Boundary time crystals (BTCs) in dissipative collective spin systems have been extensively studied using numerical, mean-field, and perturbative approaches. However, an explicit Liouvillian description governing the long-time dynamics deep within the time crystal phase has remained elusive. Here, we derive an effective Liouvillian that analytically captures the extreme BTC regime, where dissipation is parametrically weak and oscillatory order is maximally robust. By introducing a superspin representation of Liouville space, we obtain closed-form expressions for the Liouvillian eigenvalues to first order in the dissipation strength, providing direct access to decay rates, oscillation frequencies, and their thermodynamic scaling. Applying this framework to the canonical BTC model we analytically recover spontaneous breaking of continuous time-translation symmetry and persistent oscillations in the thermodynamic limit. In contrast, we show that other dissipative spin models exhibit only single-frequency oscillatory dynamics and therefore do not support genuine BTC phases. Our results establish a controlled analytical framework for the long-time dynamics in the extreme BTC regime.

Consider the sequential testing of binary outcomes. The a posteriori belief process and its objective conditional-probability counterpart generally differ but converge to the same result in well-defined tests. We show that unless the two processes are 'essentially identical', differing only by an a priori factor, time-homogeneous continuous decisions based on the former are path-dependent with respect to state-variables based on the latter or any other non-essentially-identical processes. Inferential error decomposes into a path-dependent and a path-independent component, whose distinct properties are relevant to error mitigation.

A well-known result in random matrix theory, proven by Kahn, Komlós and Szemerédi in 1995, states that a square random matrix with i.i.d. uniform $\{\pm 1\}$ entries is invertible with probability $1-\exp(-Ω(n))$. As a natural generalization of the model, we consider the invertibility of a class of random band matrices with independent entries where the bandwidth $d_n$ scales like $n^α$, for some $α\in(0,1)$. The band matrix model we consider is sufficiently general and covers existing models such as the block band matrix and periodic band matrix, allowing great flexibility in the variance profile. As the bandwidth is sublinear in the dimension, estimating the invertibility and least singular values of these matrices is a well-known open problem. We make progress towards the invertibility problem by showing that, when $α>\frac{2}{3}$ and when the random variables are i.i.d. uniformly distributed on $\{\pm 1+c\}$ for any fixed integer $c$, then the band matrix is invertible with probability $1-\exp(-Ω(n^{α/2}))$. Previously, even invertibility with probability $1-o(1)$ was not known for these band matrix models except in the very special case of block band matrices. We then extend the invertibility result to symmetric random band matrices with integer entries, and prove the same non-singularity probability estimate whenever $α>\frac{2}{3}$.

In this article, we present two novel variants of the contact process. In the first variant individuals carry a viral load. An individual with viral load zero is classified as healthy and otherwise infected. If an individual becomes infected it begins with a viral load of one, which then evolves according to a Birth-Death process. In this model, viral load indicates severity of the infection such that individuals with a higher load can be more infectious. Moreover, the recovery times of individual is not necessarily exponentially distributed and can even be chosen to follow a power-law distribution. In the second variant individuals are permanently infected albeit in two states: actively infected or dormant. The dynamics of these individual states are again governed by a Birth-Death process. Dormant infections do not interact with neighbouring individuals but may reactivate spontaneously. Active infections reactivate dormant neighbours at a constant rate and may become dormant themselves. We present for both variants a Poisson construction. For the first model, we study the phase transition of survival and discuss existence of a non-trivial upper invariant law. Additionally, we derive a duality relationship between the two variant, which we use to uncover a phase transition regarding invariant distributions in the second variant.

We investigate the quantum dynamics of a one-dimensional quasiperiodic system featuring a single-particle mobility edge (SPME), described by the generalized Aubry-André (GAA) model. This model offers a unique platform to study the consequences of coexisting localized and extended eigenstates, which contrasts sharply with the abrupt localization transition in the standard Aubry-André model. We analyze the system's response to a quantum quench through two complementary probes: entanglement entropy (EE) and subsystem information capacity (SIC). We find that the SPME induces a smooth crossover in all dynamical signatures. The EE saturation value exhibits a persistent volume-law scaling in the mobility-edge phase, with an entropy density that continuously decreases as the number of available extended states decreases. Complementing this, the SIC profile interpolates between the linear ramp characteristic of extended systems and the information trapping behavior of localized ones, directly visualizing the mixed nature of the underlying spectrum. Our results establish unambiguous dynamical fingerprints of a mobility edge, providing a crucial non-interacting benchmark for understanding information and entanglement dynamics in more complex systems with mixed phases.

For the simple system of a point-like particle confined to a straight line, I compile, initially in a concise table, the structural elements of quantum mechanics and contrast them with those of classical (statistical) mechanics. Despite many similarities, there are the well-known fundamental differences, resulting from the algebraic non-commutativity in the quantal structure. The latter was discovered by Werner Heisenberg (1901-1976) in June 1925 on the small island of Helgoland in the North Sea, as a consequence of understanding atomic spectral data within a matrix scheme consistent with energy conservation. I discuss the differences and exemplify their quantifications by the variance and entropic indeterminacy inequalities, by (pseudo-)classical bounds on quantum canonical partition functions, and by the correlation inequalities of John Bell (1928-1990) and others.

In this paper, we explore a ring invariant which is closely related to the Davenport constant of a group. In particular, we will calculate this invariant for a certain class of rings of integers and their orders and use it to understand factorization properties of the latter. To this end, we also examine the well-behaved class of Galois-invariant orders.

We prove an equivariant version of the CM minimization conjecture for extremal Kähler manifolds. This involves proving that, given an equivariant punctured family of polarized varieties, a relative version of the CM degree is strictly minimized by an extremal filling. This generalizes a result by Hattori for cscK manifolds with discrete automorphism group by allowing automorphisms and extremal metrics. As a main tool, we extend results by Székelyhidi on asymptotic filtration Chow stability of cscK manifolds with discrete automorphism group to the extremal setting.

We search for Lorentz invariance violation (LIV) by re-analyzing the spectral lag data for GRB 190114C from Fermi-GBM using frequentist analysis, where we deal with the astrophysical nuisance parameters using profile likelihood. For this use case, we find a global minima for the $χ^2$ as a function of energy scale of LIV ($E_{QG}$), well below the Planck scale. The best-fit $1σ$ central intervals for $E_{QG}$ are given by $2.81^{+0.50}_{-0.37}\times 10^{14}$ GeV and $9.85^{+0.84}_{-0.60}\times 10^{5}$ GeV for linear and quadratic LIV, respectively, and agree with the Bayesian estimates obtained so far in a previous work. Therefore, the results from the frequentist analysis of GRB 190114C agree with Bayesian analysis.

The control of out-of-equilibrium electron dynamics in topological insulators is essential to unlock their potential in next-generation quantum technologies. However, the role of temperature on the renormalization of the electronic band structure and, consequently, on electron scattering processes is still elusive. Here, using high-resolution time- and angle-resolved photoemission spectroscopy (TR-ARPES), we show that even a modest ($\sim$15 meV) renormalization of the conduction band of Bi$_2$Te$_3$ can critically affect bulk and surface electron scattering processes. Supported by a kinetic Monte Carlo toy-model, we show that temperature-induced changes in the bulk band structure modulate the intervalley electron-phonon scattering rate, reshaping the out-of-equilibrium response. This work establishes temperature as an effective control knob for engineering scattering pathways in topological insulators.

Machine learning has revolutionized polymer science by enabling rapid property prediction and generative design. Large language models (LLMs) offer further opportunities in polymer informatics by simplifying workflows that traditionally rely on large labeled datasets, handcrafted representations, and complex feature engineering. LLMs leverage natural language inputs through transfer learning, eliminating the need for explicit fingerprinting and streamlining training. In this study, we finetune general purpose LLMs -- open-source LLaMA-3-8B and commercial GPT-3.5 -- on a curated dataset of 11,740 entries to predict key thermal properties: glass transition, melting, and decomposition temperatures. Using parameter-efficient fine-tuning and hyperparameter optimization, we benchmark these models against traditional fingerprinting-based approaches -- Polymer Genome, polyGNN, and polyBERT -- under single-task (ST) and multi-task (MT) learning. We find that while LLM-based methods approach traditional models in performance, they generally underperform in predictive accuracy and efficiency. LLaMA-3 consistently outperforms GPT-3.5, likely due to its tunable open-source architecture. Additionally, ST learning proves more effective than MT, as LLMs struggle to capture cross-property correlations, a key strength of traditional methods. Analysis of molecular embeddings reveals limitations of general purpose LLMs in representing nuanced chemo-structural information compared to handcrafted features and domain-specific embeddings. These findings provide insight into the interplay between molecular embeddings and natural language processing, guiding LLM selection for polymer informatics.

Amid the growing need to keep learners abreast of rapid technological advancements brought about by the Fourth Industrial Revolution, this study explores perceived needs of students in virtual learning environments supported by emerging technologies. A survey was conducted across five leading open universities in Southeast Asia. The study aimed to identify student preferences regarding features of their virtual learning environments that could better prepare them as productive citizens and professionals. Findings indicate strong interest in interactive books and learning analytics, underscoring the importance of enhancing learner engagement and data-informed instruction. The results inform the development of a strategic roadmap to guide open universities in prioritizing technological and pedagogical innovations aligned with the evolving expectations of digital-age learners.

We review the notion of stable supermap from SUSY curves to a fixed target superscheme, and prove that when the target is (super)projective, stable supermaps are parameterized by a Deligne-Mumford superstack with superschematic and separated diagonal. We characterize the bosonic reduction of this moduli superstack and see that it has a surjective morphism onto the moduli stack of stable maps from spin curves to the bosonic reduction of the target, whose fibers are linear schemes; for this reason, the moduli superstack of stable supermaps is not proper unless such linear schemes reduce to a point. Using Manin-Penkov-Voronov's super Grothendieck-Riemann-Roch theorem we also make a formal computation of the virtual dimension of the moduli superstack, which agrees with the characterization of the bosonic reduction just mentioned and with the dimension formula for the case of bosonic target existing in the literature.

Thermofield dynamics (TFD) is a powerful framework to account for thermal effects in a wavefunction setting, and has been extensively used in physics and quantum optics. TFD relies on a duplicated state space and creates a correlated two-mode thermal state via a Bogoliubov transformation acting on the vacuum state. However, a very useful variant of TFD uses the vacuum state as initial condition and transfers the Bogoliubov transformation into the propagator. This variant, referred to here as the inverse Bogoliubov transformation (iBT) variant, has recently been applied to vibronic coupling problems and coupled-oscillator Hamiltonians in a chemistry context, where the method is combined with efficient tensor network methods for high-dimensional quantum propagation. In the iBT/TFD representation, the mode expectation values are clearly defined and easy to calculate, but the thermalized reduced particle distributions such as the reduced 1-particle densities or Wigner distributions are highly non-trivial due to the Bogoliubov back-transformation of the original thermal TFD wavefunction. Here we derive formal expressions for the reduced 1-particle density matrix (1-RDM) that uses the correlations between the real and tilde modes encoded in the associated reduced 2-particle density matrix (2-RDM). We apply this formalism to define the 1-RDM and the Wigner distributions in the special case of a thermal harmonic oscillator. Moreover, we discuss several approximate schemes that can be extended to higher-dimensional distributions. These methods are demonstrated for the thermal reduced 1-particle density of an anharmonic oscillator.

Multilayer networks offer a powerful framework for modeling complex systems across diverse domains, effectively capturing multiple types of connections and interdependent subsystems commonly found in real world scenarios. To analyze these networks, embedding techniques that project nodes into a lower-dimensional geometric space are essential. This paper introduces a novel hyperbolic embedding framework that advances the state of the art in multilayer network analysis. Our method, which supports heterogeneous node sets across networks and inter-layer connections, generates layer-specific hyperbolic embeddings, enabling detailed intra-layer analysis and inter-layer comparisons, while simultaneously preserving the global multilayer structure within hyperbolic space, a capability that sets it apart from existing approaches, which typically rely on independent embedding of layers. Through experiments on synthetic multilayer stochastic block models, we demonstrate that our approach effectively preserves community structure, even when layers consist of different node sets. When applied to real brain networks, the method successfully clusters disease-related brain regions from different patients, outperforming layer-independent approaches and highlighting its relevance for comparative analysis. Overall, this work provides a robust tool for multilayer network analysis, enhancing interpretability and offering new insights into the structure and function of complex systems.

We show that small perturbations of the metric of a ball in Euclidean n-space to metrics with nonpositive curvature do not reduce the isoperimetric ratio. Furthermore, the isoperimetric ratio is preserved only if the perturbation corresponds to a homothety of the ball. These results establish a sharp local version of the Cartan-Hadamard conjecture.

In this paper we study, via perturbative methods, the rates of production of $W$ bosons emitted in neutrino decays during the early stages of the Universe. We compute the transition amplitude corresponding to the first order of de Sitter electroweak perturbation theory and study its various limiting cases. The transition rates are derived using minimal subtraction and dimensional regularization. In the end we attempt to obtain the density number of $W$ bosons produced in perturbative transitions in de Sitter spacetime, using the rates obtained in this paper and in previous ones, and analyze the density number with respect to the particle momenta and renormalisation mass $μ$.

We prove a central limit theorem (CLT) for the number of joint orbits of random tuples of commuting permutations. In the uniform sampling case this generalizes the classic CLT of Goncharov for the number of cycles of a single random permutation. We also consider the case where tuples are weighted by a factor other than one, per joint orbit. We view this as an analogue of the Ewens measure, for tuples of commuting permutations, where our CLT generalizes the CLT by Hansen. Our proof uses saddle point analysis, in a context related to the Hardy-Ramanujan asymptotics and the theorem of Meinardus, but concerns a multiple pole situation. The proof is written in a self-contained manner, and hopefully in a manner accessible to a wider audience. We also indicate several open directions of further study related to probability, combinatorics, number theory, an elusive theory of random commuting matrices, and perhaps also geometric group theory.

The use of gaseous Time Projection Chambers enables the detection and the detailed study of rare events due to particles interactions with the atoms of the gas with energy releases as low as a few keV. Due to this capability, these instruments are being developed for applications in the field of astroparticle physics, such as the study of dark matter and neutrinos. To readout events occurring in the sensitive volume with a high granularity, the CYGNO collaboration is developing a solution where the light generated during the avalanche processes occurring in a multiplication stage based on Gas Electron Multiplier (GEM) is read out by optical sensors with very high sensitivity and spatial resolution. To achieve a high light output, gas gain values of the order of $10^5\text{-}10^6$ are needed. Experimentally, a dependence of the detector response on the spatial density of the charge collected in the GEM holes has been observed, indicating a gain-reduction effect likely caused by space-charge buildup within the multiplication channels. This paper presents data collected with a prototype featuring a sensitive volume of about two liters, together with a model developed by the collaboration to describe and predict the gain dependence on charge density. A comparison with experimental data shows that the model accurately reproduces the gain behaviour over nearly one order of magnitude, with a percent-level precision.

Backgrounds: Artificial intelligence (AI) is transforming healthcare, yet translating AI models from theoretical frameworks to real-world clinical applications remains challenging. The Mayo Clinic Platform (MCP) was established to address these challenges by providing a scalable ecosystem that integrates real-world multiple modalities data from multiple institutions, advanced analytical tools, and secure computing environments to support clinical research and AI development. Methods: In this study, we conducted four research projects leveraging MCP's data infrastructure and analytical capabilities to demonstrate its potential in facilitating real-world evidence generation and AI-driven clinical insights. Utilizing MCP's tools and environment, we facilitated efficient cohort identification, data extraction, and subsequent statistical or AI-powered analyses. Results: The results underscore MCP's role in accelerating translational research by offering de-identified, standardized real-world data and facilitating AI model validation across diverse healthcare settings. Compared to Mayo's internal Electronic Health Record (EHR) data, MCP provides broader accessibility, enhanced data standardization, and multi-institutional integration, making it a valuable resource for both internal and external researchers. Conclusion: Looking ahead, MCP is well-positioned to transform clinical research through its scalable ecosystem, effectively bridging the divide between AI innovation and clinical deployment. Future investigations will build upon this foundation, further exploring MCP's capacity to advance precision medicine and enhance patient outcomes.

We first present some identities involving the Pochhammer symbol (rising factorial). We also recall and present some new properties of the Jacobi polynomials. We use them to expand a general hypergeometric function in an orthogonal series of Jacobi polynomials. Then we use these expansions to discover closed forms for certain integrals of Jacobi polynomials that are multiplied by a generalized hypergeometric function and a Beta density. We can also obtain closed forms for some series involving rising factorials that generalise binomial series by using well-known properties of the hypergeometric function. In particular, we get a few new, nontrivial identities involving the Pochhammer symbol. We can also derive some simplifying identities for generalized hypergeometric functions.

We show that the Subgroup distance problem regarding the Hamming distance, the Cayley distance and the $l_\infty$ distance is NP-complete when the input group is cyclic. When we restrict the $l_\infty$ distance to fixed values we show that it is NP-complete to decide whether there are numbers $z_1,z_2 \in \mathbb{N}$ such that $l_\infty(β, α_1^{z_1}α_2^{z_2}) \leq 1$ for permutation $α_1,α_2,β\in S_n$ where $α_1$ and $α_2$ commute. However on the positive side we can show that it can be decided in NL whether there is a number $z \in \mathbb{N}$ such that $l_\infty(β, α^z) \leq 1$ for permutations $α,β\in S_n$. For the former we provide a tool, namely for all numbers $t_1,t_2,t \in \mathbb{N}$ where $t$ is required to be odd, $0 \leq t_1 < t_2 < t$ and $t_1 \not\equiv t_2 \bmod q$ for all primes $q \mid t$ we give a constructive proof for the existence of permutations $α,β\in S_t$ with $l_\infty(β, α^{t_1}) \leq 1$ and $l_\infty(β, α^{t_2}) \leq 1$.

This Letter presents measurements of long-range transverse-momentum correlations using a new observable, $v_{0}(p_\mathrm{T})$, serving as a probe of event-by-event radial-flow fluctuations, the underlying radial expansion, and the medium properties in heavy-ion collisions. Results are reported for inclusive charged particles, pions, kaons, and protons across various centrality intervals in Pb$-$Pb collisions at $\sqrt{s_\mathrm{NN}} = 5.02$ TeV, recorded by the ALICE detector. A pseudorapidity-gap technique, similar to that used in anisotropic-flow studies, is employed to suppress short-range correlations. At low $p_\mathrm{T}$, a characteristic mass ordering consistent with hydrodynamic collective flow is observed. At higher $p_\mathrm{T}$ ($> 3$ GeV/$c$), protons exhibit larger $v_{0}(p_\mathrm{T})$ than pions and kaons, in agreement with expectations from quark-recombination models. Comparisons to viscous hydrodynamic calculations with varying bulk viscosity and equation of state demonstrate the sensitivity of the $v_{0}(p_\mathrm{T})$ observable to these key medium properties. The findings establish $v_{0}(p_\mathrm{T})$ as a valuable addition to the set of observables used in Bayesian analyses for extracting the transport properties and constraining the equation of state of strongly interacting matter, while also helping to systematically explore its sensitivity and impact within such global studies.

The classic Fischer, Lynch, and Paterson impossibility proof demonstrates that any deterministic protocol for consensus in either a message-passing or shared-memory system must violate at least one of termination, validity, or agreement in some execution. But it does not provide an efficient procedure to find such a bad execution. We show that for wait-free shared memory consensus, given a protocol in which each process performs at most $s$ steps computed with total time complexity at most t, there exists an adversary algorithm that takes the process's programs as input and computes within $O(st)$ time a schedule that violates agreement. We argue that this bound is tight assuming the random oracle hypothesis: there exists a deterministic obfuscated consensus protocol that forces the adversary to spend $Ω(st)$ time to find a bad execution despite having full access to all information available to the protocol. This bound is based on a general algorithm that reduces the constructing an obfuscated consensus protocol to constructing an obfuscated threshold function that provably costs $Ω(t)$ time to evaluate on a single input, where $t$ is a tunable parameter, and for which an adversary with access to the threshold function implementation cannot extract the threshold any faster than by doing binary search. We give a particular implementation of such an obfuscated threshold function that is not very efficient but that is provably secure assuming the random oracle hypothesis. Since our obfuscated consensus protocol does not depend on the specific details of this construction, it may be possible to replace it with one that is more efficient or requires weaker cryptographic assumptions, a task we leave for future work.

We discuss the local analysis of Gaussian potential energy of modular lattices. We present examples of $2$-modular lattices -- such as the $16$-dimensional Barnes-Wall lattice -- and $3$-modular lattices -- such as the $12$-dimensional Coxeter-Todd lattice -- that are locally universally optimal among lattices (in the sense of Cohn and Kumar). We also provide other $2$- and $3$-modular lattices that are not locally universally optimal, or not even critical in the Gaussian core model.

The measurement of the bound-state $β$ decay of $^{205}\mathrm{Tl}^{81+}$ at the Experimental Storage Ring at GSI, Darmstadt, has recently been reported with substantial impact on the use of $^{205}\mathrm{Pb}$ as an early Solar System chronometer and the low-energy measurement of the solar neutrino spectrum via the LOREX project. Due to the technical challenges in producing a high-purity $^{205}\mathrm{Tl}^{81+}$ secondary beam, a robust statistical method needed to be developed to estimate the variation in the contaminant $^{205}\mathrm{Pb}^{81+}$ produced in the fragmentation reaction, which was subsequently transmitted and stored in the ESR. Here we show that Bayesian and Monte Carlo methods produced comparable estimates for the contaminant variation, each with unique advantages and challenges given the complex statistical problems for this experiment. We recommend the adoption of such methods in future experiments that exhibit unknown statistical fluctuations.

Van der Waals materials enable the construction of atomically sharp interfaces between compounds with distinct crystal and electronic properties. This is dramatically exploited in moiré systems, where a lattice mismatch or twist between monolayers generates an emergent in-plane periodicity, giving rise to electronic properties absent in the constituent materials. In contrast, vertical superlattices, formed by stacking dissimilar materials in the out-of-plane direction on the nanometer scale, have received far less attention despite their potential to realize analogous emergent phenomena in three dimensions. Through angle-resolved photoemission spectroscopy and density functional theory, we investigate six-to-eight-layer transition metal dichalcogenide (TMD) heterostructures constructed from pairs of stacked few-layer materials. Counterintuitively, we find that even these single superlattice units can host fully-delocalised bands, evidencing a robust coherent interlayer coupling across lattice-mismatched interfaces over extended spatial scales. We show how uncompensated semimetallic phases and energetically-mismatched topological surface states are readily and exclusively stabilized within such asymmetrical architectures. These findings establish two-component heterostructures in the intermediate layer-regime as platforms to invoke and control unprecedented combinations and instances of the diverse quantum phases native to many-layer TMDs.

Chiral anomaly is a key feature of Lorentz-invariant quantum field theories: in presence of parallel external electric and magnetic fields, the number of massless Weyl fermions of a given chirality is not conserved. In condensed matter, emergent chiral fermions in Weyl semimetals exhibit the same anomaly, directly tied to the topological charge of the Weyl node, ensuring a quantized anomaly coefficient. However, many condensed matter systems break Lorentz symmetry while retaining topological nodes, raising the question of how chiral anomaly manifests in such settings. In this work, we investigate this question in spin-1 fermionic systems and show that the conventional anomaly equation is modified by an additional nontopological contribution, leading to a nonquantized anomaly coefficient. This surprising result arises because spin-1 fermions can be decomposed into 2-flavor Weyl fermions coupled to a Lorentz-breaking, momentum-dependent non-Abelian background potential. The interplay between this potential and external electromagnetic fields generates the extra term in the anomaly equation. Our framework naturally generalizes to other Lorentz-breaking systems beyond the spin-1 case.

We introduce an extension of the evolution mapping framework to cosmological models that include massive neutrinos. The original evolution mapping framework exploits a degeneracy in the linear matter power spectrum when expressed in ${\rm Mpc}$ units, which compresses its dependence on cosmological parameters into those that affect its shape and a single extra parameter $σ_{12}$, defined as the RMS linear variance in spheres of radius $12 {\rm Mpc}$. We show that by promoting the scalar amplitude of fluctuations, $A_{\rm s}$, to a shape parameter, we can additionally describe the suppression due to massive neutrinos at any redshift to sub-0.01\% accuracy across a wide range of masses and for different numbers of mass eigenstates. This methodology has been integrated into the public COMET package, enhancing its ability to emulate predictions of state-of-the-art perturbative models for galaxy clustering, such as the effective field theory (EFT) model. Additionally, the updated software now accommodates a broader cosmological parameter space for the emulator, enables the simultaneous generation of multiple predictions to reduce computation time, and incorporates analytic marginalisation over nuisance parameters to expedite posterior estimation. Finally, we explore the impact of different infrared resummation techniques on galaxy power spectrum multipoles, demonstrating that any discrepancies can be mitigated by EFT counterterms without impacting the cosmological parameters.

We introduce the notion of Ramsey partition regularity, a generalisation of partition regularity involving infinitary configurations. We provide characterisations of this notion in terms of certain ultrafilters related to tensor products and dubbed Ramsey's witnesses; and we also consider their nonstandard counterparts as pairs of hypernatural numbers, called Ramsey pairs. These characterisations are then used to determine whether various configurations involving polynomials and exponentials are Ramsey partition regular over the natural numbers. In particular, this provides negative answers to several questions recently posed by Kra, Moreira, Richter and Robertson.