We present a non-perturbative multiplicative renormalization program for the massive gluon fields. This has been done within the previously formulated the mass gap approach to QCD. It is based on a new insights into its ground state true dynamical and gauge structures. Our approach makes it possible for gluons to acquire mass dynamically. The corresponding full gluon propagator has been investigated in full details. Its asymptotic properties have been analysed, including the perturbation theory limit. The peculiarities of the mass-shell structure of the full massive gluon propagator has been discussed. The inconsistency of the canonical gauge in QCD is fixed. Our approach does not allow the massive gluons to be the mass-shell objects. This prevents them to appear in the physical spectrum (confinement of massive gluon states). The massive gluons may exist in the vacuum or inside hadrons only. Expressions in Euclidean metric for the lattice simulations are also present. We have also shown that the massive solution has a correct limit to the free massless gluon propagator, when the exactly defined gluon pole mass is to be formally put zero.

The Kučera--Gács theorem is a fundamental result in algorithmic randomness. It states that every infinite sequence $X$ is Turing reducible to a Martin-Löf random $R$. This paper studies resource-bounded analogues of the Kučera-Gács Theorem, at the resource bounds of polynomial-time and finite-state computation. We prove a {quasi-polynomial-time}{ Kučera-Gács Theorem}, showing that every infinite sequence $X$ is quasi-polynomial-time reducible to a \emph{polynomial-time random} sequence $R$. We also show that for any $X$, the oracle use of $R$ is $n+o(n)$ bits for obtaining the first $n$ bits of $X$. We then study the relationship between compressibility and Turing reductions, in the polynomial-time setting. We establish that $ρ^-_{\mathsf{poly}}(X) = K_{poly}(X)$, demonstrating that the lower polynomial-time Turing decompression ratio is precisely characterized by the polynomial-time Kolmogorov complexity rate. We note that this characterization fails for the polynomial-time dimension if one-way functions exist, resolving an open problem from Doty's work. We use these results to strengthen the {quasi-polynomial-time}{ Kučera-Gács Theorem}. We show that every infinite sequence $X$ is quasi-polynomial-time reducible to a {polynomial-time random} sequence $R$, where the lower oracle use rate of the reduction is less than ${K}_{poly}(X)$. We also show that any sequence extracted from the (even larger) set of \emph{normal sequences} by a finite-state reduction must have a convergent asymptotic frequency for its symbols. Since sequences lacking this invariant property exist, they cannot be finite-state reduced from any normal sequence. Hence we show that the Kučera-Gács theorem \emph{fails} for finite-state reductions.

Large language model (LLM) agents are increasingly used to migrate legacy code to modern stacks. We ask a deceptively simple question: when an LLM modernizes legacy code, can the same model be relied upon to recognize when its own output silently changes observable behavior? We run 1,980 real modernization calls across 11 production LLMs from 7 distinct families on a balanced 60-snippet legacy-Python-2 corpus, evaluate every output with a type-strict behavioral oracle, and then ask each model to judge whether its own output preserves behavior. We report four findings. (1) Semantic-preservation drift is prevalent and sharply separable from a cleanly-controlled baseline: semantic-trap snippets drift in 39.7% of attempts versus 7.0% on benign-control code that requires no real modernization (+32.7 percentage points; n=660 each). (2) Drift concentrates on specific snippets that fail across models: pairwise model agreement on which snippets are hard is high (mean Pearson r=0.52), and a small core of numeric-semantics snippets fails for nearly every model and every prompt phrasing. (3) Self-review by the producing model is not a reliable safety net: across all semantic drift cases, 31.7% are silently endorsed by the same model that produced them (83/262), and the per-model self-miss rate is strongly bimodal -- ranging from 0% on five models to 100% on one widely deployed model -- with several models explicitly articulating the very Py2/Py3 semantic distinction that broke their output, then declaring behavior preserved. (4) Drift rate is non-monotone in model capability and price: per-model rates range 5.6%-46.7% and do not track model capability cleanly, indicating the failure is task-structural rather than driven by model scale. All code, prompts, the 60-snippet corpus, the behavioral oracle, the output extractor, and the raw model outputs are released.

Among 755,004 Philadelphia landlord--tenant records filed during 1969-2022, 396,163 residential cases involve tenants who appear exactly once in the observed docket. In unadjusted comparisons, single-appearance cases handled by high-volume plaintiff-side counsel are more likely to advance to the writ-of-possession and served-writ stages, but no more likely to end in default. Comparisons within the same plaintiff, and within the same plaintiff at the same property, show no broad premium on adverse case outcomes such as default, judgment, or fees. The clearer pattern is organizational: after a plaintiff adopts or switches into high-volume counsel, monthly filings rise by about 2-5% and the number of distinct buildings reached rises by a similar margin; near the prior-year top-10 attorney threshold, cases display local differences in default and enforcement; and continuances under specialist counsel are more closely linked to default. Non-flat pre-treatment trends and imprecise reverse-direction estimates from attorney exits restrict the strength of any causal claim. High-volume plaintiff-side counsel therefore functions as a mechanism of filing scale and procedural sequence, not as a uniform escalator of case outcomes or as a cause of any individual tenant becoming single-appearance.

Dennis Lindley once said that there is only one thing worse than a frequentist, and that is an empirical Bayesian. The quip has the air of caricature, but its technical content is serious: empirical Bayes uses the same data twice, conflates levels of a hierarchy, and produces posterior-shaped summaries whose uncertainty quantification differs from what a fully hierarchical model delivers. David Blei's 2026 IMS Medallion Lecture, "A Fresh Look at Empirical Bayes," revives the program under three new banners: empirical Bayes via probabilistic symmetries (rebranded "Bayesian empirical Bayes"), empirical Bayes with implicit likelihoods through simulation-based inference, and empirical Bayes for combining experimental and observational data through calibration studies. This is a continuation of Blei and Kucukelbir's earlier "population empirical Bayes" (PopEB, 2015). We argue, in the spirit of Lindley, I. J. Good, William DuMouchel, Thomas Louis, and our own recent work with Datta, that Blei's machinery targets inferential objects distinct from the posterior conditional on the realized data, and that the cost of maintaining the full hierarchical discipline has fallen low enough that the computational trade-off no longer favors the shortcut. The case study is the Tweedie formula. Efron's f-modeling empirical Bayes plugs an estimated score function into a posterior-mean identity, but a smoothed score need not arise from any prior. The horseshoe Tweedie formula does. We conclude by recommending that the impressive computational machinery of modern empirical Bayes (variational inference, neural amortization, simulation-based inference) be redeployed in service of properly hierarchical Bayes.

Massive scalar perturbations of asymptotically de Sitter black holes in generalized Proca theory display a sharp interplay between primary hair, horizon structure, and field mass. Using high-order WKB calculations supplemented by time-domain evolution, we analyze representative black-hole backgrounds and compare the full black-hole spectrum with the exact pure de Sitter benchmark. We show that increasing the scalar mass drives the frequencies into a simple large-mass regime in which the real part grows linearly while the damping rate approaches a nonzero geometry-dependent constant, so true quasi-resonances do not occur within the regime studied here. We also identify how the spectrum shifts with black-hole size and Proca hair, derive a compact analytic large-$μ$ formula, and comment on the implications of the de Sitter-like sector for strong cosmic censorship in the charged three-horizon regime.

Code contracts provide a robust way to specify functional requirements of safety-critical software in embedded systems. For example, the ANSI/ISO C Specification Language (ACSL) can be used to specify the functional behavior of C code that is then formally verified by the Frama-C framework's Wp plugin. However, non-functional requirements, such as restrictions on control flow and data flow, are also important for embedded systems safety. Untrusted code developed by subcontractors, junior developers, or generated by large language models, can be verified by Wp but may nevertheless call unsafe functions or use uninitialized program variables. To address this problem, we constructed a set of general rules concerning non-functional requirements of C code in safety-critical embedded systems. Our rules are orthogonal to popular C rulesets such as MISRA-C and center on modules and their interaction through interfaces. To enable checking our rules, we propose an interface specification contract language for C modules. We implemented a checker for our rules as a Frama-C plugin, which takes as input a C module and its contract and checks control flow and data flow properties, ensuring, e.g., that only permitted functions are called by the module. We integrated our checker in a toolchain to enable specification and verification of module contracts and ACSL contracts for untrusted code. We report on two case studies on safety-critical C code using software in Scania trucks, where we defined module contracts and ACSL function contracts based on informal system requirements and verified them using our toolchain.

Gravitational-wave detectors operate in inherently non-stationary environments, requiring robust detector characterization (DetChar) to distinguish instrumental transients from astrophysical signals. Traditional DetChar frameworks typically rely on morphological classifiers or energy-based projections, such as band-limited root-mean-square (BLRMS) metrics, which can conflate global amplitude scaling with physical reconfigurations of the spectrum. In this work, we introduce Fisher information velocity, a novel geometric channel that models the detector's power spectral density (PSD) as a point on a Riemannian manifold. By tracking the kinematic drift of the noise floor and utilizing exterior algebra to calculate tangent divergence ($\sin θ$), we mathematically decouple simple energy surges from spectral warps, or differential redistributions of power across frequency bands. Applying this framework via the sgn-drift streaming pipeline to ~40 hours of high-cadence Advanced LIGO O4a data, we evaluate N=282,080 independent manifold velocity samples. High-resolution phase space mapping reveals a bimodal taxonomy of severe instrumental non-stationarity, classifying events into structural pivots (87.2%) and isotropic surges (12.8%). Among co-detected events, the geometric channel achieves higher significance than standard BLRMS monitors in 74% of cases with a median sensitivity ratio of $Γ= 1.65$. The two channels detect largely non-overlapping populations, increasing the total anomaly catalog by 87% over BLRMS alone. Systematic validation on 10 confirmed GWTC-4.0 events and ~5,000 simulated injections demonstrates robust insensitivity to astrophysical signals, establishing this geometric channel as a sensitive, complementary, and veto-safe diagnostic for current and next-generation detector networks.

We introduce Pairwise Distance-Diffusion Analysis (PDDA), a geometric framework for estimating the Hurst exponent from distance plots of long-memory stochastic processes. A single construction yields two complementary routes: R/S-PDDA, a geometric reformulation of the classical rescaled-range definition, and MSD-PDDA, based on mean-squared-displacement scaling, classically used in anomalous diffusion. We extend PDDA to multivariate isotropic and anisotropic processes and derive an explicit link between temporal persistence, range dimension, and recurrence statistics, providing a unified distance-based foundation for Hurst analysis.

Let $I_k = [(2k-1)^2, (2k+1)^2)$ for $k \geq 1$. Starting from the odd-composite matrix $(b_{ij})$ with $b_{ij} = (2i-1)(2j-1)$, introduced by the author in [1], we define for each odd integer $n$ the \emph{matrix multiplicity} $r(n)$, the number of times $n$ appears in $B$. We prove the exact identity \[ P_k = N_k - S_k + E_k \] where $P_k = \#\{\text{primes in } I_k\}$, $N_k = 4k$ counts the odd integers in $I_k$, $S_k = \sum_{n \in I_k \text{ odd}} r(n)$ is the total matrix multiplicity, and $E_k = \sum_{n \in I_k \text{ odd}} (r(n)-1)$ measures the excess multiplicity of non-semiprime odd composites. All three quantities $N_k$, $S_k$, $E_k$ are computable from the divisor structure of odd integers in $I_k$ without primality testing. The formula yields the equivalent combinatorial condition: \[ P_k \geq 1 \iff E_k \leq S_k - N_k. \] We verify $P_k \geq 1$ for all $k \leq 10^8$ by direct computation and establish $P_k \geq 1$ for all $k \leq 1.37 \times 10^{17}$ using the Baker-Harman-Pintz theorem [2]. Whether $P_k \geq 1$ for all $k$ (a weaker statement than Legendre's conjecture) remains an open problem, now equivalent to the purely combinatorial inequality $E_k \leq S_k - N_k$ for all $k$.

The Versatile Video Coding (VVC) standard, introduced in 2020, offers 40-50% bitrate savings for equivalent visual quality of reconstructed videos over its predecessor, High Efficiency Video Coding (HEVC), at the cost of significantly increased encoding complexity. This growth in encoding complexity is mainly due to the addition of the Quad Tree Multi Type Tree (QTMTT) partitioning structure, which increases the split combinatorial complexity. This paper presents a critical evaluation of state-of-the-art (SOTA) partitioning acceleration techniques designed to reduce the complexity of the partitioning search in VVC. Particular attention is given to how these methods have evolved alongside successive versions of the VVC Test Model (VTM), which serves as the reference software for benchmarking coding tools. These techniques are analyzed in the context of their adaptation to internal changes in VTM, such as updated heuristics for fast partitioning decisions. The study also highlights the challenges involved in improving the trade-off between encoding complexity and compression efficiency. This challenge becomes more pronounced when evaluating methods across diverse VTM configurations and multiple software versions.

We develop a general finite-alphabet framework for Euler-type sums based on the notion of a monoidal alphabet. An alphabet of summand letters is called monoidal when it is closed under pointwise multiplication, thereby inducing the usual stuffle, or quasi-shuffle, algebra on the associated nested sums. This viewpoint places classical multiple harmonic numbers, colored harmonic sums, and several generalized Euler sums under a common structural mechanism. We focus on three fundamental families of monoidal alphabets: the ordinary power alphabet generated by $n$, the affine alphabet generated by linear factors $an+b$, and the polynomial-base alphabet generated by polynomial factors $P(n)$. The resulting classes of multiple harmonic numbers, multiple affine harmonic numbers, and multiple polynomial-base harmonic numbers provide systematic containers for a wide range of finite and infinite Euler-type sums. We prove closure and lifting results showing that nested sums whose summands are built from these alphabets, possibly multiplied by harmonic-number factors, reduce to the corresponding finite harmonic-number objects. As consequences, the framework recovers many known Euler-sum identities and produces many new identities in a uniform way. While reduction to simpler functions remains a separate and often difficult problem, the monoidal-alphabet perspective provides a unified algebraic language for organizing, transforming, and extending harmonic-sum identities.

In this paper, we investigate the combinatorial structure and asymptotic distribution of the solution set of the equation $σ(n+1) = kσ(n)$ for a given integer $k>1$. From a combinatorial perspective, the solutions to this equation are closely related to the concept of $k$-layered numbers, which are a generalization of Zumkeller numbers. In the analytic section, which constitutes the core of this research, we employ the framework of probabilistic number theory and an extension of the classical Kubilius model to study the oscillatory and local behavior of the sum-of-divisors function. Utilizing the truncation technique for arithmetic functions and applying the Chinese Remainder Theorem, the problem is reduced to a synthetic measure space equipped with independent random variables. Subsequently, by applying the optimized version of the Kolmogorov-Rogozin anti-concentration inequality (Petrov's theorem) to the difference of additive variables and finely tuning the error parameters, we prove that the natural density of this set is zero. The main quantitative outcome of this approach is the derivation of the explicit upper bound $A_k(x) \ll_k \frac{x}{\sqrt{\log \log \log x}}$ for the counting function of the solutions. Finally, alongside the zero asymptotic density, relying on the framework of polynomials and Schinzel's H Hypothesis, we establish the conditional infinitude of the solution set for the case $k=2$ and formulate the existential results.

Osborne and Dredze (2014) reported that Twitter was the timeliest social-media source of breaking news, trailing only newswire. Twelve years on, the platform landscape has shifted - Google+ is gone, X replaced Twitter, Bluesky and Threads have appeared - and platform data now flows almost exclusively through commercial social-listening providers that redact key fields. We revisit the question with two sampling designs run through the same downstream pipeline. Sample A draws N = 50 events from the Wikipedia Current Events Portal (WCEP) ranked by article pageviews. Sample B draws N = 109 events from Polymarket prediction markets ranked by USD trading volume, with each event's news moment pinned to the largest 1-hour trade-volume spike. Both samples are pulled from one commercial provider across nine indexed channels. We report three findings. (1) The X-vs-news direction depends on the sample. News leads X by a median of 21.6 min on Sample A (n = 6 paired); the same comparison is tied at -0.02 min on Sample B (n = 16 paired, X earliest in 38%). (2) The channel ecosystem has diversified. Bluesky, Facebook public, and YouTube together account for 24-32% of earliest channel wins; the 2014 "X versus newswire" framing no longer fits. (3) Coverage gaps are structural. Even with U.S.-relevance filtering and a pageview prior, the provider's index returns no on-topic evidence on 24% of randomly-sampled WCEP events. The paper's contribution is the cross-surface design that exposes the sample dependency in (1).

Molecular spin qubits offer a versatile platform for quantum information processing due to their synthetic tunability and well-defined electronic structure. Here, a fitted-parameter-free computational framework combining density functional theory (DFT), time-dependent DFT (TD-DFT), and Redfield theory is applied to investigate the longitudinal spin-lattice relaxation time $T_1$ of the Eu nuclear spin qubit Eu(dpphen)(NO3)3. Using a single-molecule gas-phase model, the experimental long relaxation component $T_{1,\mathrm{long}} = 41.39$ s is reproduced within a factor of 1.4 (calculated: 55.88 s at 4.2 K), indicating that the slow relaxation channel is governed by intramolecular vibronic coupling. In contrast, the calculated $T_{1,\mathrm{short}}$ deviates by a factor of 66, highlighting the importance of crystal lattice and intermolecular effects absent from the model. The experimental $^5D_0 \rightarrow {}^7F_0$ optical transition is reproduced to within 1.1%, supporting the accuracy of the electronic structure description. Vibrational analysis identifies a large-amplitude dpphen rocking mode at a frequency of $332.02~\mathrm{cm}^{-1}$ as the dominant vibronic coupling channel, while electric field gradient (EFG) derivative analysis independently identifies another nitrate-rocking mode at $180.57~\mathrm{cm}^{-1}$ as the primary modulator of the nuclear spin environment via nitrate motion. These results are consistent with a near-maximal quadrupole asymmetry parameter $η= 0.941$, which creates state mixing through off-diagonal quadrupolar terms. Overall, the results establish a single-molecule relaxation baseline and suggest targeted ligand rigidification and substitution strategies to suppress decoherence.

Erdős asked whether there are infinitely many finite sets of distinct primes $p_1<\cdots<p_k$ and positive integers $m$ such that \begin{equation}\label{eq:erdos-original} \frac1{p_1}+\cdots+\frac1{p_k}=1-\frac1m. \end{equation} This is Erdős Problems \#313~\cite{ErdosProblems313}. As recalled below, it is equivalent to the infinitude of primary pseudoperfect numbers. Following Butske, Jaje, and Mayernik~\cite{ButskeJajeMayernik}, a squarefree positive integer $n$ is a \emph{primary pseudoperfect number} if \begin{equation}\label{eq:ppn-def} \frac1n+\sum_{p\mid n}\frac1p=1, \end{equation} where the sum is over the prime divisors of $n$. OEIS A054377~\cite{OEISA054377} records the initial values \[ \begin{array}{c} 2,\ 6,\ 42,\ 1806,\ 47058,\\[2pt] 2214502422,\ 52495396602. \end{array} \] and the eight-prime-factor example \[ \text{\seqsplit{8490421583559688410706771261086}}. \] Butske, Jaje, and Mayernik proved by computation that for each $r\le 8$ there is exactly one primary pseudoperfect number with $r$ distinct prime factors~\cite{ButskeJajeMayernik}. This result gives a useful baseline, but it does not address later layers or the infinitude problem. This paper uses a local language for residual equations. A \emph{port} is a pair $(R,c)$, and a squarefree integer $B$ fills it if \[ Δ_{R,c}(B):=cB-R\partial(B)=1. \] The corresponding reciprocal form is \[ \sum_{q\mid B}\frac1q+\frac1{RB}=\frac cR. \] The product rule for the arithmetic derivative gives the composition law for ports. This law separates fillings inherited from smaller primary pseudoperfect numbers from fillings that are primitive relative to the fixed residual equation. The unconditional results of the paper are as follows.

The web is often treated as a durable record of institutional and social life, yet in practice it is fragile, revisable, and frequently ephemeral. Domains change, redesigns erase earlier material, institutions relocate, maintainers graduate, platforms impose silent limits, and periods of political instability can interrupt digital access entirely. This paper argues that archiving should not remain a niche activity practiced by a few specialists at the margins, but should become a proactive part of website maintenance. I motivate this claim through a case study centered on the Pakistan Embassy International School and College Tehran, whose domain, visual identity, leadership, and physical location all changed within a short period after my graduation. In response, I built and deployed a lightweight automated archival system using Python and GitHub Actions to submit pages and media from the site to the Internet Archive's Wayback Machine. The project shows both that archival preservation can be automated with modest infrastructure and that archival systems are themselves vulnerable to interruption, as illustrated by GitHub's automatic disabling of scheduled workflows after repository inactivity. Drawing on personal experience with internet shutdowns in Iran, open-source sustainability lessons from RPI's RCOS, and the operational history of the archiver, I argue that the ephemerality of the web is not an exception but a structural condition. If digital societies wish to preserve institutional memory and public history without leaving preservation to chance, proactive archiving should become a commonplace part of website maintenance.

In this article, we investigate the statistical distribution and asymptotic behavior of the family of monic integer polynomials of degree $n$ having at least one root in a fixed number field $K$. Although the framework of thin sets implies that the natural density of this family in the parameter space of bounded height is zero, explicitly quantifying this vanishing rate is a central challenge in arithmetic statistics. Employing a hybrid approach that integrates the Mahler measure, Dirichlet's unit theorem, and residue analysis of the Dedekind zeta function, we demonstrate that the rate of convergence of this density to zero is strictly dependent on the degree $n$. Specifically, we prove that the degrees of the factors induce a phase transition in the asymptotic behavior; for polynomials of degree $n = 2$, the decay rate is bounded by $O(H^{-1} \log H)$, whereas for higher degrees, the asymptotic behavior is dominated by the contribution of rational roots, yielding a bound of $O(H^{-1})$. Beyond deriving these asymptotic estimates, we apply principles from the geometry of numbers to establish explicit combinatorial bounds for counting both the reducible and irreducible components of these polynomials. These explicit bounds provide practical tools for computational evaluations within this domain.

In this paper we discuss extensions of the canonical quantization procedure in quantum field theories. We focus specifically on S-matrix representation as a T-exponent. This extension involves flat bundles on certain infinite dimensional functional manifolds of local time. The motivating problem is first principles treatment of bound states in quantum chromodynamics as well as precision physics of hydrogen atom and the muonium. Our main results include systematic treatment of flat bundles in an infinite dimensional setting, generalization of Hamiltonian evolution and functional renormalization group evolution equations in quantum field theories. We discuss several results from finite dimensional theory that have analogies in the functional setting. This includes construction of moduli space of flat connections and isomonodromic deformations. One of the outcomes of our analysis is a construction of a rich family of functional flat bundles with rational connections. This class of connections exhibits a rich set of mathematical properties. In particular, we construct examples of spaces fundamental groups of which have a definable continuum of generators. Physical states correspond to points in the moduli space of bundles on these spaces. On the physics side of things, we conclude that spacetime notions, such as spaces of particle configurations, emerge effectively as spectral sets of functional differential operators.

The dependence of differential cross-section of prompt photon production in bremsstrahlung \(qq \rightarrow qqγ\) at collisions of nonpolarized and longitudinally polarized protons at \(\sqrt{s}\)=10 GeV NICA energies on the kinematic parameters: sum of energy of the colliding protons \(\sqrt{s}\), the transverse momentum \emph{p\textsubscript{T}}, the cosine of the scattering angle \emph{Cos(θ)}, the rapidity \emph{y} of photon and \emph{x\textsubscript{T}} has been investigated. Differential cross-section of bremsstrahlung accounts for 0.03\% of the total diferential cross section for the production of prompt photons in a proton-proton collisions at NICA entrgies. The polarization of protons has a large influence on the differential cross-section of bremsstrahlung \(qq \rightarrow qqγ\), at large values of the transverse momentum of prompt photons. Double spin asymmetry of process of bremsstrahlung on the kinematic parameters has been studied.

We use a newly commissioned rapid expansion aerosol chamber (REACh) facility to study the homogeneous nucleation of water vapor to form liquid droplets. We perform high-speed measurements to track the partitioning of water into vapor and droplets throughout the expansion process, including tunable diode laser absorption spectroscopy (TDLAS) to access the vapor concentration and in-line holography to track the size and concentration of nucleating droplets. We retrieve the peak saturation ratio achieved in each expansion from the TDLAS measurements in combination with adjusted thermocouple temperature readout. We monitor the number of nucleated droplets and their subsequent growth as a function of saturation ratio, and observe the onset of homogeneous nucleation of water vapor occurring at a threshold saturation ratio near $S=5$, in agreement with prior literature and classical nucleation theory. The trends we observe in average diameter and droplet concentration suggest that warm air pockets near the chamber walls inhomogeneously mix with cold air at the center of the chamber following expansion. Active forced mixing with fans yields more spatially uniform temperature readings across the chamber, but also significantly broadens the droplet size distribution. Our results demonstrate the capability of TDLAS and holography techniques to track both water vapor and liquid water in the high saturation ratio environments necessary for the homogeneous nucleation of droplets. Our findings also reveal that droplet nucleation and growth dynamics are highly sensitive to turbulence.

Computational functionalism about consciousness is often criticized for relying on observer-relative interpretations of physical systems. This paper proposes a mathematical refinement of functionalism that avoids this problem. The central idea is that consciousness-relevant functional organization should be identified not with arbitrary input-output mappings, semantic labels, or externally imposed computational descriptions, but with a system's canonical functional structure: the minimal state-transition structure obtained by identifying internal states that have identical future behavior under all possible continuations. On this view, a state is functionally defined by its complete counterfactual role: how the system would evolve and respond from that state under possible future interactions. We call this position canonical functionalism. The framework does not claim to identify which systems are conscious, nor to show that functional organization is sufficient for consciousness. Rather, it identifies the canonical object over which functionalist theories of consciousness should be formulated: the task is to specify consciousness-relevant invariants, measures, or structural conditions over canonical functional structures, rather than over arbitrary semantic interpretations or superficial behavioral profiles. This reframes familiar objections about lookup tables, simulations, unfolding, and observer-relative computation: such cases do not by themselves refute functionalism, but force the functionalist to specify whether the relevant canonical structure is preserved, and if not, which additional structural features are missing.

Future arms control treaties may need to reliably verify warheads for dismantlement as part of the treaty verification process without exposing carefully guarded weapons information. Neutron Resonance Transmission Analysis has been proposed as a strategy to verify the authenticity of nuclear warheads and warhead components slated for dismantlement in an arms control verification exercise. Most actinides have resonant neutron absorption lines in the eV region, so by measuring the energy resolved transmission of neutrons and observing the resulting isotope-specific absorption lines, the authenticity of a nuclear device can be verified. To ensure acceptance of this technique by treaty partners, the measurement should minimize information learned about the warhead, including both geometric and isotopic features. Past implementations of transmission analysis acquired and compared neutron time-of-flight spectra. We have developed an analog electric cryptographic measurement proof of concept system where only counts in specific resonance energy windows are observed. The system uses discrete analog components, producing a complete data acquisition and analysis circuit. By limiting the design to easily verifiable parts, the entire apparatus is transparent to authentication and certification. The information security provided by this analog measurement technique may make it the verification basis of future ambitious arms control treaties that explicitly stipulate the dismantlement of nuclear weapons.

Along with the development of the scripting technology in cartography, such as the GMT and libraries of R programming language, geologic and geophysical mapping is being vigorously promoted, where the integration of the thematic data, such as GEBCO, EGM-2008 and geological raster and vector layers is one of the primary datasets that provides the high-resolution raw sources for cartographic visualization in the geologically complex regions like Pakistan. This study aims to integrate scripting methods of automated cartography, methods of applied geoinformatics for geomorphometric analysis and technical data processing (formatting, projecting, plotting), to provide a synthesis of the geological, geophysical and geomorphological maps of Pakistan they as new information supporting analysis of the geospatial variations of geology, geomorphology, tectonics and gravity fields with a special focus on the geologically remarkable region of Pakistan: Sulaiman Fold Belt and Muslim Bagh ophiolite complex. This study presents new 12 thematic maps, which are technically made using scripting approaches and open tools. All maps cover the region of Pakistan and they are made using open source tools: GMT, R and QGIS. A GMT and R based scripting mapping is applied for mapping Pakistan, and its algorithm steps are presented stepwise as code snippets. A system complex approach of the data integration and formats reshaping, data conversion and reformatting for a single project of the geology of Pakistan is designed and developed based on the combination of the programming and scripting techniques and with additional mapping, which integrates the geospatial datasets. Correlation between spatial phenomena of Earth's gravity, geologic evolution and tectonic movements were commented.

A computational study of higher-order derivative ratios on a time interval leading to the enstrophy peak is presented in the case of the 3D Taylor-Green vortex, a benchmark problem in the simulation of turbulent flows. The main finding is that the power law relating the ratios at time $t$ to $T^*-t$ where $T^*$ is the peak enstrophy time is of a form that allows the machinery of dynamic interpolation-sparseness to produce a lower bound on the radius of spatial analyticity sufficient to overcome an upper bound on the scale of sparseness of the super-level sets in view. As a consequence, the mechanism of turbulent dissipation engages via the harmonic measure maximum principle, furnishing a rigorous explanation for the subsequent slump of the enstrophy. This indicates that the higher-order derivative ratios -- which could be viewed as higher-order analogs of the classical Taylor and Kraichnan scales in turbulence phenomenology -- may be reasonable identifiers of the peak of the energy dissipation rate.

ECDSA signatures form the bedrock of blockchain transaction authentication, yet their security critically depends on proper nonce generation. We uncover a critical vulnerability in the Polygon MEV ecosystem: systematic nonce reuse that enables complete private key recovery. Analyzing on-chain data reveals that searchers, driven by the need for sub-second response times in sealed-bid auctions, employ predictable nonce patterns. These patterns create linear relationships between signatures, allowing passive attackers to recover private keys using elementary algebra. We provide a compact linear-system formulation for such attacks, including the dangerous case of cross-wallet nonce collisions, and present concrete evidence of exploitable patterns on Polygon. Our findings demonstrate how protocol-induced latency pressures can lead to catastrophic cryptographic failures in production blockchain systems, where a single implementation error compromises multiple accounts simultaneously.

We sought to explore and compare the perspectives of three key stakeholder groups: older adults, caregivers (formal health providers and informal caregivers), and digital health software developers on key functional and non-functional requirements. We conducted a survey, designed based on the findings from an existing systematic review, to gather and analyse data related to the three stakeholder groups' (dis)satisfaction with current aged care digital health software and their views on key future aged care software requirements. A mixed-methods survey approach integrated quantitative questionnaire data and qualitative open-ended responses from a total sample of 249, comprised of older adults (103), formal and informal caregivers (41), and software developers (105). Data analysis utilised a mixed methods approach, employing inferential statistics to compare group satisfaction levels and thematic analysis for qualitative open-ended responses. Our analysis reveals a significant "Requirements Gap". Software developers tend to prioritise advanced features and functional requirements, significantly overestimating user satisfaction with core NFRs such as ease of use and responsiveness. Conversely, developers were more critical of existing functional features compared to older adults and caregivers, who prioritised simplicity and reliability over feature density. By combining quantitative and qualitative analysis, we identified where stakeholder priorities align and where they diverge across functional and non-functional requirements in both the current designs they used and the future designs they desire. Our findings present a stakeholder gap analysis that can guide future co-design processes, near-term product decisions, and privacy-by-design recommendations in aged care digital health.

We investigate infinite-exponent partition relations on arbitrary relational structures, with a focus on linear orders and graphs. Any such relation contradicts the Axiom of Choice. We show that there are some such relations which are consistent with ZF which imply the failure not just of Choice but also of the Kinna-Wagner Selection Principle KWP$_1$ and the Ordering Principle O.

We develop an adaptive jump test for discretely observed high-frequency semimartingales by combining the A"it-Sahalia--Jacod ratio statistic (A"it-Sahalia and Jacod, 2009) and the Lee--Mykland extreme-return statistic (Lee and Mykland, 2008) with the Cauchy combination rule. Allowing stochastic It^o drift, volatility, and leverage, we show asymptotic independence under the continuous-path null and dense local alternatives, yielding an analytically calibrated test with closed-form power; under finite-activity jumps, the test is consistent. We also extend the method to additive microstructure noise. Simulations show that the combined procedure performs well under both dense and sparse alternatives and is typically best overall.

Temporal ghost imaging (TGI) enables ultrafast temporal signal recovery using slow detectors, offering a promising route for high-speed mid-infrared (MIR) detection. However, conventional schemes remain limited in temporal resolution by the modulation bandwidth or pattern timescale, and are mostly confined to structured illumination. Here, we demonstrated a high-resolution MIR single-photon computational TGI system, which integrated nonlinear structured detection with sub-pixel temporal shifting. A pre-programmed near-infrared pump serves as a temporally optical gate to drive sum-frequency generation in a nonlinear crystal. Consequently, MIR waveforms at 3.4 $μ$m were upconverted, and captured by a room-temperature silicon detector. We realized sub-pixel operation by fractional-bin temporal stepping of the gate and multi-shot fusion via pseudo-inverse reconstruction. The sub-pixel shifting strategy decouples the achievable resolution from modulation speed, enabling 40 ps temporal precision at a driving rate of only 3.125 Gbps. This performance surpasses both detector jitter and pattern-rate limits, while maintaining single-photon sensitivity. The presented paradigm establishes a versatile route for ultrafast MIR waveform reconstruction, opening new opportunities in high-resolution infrared sensing and quantum photonics.