We dig into the semi-classical description of gravity by studying one-loop corrections to primordial power spectra generated during cosmic inflation from gravitational nonlinear interactions. In the realm of the Effective Field Theory (EFT) of inflationary fluctuations, we renormalize the quadratic Lagrangian dictating the linear dynamics of gauge-invariant perturbations. Since gravity is a non-renormalizable theory, this procedure is performed perturbatively in terms of negative powers of the EFT strong coupling scales. Since the interactions we consider are purely gravitational, they are ubiquitous and independent of the details of the EFT. Our results are thus relevant for a large class of approximately scale-invariant inflationary scenarios, be them driven by a single scalar field with canonical kinetic terms, or with a non-canonical structure \textit{à la} $P(X,ϕ)$, or for an effective single-field description at the level of fluctuations only and emerging from a covariant multifield theory. Using dimensional regularization, we show that time-dependent Ultra-Violet (UV) divergences appearing at the loop level can be canceled at all times by an appropriate splitting of the bare Lagrangian into renormalized operators and counterterms. Moreover, we explicitly compute all finite contributions to the loops and we prove that, taking into account backreaction, the final one-loop renormalized power spectra of both the primordial curvature perturbation and of gravitational waves are exactly conserved on super-horizon scales. Conclusions of our work imply that the scalar and tensor propagation speeds are immune to radiative corrections from gravitational nonlinearities. We discuss a first application to multifield inflation.

We propose an experiment to test the non-classicality of the gravitational interaction. We consider two optomechanical systems that are perfectly isolated, except for a weak gravitational coupling. If a suitable resonance condition is satisfied, an optical signal can be transmitted from one system to the other over a narrow frequency band, a phenomenon that we call gravitationally induced transparency. In this framework, the challenging problem of testing the quantum nature of gravity is mapped to the easier task of determining the non-classicality of the gravitationally-induced optical channel: If the optical channel is not entanglement-breaking, then gravity must have a quantum nature. This approach is applicable without making any assumption on the, currently unknown, correct model of gravity in the quantum regime. In the second part of this work, we model gravity as a quadratic Hamiltonian interaction (e.g. a weak Newtonian force), resulting in a Gaussian thermal attenuator channel between the two systems. Depending on the strength of thermal noise, the system presents a sharp transition from an entanglement-breaking to a non-classical channel capable not only of entanglement preservation but also of asymptotically perfect quantum communication.

Theoretical computation of cosmological observables is an intensive process, restricting the speed at which cosmological data can be analysed and cosmological models constrained, and therefore limiting research access to those with high performance computing infrastructure. Whilst the use of machine learning to emulate these computations has been studied, most existing emulators are specialised and not suitable for emulating a wide range of observables with changing physical models. Here, we investigate the Model-Agnostic Meta-Learning algorithm (MAML) for training a cosmological emulator. MAML attempts to train a set of network parameters for rapid fine-tuning to new tasks within some distribution of tasks. Specifically, we consider a simple case where the galaxy sample changes, resulting in a different redshift distribution and lensing kernel. Using MAML, we train a cosmic-shear angular power spectrum emulator for rapid adaptation to new redshift distributions with only $O(100)$ fine-tuning samples, whilst not requiring any parametrisation of the redshift distributions. We compare the performance of the MAML emulator to two standard emulators, one pre-trained on a single redshift distribution and the other with no pre-training, both in terms of accuracy on test data, and the constraints produced when using the emulators for cosmological inference. We observe that within an MCMC analysis, the MAML emulator is able to better reproduce the fully-theoretical posterior, achieving a Battacharrya distance from the fully-theoretical posterior in the $S_8$ -- $Ω_m$ plane of 0.008, compared to 0.038 from the single-task pre-trained emulator and 0.243 for the emulator with no pre-training.

In safety-critical control systems, ensuring both system safety and smooth control input is essential for practical deployment. Existing Control Barrier Function (CBF) frameworks, especially High-Order CBFs (HOCBFs), effectively enforce safety constraints, but also raise concerns about the smoothness of the resulting control inputs. While smoothness typically refers to continuity and differentiability, it does not by itself ensure bounded input variation. In contrast, Lipschitz continuity is a stronger form of continuity that not only is necessary for the theoretical guarantee of safety, but also bounds the rate of variation and eliminates abrupt changes in the control input. Such abrupt changes can degrade system performance or even violate actuator limitations, yet current CBF-based methods do not provide Lipschitz continuity guarantees. This paper introduces Filtered Control Barrier Functions (FCBFs), which extend HOCBFs by incorporating an auxiliary dynamic system-referred to as an input regularization filter-to produce Lipschitz continuous control inputs. The proposed framework ensures safety, control bounds, and Lipschitz continuity of the control inputs simultaneously by integrating FCBFs and HOCBFs within a unified quadratic program (QP). Theoretical guarantees are provided and simulations on a unicycle model demonstrate the effectiveness of the proposed method compared to standard and smoothness-penalized HOCBF approaches.

We study the competition between random multiplicative growth and redistribution/migration in the mean-field limit, when the number of sites is very large but finite. We find that for static random growth rates, migration should be strong enough to prevent localisation, i.e. extreme concentration on the fastest growing site. In the presence of an additional temporal noise in the growth rates, a third partially localised phase is predicted theoretically, using results from Derrida's Random Energy Model. Such temporal fluctuations mitigate concentration effects, but do not make them disappear. We discuss our results in the context of population growth and wealth inequalities.

We give a local treatment of finite alignment by identifying the finitely aligned part of any (not necessarily finitely aligned) higher-rank graph. We show the finitely aligned part is itself a constellation and forms a finitely aligned relative category of paths together with the original higher-rank graph. We show that the elements of the finitely aligned part are precisely those whose cylinder sets are compact, which allows us to give novel definitions of locally compact path and boundary-path spaces for nonfinitely aligned higher-rank graphs. We extend a semigroup action and the associated semidirect product groupoid developed by Renault and Williams to define ample Hausdorff path and boundary-path groupoids. The groupoids are amenable for nonfinitely aligned k-graphs by a result of Renault and Williams. In the finitely aligned case, the path groupoids coincide with Spielberg's groupoids, and the boundary-path groupoid has an inverse semigroup model via a result of Ortega and Pardo.

We introduce a restricted latent class exploratory model for longitudinal data with ordinal attributes and respondent-specific covariates. Responses follow a time inhomogeneous hidden Markov model where the probability of a respondent's latent state at the current time point is conditional on the respondent's latent state at the previous time point as well as the respondent's covariates at the current time point. We prove that the model is identifiable, state a Bayesian formulation, and demonstrate its efficacy in a variety of scenarios through two simulation studies. We apply the model to response data from a mathematics examination, comparing the results to a previously published confirmatory analysis, and also apply it to emotional state response data which was measured over a several-day period.

In this paper we prove that giving a right actegory with hom-objects is equivalent to giving a right-enriched category with copowers. While this result is known in the closed symmetric setting, our contribution extends the equivalence to non-closed and non-symmetric monoidal bases. This generalization is motivated by the semantics of higher-order message passing in the Categorical Message Passing Language (CaMPL), a concurrent language whose semantics is given by a linear actegory. A desirable feature for this language is the support of higher-order processes: processes that are passed as first class citizens between processes. While this ability is already present in any closed linear type systems -- such as CaMPL's -- to support arbitrary recursive process definitions requires the ability to reuse passed processes. Concurrent resources in CaMPL, however, cannot be duplicated, thus, passing processes as linear closures does not provide the required flexibility. This means processes must be passed as sequential data and the concurrent side must be enriched in the sequential side, motivating the technical result of this paper.

The SPE processing function (PF) of the \Euclid pipeline is dedicated to the automatic analysis of one-dimensional spectra to determine redshifts, line fluxes, and spectral classifications. The first \Euclid Quick Data Release (Q1) delivers these measurements for all $H_\mathrm{E}<22.5$ objects identified in the photometric survey. In this paper, we present an overview of the SPE PF algorithm and assess its performance by comparing its results with high-quality spectroscopic redshifts from the Dark Energy Spectroscopic Instrument (DESI) survey in the Euclid Deep Field North. Our findings highlight remarkable accuracy in successful redshift measurements, with a bias of less than $3 \times 10^{-5}$ in $(z_{\rm SPE}-z_{\rm DESI})/(1+z_{\rm DESI})$ and a high precision of approximately $10^{-3}$. The majority of spectra have only a single spectral feature or none at all. To avoid spurious detections, where noise features are misinterpreted as lines or lines are misidentified, it is therefore essential to apply well-defined criteria on quantities such as the redshift probability or the \ha\ flux and signal-to-noise ratio. Using a well-tuned quality selection, we achieve an 89\% redshift success rate in the target redshift range for cosmology ($0.9<z<1.8$), which is well covered by DESI for $z<1.6$. Outside this range where the \ha\ line is observable, redshift measurements are less reliable, except for sources showing specific spectral features (e.g., two bright lines or strong continuum). Ongoing refinements along the entire chain of PFs are expected to enhance both the redshift measurements and the spectral classification, allowing us to define the large and reliable sample required for cosmological analyses. Overall, the Q1 SPE results are promising, demonstrating encouraging potential for cosmology.

This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We propose a notion of a spectral decomposition system which brings together a wide array of settings underlying important applications such as Fourier-phase-invariant functions, mixed-norm regularization, and functions of eigenvalues or (signed) singular values of matrices. We are particularly motivated by algorithmic requirements for evaluating convex analytical objects. Thus, a central contribution is a novel reduced minimization principle that enables the constructive reduction of minimization problems involving spectral functions to those of the simpler associated invariant functions. This result is then leveraged to explicitly evaluate the conjugates, subgradients, and set-valued Bregman proximity operators of spectral functions.

We replace the familiar Stokes vector by a tensor. This allows us to introduce, for example, polar-coordinate components of the Stokes vector. From the tensor we can derive the skyrmion field for mapping the polarization in structured light beams. These ideas have wider application in optics and in electromagnetic theory. We illustrate this with an example from non-paraxial optics and for Poynting's vector.

Unlike ordinary conductors and semiconductors, which conduct electricity through individual electrons, superconductors usually conduct electricity through electron pairs, known as Cooper pairs. Even after 4 decades of intense study, no one knows what holds electrons together in high-$T_c$ cuprates. Here, targeting the critical challenge of pairing mechanism behind high-$T_c$ superconductivity in oxides and considering the dominance of eV-scale ionic bonding, affinity of O$^-$ (1.46 eV) and O$^{2-}$ (-8.08 eV) and large two-electron ionization energy ($\sim$15-28 eV) of metal atoms, we propose an innovative idea of electron e$^-$ (hole h$^+$) pairing bridged by oxygen O (metal M) atoms, i.e., the ionic-bond-driven $\mathbf{e^--O-e^-}$ ($\mathbf{h^+-M-h^+}$) itinerant Cooper pairing formed at pseudogap temperature $T^*>T_c$, by following the principle of "tracing electron footprints to explore pairing mechanisms" and by standing on the solid foundation of chemical-bond$\rightarrow$structure$\rightarrow$property relationship. It is applicable to cuprates, nickelates, iron-based and other new ionic superconductors. Its correctness and universality are confirmed by 32 diverse experimental evidences, especially, the STM image in the CuO$_2$ plane combining with the small pair size. Any other sub-eV and covalent-binding pairing mechanisms would be doubtful. Our findings, which provide the missing link between ionic bonding and superconductivity, resolve a 40-year puzzle and validate the feasibility of room-temperature carrier-pairing in ionic superconductors. We further create a new theoretical framework rooted in our universal $\mathbf{e^--O-e^-}$ ($\mathbf{h^+-M-h^+}$) picture with the strongest pairing strength and Bose-Einstein condensation, which opens a new avenue for understanding high-$T_c$ mechanism and brings the dream of room-temperature superconductivity one step closer.

It has recently been proposed that all achiral non-centrosymmetric crystals host so-called Kramers nodal lines, which are doubly degenerate band crossings connecting time-reversal invariant momenta in the Brillouin zone that arise due to spin-orbit coupling. When Kramers nodal lines intersect the Fermi level, they form exotic three-dimensional Fermi surfaces which is certain configurations can be fully described by two-dimensional massless Dirac fermions. These Fermi surfaces are predicted to realize a quantized optical conductivity with multiple quantized levels a large light- and field-induced anomalous Hall effect. However, until now, no Kramers nodal line metal with such unconventional Fermi surfaces has been experimentally observed. Here, we extend the search for Kramers nodal line metals beyond the previously considered case in which the Fermi surfaces enclose a single time-reversal invariant momentum. Using angle-resolved photoelectron spectroscopy measurements and ab-initio calculations, we present evidence that the 3R polytypes of TaS$_2$ and NbS$_2$ are Kramers nodal line metals with open Octdong and Spindle-torus Fermi surfaces, respectively. We show that by reducing the band filling, a transition between these two configurations can be observed. Moreover, our data suggests a naturally occurring size quantization effect of inclusions of 3R-TaS$_2$ in commercially available 2H-TaS$_2$ crystals, which could enable the observation of quantized optical conductivity. Finally, since the open Fermi-surfaces encircle two time-reversal invariant momenta each, we predict a phase transition from a Kramers nodal line metal to a conventional metal by strain or uniaxial pressure. Our work establishes the 3R phase of metallic transition metal dichalcogenides as a tunable platform to explore new phenomena expected from exotic Fermi surfaces in Kramers nodal line metals.

Directed wiring diagrams can be used as a composition pattern for composing input/output systems such as Moore machines. In a Moore machine, the input parametrizes an internal state and the internal state defines the output. Because the value of the output is shielded from the input by the internal state, Moore machines can compose by connecting the output of any machine to the input of any other machine. These connections are defined by the trace wires in a directed wiring diagram. Unlike Moore machines, Mealy machines allow the output to be directly and instantaneously affected by the input. In order to compose such machines via directed wiring diagrams, it is necessary to avoid cycles between trace wires in the wiring digram and dependencies of outputs on inputs. To capture these patterns of composition, we introduce an operad of dependent directed wiring diagrams. We then define an algebra of Mealy machines on this operad and an algebra of stock and flow diagrams in which the values of auxiliary variables are parameterized by inputs. Finally, we give a semantics for this algebra of stock and flow diagrams by giving a morphism of algebras from stock and flow diagrams into Mealy machines.

We show that the $\infty$-category of normed algebras in genuine $G$-spectra, as introduced by Bachmann-Hoyois, is modelled by strictly commutative algebras in $G$-symmetric spectra for any finite group $G$. We moreover provide an analogous description of Schwede's ultra-commutative global ring spectra in higher categorical terms. Using these new descriptions, we exhibit the $\infty$-category of ultra-commutative global ring spectra as a partially lax limit of the $\infty$-categories of genuine $G$-spectra for varying $G$, in analogy with the non-multiplicative comparison of Nardin, Pol, and the second author. Along the way, we establish various new results in parametrized higher algebra, which we hope to be of independent interest.

Quantum communication at microwave frequencies has been fundamentally constrained by the susceptibility of microwave photons to thermal noise, hindering their application in scalable quantum networks. Here we demonstrate a thermal-noise-resilient microwave quantum network that establishes coherent coupling between two superconducting qubits through a 4 K thermalized niobium-titanium transmission line. By overcoupling the communication channel to a cold load at 10 mK, we suppress the effective thermal occupancy of the channel to 0.06 photons through radiative cooling -- a two-order-of-magnitude reduction below ambient thermal noise. We then decouple the cold load and rapidly transfer microwave quantum states through the channel while it rethermalizes, achieving a 58.5% state transfer fidelity and a 52.3% Bell entanglement fidelity, both exceeding the classical communication threshold. Our architecture overcomes the temperature-compatibility barrier for microwave quantum systems, providing a scalable framework for distributed quantum computing and enabling hybrid quantum networks with higher-temperature semiconductor or photonic platforms.

Motivated by the work of Boston, Jones and Goksel, we propose a Markov model for the factorisation of post-critically finite (PCF) cubic polynomials f. Using the information encoded in the critical orbits, we define a Markov model for PCF cubic polynomials with combined critical orbits of lengths one and two. Thanks to the work of Anderson et al., a complete list of PCF cubic polynomials over $\mathbb{Q}$ is available. Some of these polynomials have already been studied, such as those with colliding critical orbits analysed by Benedetto et al., which align with our model. We construct groups $M_n$ and prove that they follow our Markov model. These groups $M_n$ are conjectured to contain $\mathrm{Gal}(f^n)$.

The Nested Error Regression Model with High-Dimensional Parameters (NERHDP) is extended to address challenges in small area poverty estimation. A robust and flexible framework is proposed to derive empirical best predictors (EBPs) of small area poverty indicators while accommodating heterogeneity in regression coefficients and sampling variances across areas. To mitigate the computational limitations of the existing algorithm, an efficient estimation procedure is introduced, substantially reducing computation time and enhancing scalability for large datasets. A novel approach for generating area-specific poverty estimates in out-of-sample areas is also developed, improving the reliability of synthetic estimates. Uncertainty is quantified through a parametric bootstrap method specifically tailored to the extended model. Under heterogeneous data-generating scenarios, the proposed method yields lower relative bias and relative root mean squared prediction error than existing approaches. The methodology is further illustrated using data from the 2002 Albania Living Standards Measurement Survey, combined with auxiliary information from the 2001 census, to estimate poverty indicators for 374 municipalities.

Ruzsa's conjecture asserts that any sequence $(a_n)_{n \geq 0}$ of integers that preserves congruences, $\textit{i.e.}$, satisfies $ a_{n+k} \equiv a_n \mod k $, and has the growth condition $\limsup_{n \to +\infty} |a_n|^{1/n} < e$, must be a polynomial sequence. While previous results by Hall, Ruzsa, Perelli, and Zannier have confirmed this conjecture under stricter growth bounds, the general case remains open. In this paper, we establish a new partial result by proving that if in addition the generating series $ f = \sum_{n \geq 0} a_n x^n $ has at most two singular directions at $ x = 0 $, then $(a_n)_{n \geq 0}$ is necessarily a polynomial sequence. Our approach is based on an adaptation of Carlson's method, originally developed for the Pólya-Carlson dichotomy, combined with a refined analysis of Hankel determinants. Specifically, we derive an upper bound on these determinants using Pólya's inequality and a transfinite diameter argument of Dubinin, while a non-Archimedean divisibility condition on Hankel determinants yields a lower bound, ultimately leading to the rationality of $ f $. This confirms that counterexamples to Ruzsa's conjecture, if they exist, must exhibit at least three singular directions.

Ferroelectric HfO$_2$ has emerged as a highly promising material for high-density nonvolatile memory and nanoscale transistor applications. However, the uncertain origin of polarization in HfO$_2$ limits our ability to fully understand and control its ferroelectricity. Ferroelectricity, the emergence of a spontaneous and switchable polarization in solids, is conventionally understood to be governed by unstable structural modes (phonons), arising either directly from an unstable polar phonon or indirectly through coupling of unstable nonpolar phonons with a polar mode. While these 'proper' and 'improper' mechanisms successfully explain ferroelectricity for most systems, they do not encompass all possible phenomena. Here, we present a novel mechanism of 'hybrid-triggered' ferroelectricity, where a polar order emerges through trilinear coupling without any structural instabilities. Our group theoretical analysis starting from a high-symmetry reference structure shows that this mechanism is realized in intensely-debated ferroelectric HfO$_2$, along with quantitative confirmation from first-principles calculations. We also show that dynamical charges in this material are highly unconventional, and a significant contribution to the total polarization arises solely from high-order couplings of nonpolar phonons. These findings underline that even simple crystal structures can host surprisingly complicated interplay between different structural orders, elucidate the origin of ferroelectricity and antiferroelectricity in fluorite-related structures, and provide foundational understanding for designing superior ferroelectric materials.

We define a finite element method for the coupling of Stokes and nonlinear Poisson--Boltzmann equations. The novelty in the formulation is that the coupling from the electric potential to the drag in the momentum balance is rewritten as a weighted advection term. Using Banach's contraction principle, the Babuška--Brezzi theory, and the Minty--Browder theorem, we show that the governing equations have a unique weak solution. We also show that the discrete problem is well-posed, establish Céa estimates, and derive convergence rates. We exemplify the properties of the proposed scheme via some numerical experiments showcasing convergence and applicability in the study of electro-osmotic flows in micro-channels.

Let $f$ be a holomorphic Hecke cusp form of weight $k$ for $\mathrm{SL}_2(\mathbb{Z})$, and let $(λ_f(n))_{n\geq1}$ denote its sequence of Hecke eigenvalues. We compute the first and second moments of the sums $S(x,f)=\sum_{x\leq n\leq 2x}λ_f(n)$, on average over forms $f$ of large weight $k$, in the regime where the length of the sums $x$ is smaller than $k^2$. We observe transitions in the size of the sums when $x\approx k$ and $x\approx k^2$. In subsequent work (part II), it will be shown that once $x$ is larger than $k^2$ (where the latter transition occurs), the average size of the sums $S(x,f)$ becomes dramatically smaller.

Despite the transmission efficiency gains of semantic communication (SemCom) over traditional methods, most existing SemCom schemes still operate at a fixed transmission rate regardless of channel conditions and transmitted content, resulting in wasted resources in favorable channels and degraded performance in harsh channels. To address this issue, we propose a novel SemCom framework that incorporates an entropy-and-channel-aware adaptive rate control mechanism over MIMO Rayleigh fading channels. Specifically, we embed a joint representation of the channel state information (CSI) and the signal-to-noise ratio (SNR) into both the semantic encoder and decoder, thereby realizing channel-aware semantic coding and decoding. Moreover, the proposed method jointly exploits the CSI, the SNR, the feature maps, and their 2D entropy via two policy networks to selectively transmit only a subset of feature maps and, within each selected feature map, only a subset of symbols. Thereby, it achieves finer-grained adaptive rate control than existing methods. At the receiver, leveraging the strong visual understanding capability of multimodal large language models (MLLMs), we deploy the lightweight visual encoder (InternViT-300M) of the pre-trained InternVL3.5 model to compensate for discarded feature maps and symbols, and we fine-tune InternViT using low-rank adaptation (LoRA) for parameter-efficient training. Experimental results show that, with a carefully designed channel-aware loss function, our system automatically allocates more communication resources under poor channels to enhance task performance while reducing resource usage under favorable channels and maintaining high task performance.

In semiconductor hole spin qubits, low magnetic field ($B$) operation extends the coherence time ($T_\mathrm{2}^*$) but proportionally reduces the gate speed. In contrast, singlet-triplet (ST) qubits are primarily controlled by the exchange interaction ($J$) and can thus maintain high gate speeds even at low $B$. However, a large $J$ introduces a significant charge component to the qubit, rendering ST qubits more vulnerable to charge noise when driven. Here, we demonstrate a highly coherent ST hole spin qubit in germanium, operating at both low $B$ and low $J$. By modulating $J$, we achieve resonant driving of the ST qubit, obtaining an average gate fidelity of $99.68\%$ and a coherence time of $T_\mathrm{2}^*=1.9\,μ$s. Moreover, by applying the resonant drive continuously, we realize a dressed ST qubit with a tenfold increase in coherence time ($T_\mathrm{2ρ}^*=20.3\,μ$s). Frequency modulation of the driving signal enables universal control, with an average gate fidelity of $99.63\%$. Our results demonstrate the potential for extending coherence times while preserving high-fidelity control of germanium-based ST qubits, paving the way for more efficient operations in semiconductor-based quantum processors.

Let $γ_{n}= O (\log^{-c}n)$ and let $ν$ be the infinite product measure whose $n$-th marginal is Bernoulli$(1/2+γ_{n})$. We show that $c=1/2$ is the threshold, above which $ν$-almost every point is simply Poisson generic in the sense of Peres-Weiss, and below which this can fail. This provides a range in which $ν$ is singular with respect to the uniform product measure, but $ν$-almost every point is simply Poisson generic.

Oncolytic viral therapy (OVT) is an emerging precision therapy for aggressive and recurrent cancers. However, its clinical efficacy is hindered by the complexity of tumor-virus-immune interactions and the lack of predictive models for personalized treatment. This study develops a data-driven, AI-powered computational model combining time-delayed Generalized Lotka-Volterra equations with advanced optimization algorithms, including Genetic Algorithms, Differential Evolution, and Reinforcement Learning, to optimize OVT oscillations' growth and damping. We hypothesize that the model can provide accurate, real-time predictions of OVT responses while identifying key biomarkers to enhance therapeutic efficacy. The model demonstrates strong predictive accuracy, achieving mean squared error (MSE) < 0.02 and R-squared > 0.82. It also identifies experimentally validated biomarkers such as TNF, NFkB, CD81, TRAF2, IL18, and BID, among other inflammatory cytokines and extracellular matrix reconstruction factors, despite being causally agnostic and unaware of specific experimental conditions or therapeutic combinations. Gene set enrichment analysis confirmed these biosignatures as critical predictors of tumor progression and indicated that photodynamic therapy activates immune responses similar to those elicited by combined OVT and immune checkpoint inhibitors. This hybrid model represents a significant step toward precision oncology and computational medicine, enabling longitudinal, adaptive treatment regimens and developing targeted immunotherapies based on molecular signatures, potentially improving patient outcomes.

In the context of voting with ranked ballots, an important class of voting rules is the class of margin-based rules (also called pairwise rules). A voting rule is margin-based if whenever two elections generate the same head-to-head margins of victory or loss between candidates, the voting rule yields the same outcome in both elections. Although this is a mathematically natural invariance property to consider, whether it should be regarded as a normative axiom on voting rules is less clear. In this paper, we address this question for voting rules with any kind of output, whether a set of candidates, a ranking, a probability distribution, etc. We prove that a voting rule is margin-based if and only if it satisfies some axioms with clearer normative content. A key axiom is what we call Preferential Equality, stating that if two voters both rank a candidate $x$ immediately above a candidate $y$, then either voter switching to rank $y$ immediately above $x$ will have the same effect on the election outcome as if the other voter made the switch, so each voter's preference for $y$ over $x$ is treated equally.

The Explorer-Director game, first introduced by Nedev and Muthukrishnan (2008), simulates a Mobile Agent exploring a ring network with an inconsistent global sense of direction. Two players, the Explorer and the Director, jointly control a token's movement on the vertices of a graph $G$ with initial location $v$. Each turn, the Explorer calls any valid distance, $d$, aiming to maximize the number of vertices the token visits, and the Director moves the token to any vertex distance $d$ away aiming to minimize the number of visited vertices. The game ends when no new vertices can be visited, assuming optimal play, and we denote the total number of visited vertices by $f_d(G,v)$. Here we study a variant where, if the token is on vertex $u$, the Explorer is allowed to select any valid \emph{path length}, $\ell$, and the Director now moves the token to any vertex $v$ such that $G$ contains a $uv$ path of length $\ell$. The corresponding parameter is $f_p(G,v)$. In this paper, we explore how far apart $f_d(G,v)$ and $f_p(G,v)$ can be, proving that for any $n$ there are graphs $G$ and $H$ with $f_p(G,v)-f_d(G,v)>n$ and $f_d(H,v)-f_p(H,v)>n$.

Rapid Serial Visual Presentation (RSVP)-based Brain-Computer Interfaces (BCIs) facilitate high-throughput target image detection by identifying event-related potentials (ERPs) evoked in EEG signals. The RSVP-BCI systems effectively detect single-class targets within a stream of images but have limited applicability in scenarios that require detecting multiple target categories. Multi-class RSVP-BCI systems address this limitation by simultaneously identifying the presence of a target and distinguishing its category. However, existing multi-class RSVP decoding algorithms predominantly rely on single-modality EEG decoding, which restricts their performance improvement due to the high similarity between ERPs evoked by different target categories. In this work, we introduce eye movement (EM) modality into multi-class RSVP decoding and explore EEG and EM fusion to enhance decoding performance. First, we design three independent multi-class target RSVP tasks and build an open-source dataset comprising EEG and EM signals from 43 subjects. Then, we propose the Multi-class Target RSVP EEG and EM fusion Network (MTREE-Net) to enhance multi-class RSVP decoding. Specifically, a dual-complementary module is proposed to strengthen the differentiation of uni-modal features across categories. To improve multi-modal fusion performance, we adopt a dynamic reweighting fusion strategy guided by theoretically derived modality contribution ratios. Furthermore, we reduce the misclassification of non-target samples through knowledge transfer between two hierarchical classifiers. Extensive experiments demonstrate the feasibility of integrating EM signals into multi-class RSVP decoding and highlight the superior performance of MTREE-Net compared to existing RSVP decoding methods. The proposed MTREE-Net and open-source dataset provide a promising framework for developing practical multi-class RSVP-BCI systems.

Rapid Serial Visual Presentation (RSVP)-based Brain-Computer Interface (BCI) is an effective technology used for information detection by detecting Event-Related Potentials (ERPs). The current RSVP decoding methods can perform well in decoding EEG signals within a single RSVP task, but their decoding performance significantly decreases when directly applied to different RSVP tasks without calibration data from the new tasks. This limits the rapid and efficient deployment of RSVP-BCI systems for detecting different categories of targets in various scenarios. To overcome this limitation, this study aims to enhance the cross-task zero-calibration RSVP decoding performance. First, we design three distinct RSVP tasks for target image retrieval and build an open-source dataset containing EEG signals and corresponding stimulus images. Then we propose an EEG with Language-Image Prior fusion Transformer (ELIPformer) for cross-task zero-calibration RSVP decoding. Specifically, we propose a prompt encoder based on the language-image pre-trained model to extract language-image features from task-specific prompts and stimulus images as prior knowledge for enhancing EEG decoding. A cross bidirectional attention mechanism is also adopted to facilitate the effective feature fusion and alignment between the EEG and language-image features. Extensive experiments demonstrate that the proposed model achieves superior performance in cross-task zero-calibration RSVP decoding, which promotes the RSVP-BCI system from research to practical application.