate depends critically on the boson mass, potentially yielding an enhancement of several orders of magnitude over spontaneous processes. For representative mass ranges, these amplified signals bridge the sensitivity gap between ground-based interferometers and pulsar timing arrays. These findings suggest that superradiant clouds can effectively boost previously undetectable signals, offering a novel observational frontier for exploring ultralight fields and the Kerr spacetime environment.

In this paper, we establish the equivalence between minimal time and minimal norm control problems for controllable stochastic differential equations (SDEs). The core of this equivalence lies in proving the continuity of the minimal norm function. Unlike the deterministic setting, where the time translation technique is effective, this approach is not applicable due to the adapted nature of the admissible controls in SDEs. To address this challenge, we construct the minimal norm control explicitly, thereby achieving the desired continuity. This constructive approach not only proves theoretical equivalence but also facilitates the design of efficient numerical schemes for minimal norm and time controls.

The reachability diameter ($\mathrm{ReachDiam}$) of a directed graph is the maximum distance over all pairs $u,v$ where $v$ is reachable from $u$. This notion is present in the definition of shortcut sets, and the name was recently coined in that context by Haeupler, Jiang, and Saranurak [SOSA 2026]. While this is a very natural notion of diameter in directed graphs, and especially DAGs, it is so far not computationally explored. Other definitions of diameter in directed graphs are either trivial (infinite) in graphs that are not strongly connected (e.g., the classical definition) or are non-trivial only in highly restrictive graph classes (e.g., Min-Diameter). We initiate the problem of computing the (approximate) reachability diameter from a fine-grained complexity point of view. Under certain fine-grained assumptions, we prove that there is no algorithm in time $\mathcal{O}(n^{ω- \varepsilon}$) that gives any approximation of $\mathrm{ReachDiam}$ in weighted graphs. Similarly, there is no algorithm with better than $2$-approximation for unweighted graphs in this time. To supplement this, we provide algorithmic upper bounds that lead to additive approximation of $\mathrm{ReachDiam}$ for unweighted graphs. Hence, we establish a strong separation between the weighted and unweighted cases, which makes this type of diameter different in nature than other known notions. Considering the hardness in general weighted graphs, we also study special graph classes and get small constant approximations for DAGs with bounded width or graphs with bounded treewidth. Interestingly, our techniques also lead to exact hopsets with hopbound $2$ for bounded treewidth graphs. This and some of our upper bounds for general graphs show technical connections between approximating $\mathrm{ReachDiam}$ and computing shortcut sets and hopsets.

For $0\leq k\leq n$, let $u(n,k)$ be the largest divisor of $\binom nk$ whose prime factors are at most $k$. Erdős Problem #684 concerns the special threshold $u(n,k)>n^2$ and asks how early this small-prime part can be forced to become large. We prove the density-one analogue for every fixed power threshold. If $f_c(n)$ is the least $k$ for which $u(n,k)>n^c$, then, for each fixed $c>0$, \[ f_c(n)=\left(\frac{c}{1-γ}+o(1)\right)\log n \] for almost all positive integers $n$. In particular, \[ f_2(n)=\left(\frac{2}{1-γ}+o(1)\right)\log n =(4.730544237\ldots+o(1))\log n \] for the Erdős #684 threshold. This is a normal-order theorem, not a pointwise resolution of the corresponding worst-case problem. The constant $1-γ$ is arithmetic. Kummer's theorem rewrites $\log u(n,k)$ as a sum of carry indicators, and complete-residue averaging gives \[ m(k)=k\sum_{p\leq k}\frac{\log p}{p-1}-\log k!=(1-γ)k+o(k). \] The cancellation in this formula moves the typical crossing from the naive scale $c\log n$ to $c(1-γ)^{-1}\log n$. We prove the required concentration uniformly for every $k\leq A\log X$ on one dyadic interval, after discarding a zero-density exceptional set caused by large powers of small primes dividing one of the nearby integers $n,n-1,\ldots$. We also prove Gaussian fluctuations in the logarithmic range. If $k=k(X)\to\infty$, $k\leq A\log X$, and $n$ is uniform in $[X,2X)\cap\mathbb Z$, then \[ \frac{\log u(n,k)-m(k)}{\sqrt{V(k)}}\Rightarrow \mathcal N(0,1), \qquad V(k)\sim (2-\log(2π))k\log k. \] Higher prime powers are needed for the mean, but after centering their aggregate is $L^2$-negligible on the Gaussian scale; the variance comes only from the prime levels.

In this paper the Clifford groups of general multipartite quantum systems with configuration space $\mathbb{Z}_{n_1}\oplus\cdots\oplus\mathbb{Z}_{n_k}$, $k\geq 1$ are studied. It is known that the Clifford group is a natural semidirect product provided the dimension $N=n_1\cdots n_k$ of the corresponding Hilbert space is an odd number. For even $N$ special results on the Clifford groups are scattered in the mathematical literature, but they do not concern the semidirect product structure. Using the relation of generators of the associated symplectic group $\mathrm{Sp}_{[n_1,\dots,n_k]}$ we prove that for even $N=n_1\cdots n_k$ both Clifford group and the projective Clifford group are natural semidirect products if and only if $N$ is not divisible by four.

The so called Harada gravity with non conserved energy-momentum tensor is here taken into account. It includes Rastall gravity as a special case. The field equations are written as Einstein equations where the source is supplemented by a divergence-free conformal Killing tensor and a tensor proportional to the metric, linear in the scalar curvature and the trace of the energy-momentum tensor. These terms can be natural candidates for dark sector and give rise to a coupling of the dark sector with the matter content. The field equations are the conformal Killing extension of Rastall gravity, and include Unimodular gravity. In a Friedmann-Robertson-Walker background, the Cosmic Microwave Background restricts parameters so that the dark sector only couples with the trace of the energy-momentum tensor. The explicit form of the tensor for the dark sector is found, and the Friedmann and continuity equations are presented, with a standard cosmological analysis. The sum of energy-momentum tensors of dust matter and of dark fluid is conserved, and the dust energy density evolves with the scale function with exponent -3/(1+tau), modified by the coupling tau with the dark fluid.

Proof of Reserves (PoR) enables centralized crypto exchanges to demonstrate that on-chain reserves are sufficient to cover customer liabilities. However, existing approaches, including Merkle-tree-based proofs and zero-knowledge PoR systems, remain difficult for everyday users to verify in practice, resulting in limited participation and weakened transparency. We introduce LPOR, a layered, usability-focused PoR framework that separates lightweight user-side checks from auditor-level cryptographic verification, enabling non-technical users to verify inclusion and publicly recompute total liabilities with minimal friction. By lowering verification barriers, LPOR increases user participation and substantially improves the probability of detecting omitted liabilities. We evaluate its scalability and omission detectability at a multi-million-user scale.

Financial returns are often called ``random,'' but the word conflates ontic chance, epistemic ignorance, strategic feedback, and model instability. This essay argues that financial markets are not random in the ontic sense in which a quantum measurement is random. They are causal economic systems whose future is hard to predict because relevant causes are hidden, costly to observe, strategically used, capacity constrained, and sometimes governed by a changing law. The formal language of finance already encodes this distinction. Prices live on filtered probability spaces because agents have partial information; derivatives are priced under a risk-neutral measure $\Q\ne\Prob$ because pricing is an instrumental change of measure rather than a statement about the real data-generating law; and no-arbitrage gives martingality under an equivalent pricing measure, not full predictability failure under every real-world information set. The paper separates no-arbitrage, informational efficiency, and net exploitability; uses the Doob decomposition to isolate risk-compensated predictable drift from martingale innovation; adds a capacity-and-survival layer explaining why positive signals need not be scalable; relates the $\Prob$--$\Q$ wedge to stochastic-discount-factor geometry and relative entropy; formalises filtration sufficiency, model-selection landscape risk, and intervention-stable causality; and connects reflexivity, microstructure, and Knightian ambiguity to a unified entropy ledger. The disciplined thesis is therefore not that markets are unknowable, nor that they are literally random. Markets are hard to predict, and hardest exactly where prediction is costly, competitive, self-defeating, capacity limited, or invalidated by regime change.

We develop a tractable, rigorous approach to risk-aware control for a class of nonlinear systems. While many classical control methods reduce uncertainty to a simple average or a worst-case outcome, risk-aware control aims to equip systems with a refined awareness of uncertainty. Efficient methods for risk-aware control of linear systems are available, but there is a paucity of tools for tractable, risk-aware control of nonlinear systems. To bridge this gap, we develop an analytical, suboptimal controller with respect to a risk-aware performance criterion for systems with nonlinearities characterized by cone-like bounds. Numerical examples demonstrate benefits of the characterization of nonlinearities and risk that we consider.

Urban spatial structure is commonly evaluated through the spatial distribution of homes and jobs or through aggregate commuting outcomes. Yet these approaches do not reveal how the opportunities created by urban form are selectively transformed into actual residence-workplace connections. This study introduces opportunity-normalized residence-workplace matching by comparing observed commuting distance distributions with opportunity-based distributions constructed from all within-city residence-workplace pairs weighted by residential and employment mass. Using Output Area-level data for nine British cities, we show that realized pairings are systematically more concentrated at shorter distances than the urban opportunity structure alone would predict. After normalization, matching intensity declines with distance in a recurrent but heterogeneous pattern that is approximately linear in log-log space in many cities and can be summarized by a city-specific distance-decay coefficient. London further reveals that this regularity is scale-sensitive: a comparatively flattened citywide pattern separates into consistently negative but heterogeneous relationships across employment-centered subsystems. Supplementary evidence from New York and Chicago shows similar attenuation patterns. These findings identify realized residence-workplace matching as a distinct layer of urban structure and suggest that, in complex metropolitan systems, meaningful spatial regularities may reside in coherent matching fields rather than in aggregate city boundaries.

We prove that for any Lie ring $\mathfrak{R}$ and any commutator-preserving bijection $α: \mathfrak{gl}_n(K) \rightarrow \mathfrak{R}$, the map $α$ is additive on $\mathfrak{sl}_n(K)$, where $n \ge 2$ and $K$ is an arbitrary field. Using this result we find criteria for Lie rings $\mathfrak{gl}_n(K)$ and $\mathfrak{sl}_n(K)$ to be unique addition. We also show that any commutator-preserving injection of Lie rings $β: \mathfrak{sl}_2(K) \rightarrow \mathfrak{S}$ is additive. This is the first result on additivity of commutator-preserving injections.

We study Birkhoff genericity for a simple uniformly expanding diagonal flow on $\mathrm{SL}_{n+1}(\mathbb R)/\mathrm{SL}_{n+1}(\mathbb Z)$, with initial points restricted to affine subspaces of the expanding horospherical orbit through the identity coset. We prove that almost every point on such an affine subspace is Birkhoff generic, except possibly in two situations: either the defining matrix of the affine subspace has Diophantine exponent at least $n$, or the affine subspace is arbitrarily well approximable by affine subspaces of dimension $(r-1)$ defined over a real number field of degree $m\ge 2$, with $n+1=mr$. As applications, we obtain Dirichlet non-improvability and logarithmic density results for almost every point on these affine subspaces.

Despite their growing popularity, in-ear Earable / Hearable devices (i.e., ear-mounted wearables) face interaction challenges due to limited input space and compact form factors. To enhance interaction capabilities, researchers are exploring off-device hand-based input spaces above the neck using midair and onskin gestures. However, existing literature primarily focuses on axial swipes (i.e., horizontal and vertical), leaving nonaxial swipes (i.e., unidirectional swipes with varied orientations) and angular swipes (e.g., L, U, or V) largely underexplored despite their potential interaction advantages. To address this gap, we conducted a within-subject gesture motion analysis study with 24 participants, analyzing 5,568 swipes of varying shape, orientation, and complexity. Our results revealed preferred starting and ending regions for different unidirectional and angular swipe shapes, as well as intuitive swipe shapes within the off-device, above-neck manual interaction space. We further examine off-device swipe characteristics, discuss the feasibility of recognizing these earable gestures with current sensing technologies, and highlight their potential application in various scenarios. These findings broaden the understanding of off-device earable gestures and provide design insights for integrating suitable nonaxial and angular swipes alongside traditional axial gestures to enhance interaction with in-ear earable devices.