Quantum phase estimation is a core task in quantum technologies ranging from metrology to quantum computing, where it appears as a key subroutine in various algorithms. Here, we quantitatively connect the performance of phase estimation protocols with quantum coherence. To achieve this, we construct and characterize resource theories of quantum networks that cannot generate coherence. Given multiple copies of a unitary encoding an unknown phase and access to a fixed coherent state, we estimate the phase using such networks. For a unified and general approach, we assess the quality of the estimate using a generic cost function that penalizes deviations from the true value. We determine the minimal average cost that can be achieved in this manner and explicitly derive optimal protocols. From this, we construct a family of coherence measures that directly connect a state's coherence with its value for phase estimation, demonstrating that every bit of coherence helps. This establishes coherence as a resource that quantifies the performance of phase estimation, and, thus, of any quantum technology relying on it as a subroutine.

The theory of a two-level $η$-Hermitian Hamiltonian with $\mathcal{PT}$ symmetry is reviewed and extended to include open system dynamics. A first-principles derivation of the generalized Gorini-Kossakowski-Sudarshan-Lindblad master equation appropriate for a $\mathcal{PT}-$symmetric Hamiltonian is presented. Inspired by a simple light matter interaction open system model, information theoretic quantities like a non-Markovian witness and fidelity are calculated for the $\mathcal{PT-}$symmetric Hamiltonian, and the results are compared with their corresponding two-level Hermitian counterparts. The nature of entanglement between two $\mathcal{PT-}$symmetric and Hermitian open quantum systems is calculated, and the contrast observed.

We study an agency problem between a leader (the principal) seeking to design an optimal incentive scheme to a follower (the agent) to increase the value of a risky project subjected to accidents and volatility uncertainty. The agency problem is formulated as a max-min bilevel stochastic control problem with accidents and ambiguity. We show that the problem of the follower is reduced to solve a second order BSDE with jumps, reducing the problem of the leader to solve an integro-partial Hamilton-Jacobi-Bellman-Isaacs (HJBI) equation. By extending stochastic Perron's method to our setting, we obtain viscosity sub- and supersolution envelopes for the Principal's integro-HJBI equation. Under an additional comparison principle in a suitable polynomial growth class, these envelopes coincide and the Principal's value is identified with the unique viscosity solution. The holding company seeks to design an optimal incentive scheme to mitigate these losses. In response, the subsidiary selects an optimal cybersecurity investment strategy, modeled through a stochastic epidemiological SIR (Susceptible-Infected-Recovered) framework. The cyber threat landscape is captured through an L-hop risk framework with two primary sources of risk, internal risk propagation via the contagion parameters in the SIR model, and external cyberattacks from a malicious external hacker. The uncertainty and adversarial nature of the hacking lead to consider a robust stochastic control approach that allows for increased volatility and ambiguity induced by cyber incidents. We illustrate our results with numerical simulations showing how the contracting mechanism enhances the quality of a cluster under cyber threats.

We use muon spin rotation/relaxation/resonance ($μ$SR) to investigate the magnetic properties of niobium pentoxide (Nb$_2$O$_5$) and tantalum pentoxide (Ta$_2$O$_5$) thin films. In both oxides, we observe a magnetic response at the lowest available temperature of 2.8 K. This response appears to be structurally dependent: thermally oxidized Ta$_2$O$_5$ with low crystallinity demonstrates suppressed magnetism, while fully amorphous Ta$_2$O$_5$ demonstrates local static magnetism. In contrast, amorphous Nb$_2$O$_5$ is dominated by magnetic fluctuations and is strongly magnetically disordered compared to Ta$_2$O$_5$. Our results suggest that these fundamental differences in the magnetism of Ta and Nb oxides could explain the performance limitations in superconducting qubits and resonators.

Quality-Diversity (QD) algorithms seek to discover diverse, high-performing solutions across a behavior space, in contrast to conventional optimization methods that target a single optimum. Adversarial problems present unique challenges for QD approaches, as the competing nature of opposing sides creates interdependencies that complicate the evolution process. Existing QD methods applied to such scenarios typically fix one side, constraining the open-endedness. We present Generational Adversarial MAP-Elites (GAME), a coevolutionary QD algorithm that evolves both sides by alternating which side is evolved at each generation. By integrating a vision embedding model (VEM), our approach eliminates the need for domain-specific behavior descriptors and instead operates on video. We validate GAME across three distinct adversarial domains: a multi-agent battle game, a soft-robot wrestling environment, and a deck building game. We validate that all its components are necessary, that the VEM is effective in two different domains, and that GAME finds better solutions than one-sided QD baselines. Our experiments reveal several evolutionary phenomena, including arms race-like dynamics, enhanced novelty through generational extinction, and the preservation of neutral mutations as crucial stepping stones toward the highest performance. While GAME successfully illuminates all three adversarial problems, its capacity for truly open-ended discovery remains constrained by the nature of the search spaces used in this paper. These findings show GAME's broad applicability and highlight opportunities for future research into open-ended adversarial coevolution. Code and videos are available at: https://github.com/Timothee-ANNE/GAME

Advanced sound zone control (SZC) techniques typically rely on massive multi-channel loudspeaker arrays to create high-contrast personal sound zones, making single-loudspeaker SZC seem impossible. In this Letter, we challenge this paradigm by introducing the multi-carrier parametric loudspeaker (MCPL), which enables SZC using only a single loudspeaker. In our approach, distinct audio signals are modulated onto separate ultrasonic carrier waves at different frequencies and combined into a single composite signal. This signal is emitted by a single-channel ultrasonic transducer, and through nonlinear demodulation in air, the audio signals interact to virtually form multi-channel outputs. This novel capability allows the application of existing SZC algorithms originally designed for multi-channel loudspeaker arrays. Simulations validate the effectiveness of our proposed single-channel MCPL, demonstrating its potential as a promising alternative to traditional multi-loudspeaker systems for achieving high-contrast SZC. Our work opens new avenues for simplifying SZC systems without compromising performance.

Radio-frequency (RF) sensing underpins applications ranging from radar and wireless communication to biomedical and quantum measurement, where detection sensitivity at low signal-to-noise ratio (SNR) directly limits the achievable range, resolution, and information capacity. Machine learning has been widely applied to enhance sensing performance, but predominantly as post-detection analysis of already-acquired data. At low SNR, however, the information missing from acquired data cannot be recovered downstream, making pre-detection processing essential. Here we introduce microring perceptron (MiRP) sensing, a framework that exploits RF-photonic transduction in a microring resonator, where a programmable optical pump performs three-wave mixing to implement a learned mapping from the incoming RF signal to optical feature signals prior to detection. The transducer front end and digital neural-network back end are jointly optimized within a single end-to-end training pipeline, allowing the sensing system to learn an encoding that preserves task-relevant information through detection. Across benchmark tasks, MiRP sensing achieves substantially higher task performance than conventional processing at low input RF power levels where detection noise dominates. The algorithmic gain reported here offers an orthogonal axis of improvement that composes with, and amplifies the impact of, existing and future advances along complementary dimensions, including hardware efficiency and quantum-enhanced optical sensing.

When two topologically trivial and nontrivial systems are brought together, a localized energy state is formed at the interface. For crystalline quantum and classical systems, their topology can be determined by studying the eigenmode symmetries at high symmetry points (HSPs) in the Brillouin zone. As electromagnetic systems are usually leaky, their radiations retain the eigenmode information, thus providing a means for probing the band topology. Here, we formulate the far-field characteristics of the eigenmodes at HSPs in 2D square lattice plasmonic systems and reveals, unlike the conventional tight-binding model, several polarization-dependent band inversions occur at theΓand X points, rendering subtle changes in their band topology. In particular, by carefully tuning the system geometry to facilitate trivial and non-trivial phases, polarization selective 0D and 1D edge states that possess distinct field symmetries are realized. The evolution of 0D or 1D edge state depends on the degree of bulk-edge overlapping. We perform angle- and polarization-resolved diffraction spectroscopy on 2D Au plasmonic nanohole arrays to verify the theory and observe such states. Our study demonstrates the applicability of simple far-field technique for diagnosing the band topology of various crystalline classical systems in electromagnetics and acoustics.

We provide an open-access dataset of phasor & waveform measurement units (PMUs/WMUs) of a real-world electrical distribution network. The network consists of diverse sets of generation resources (including solar panels, fuel cells, natural gas generators, and utility interconnections), loads (including large-scale electric vehicle charging, data centers, central cooling, offices), topology changes (such as line outages and load transfers), as well as a mixture of single- and three-phase networks. We describe a densely deployed PMU sensor network in a distribution grid, in which all buses with non-zero power injections are measured. This approach enables a range of applications such as state estimation, system identification, power flow optimization, and feedback control, several of which are discussed in this paper. Additionally, we provide a synchronized waveform dataset which allows the analysis of harmonics, transient events, dynamic grid impedance, and stability. Data collection started in 2023 while new data is generated continuously and made available online. A characterization of measurement error is provided. Finally, we provide circuit topology and parameters as a part of the dataset. Together, the circuit and timeseries data offer an opportunity for researchers to develop and test algorithms on a real-world system.

We analyze electroencephalography (EEG) signals using the ordinal pattern framework to investigate whether different human brain states can be distinguished based on the disorder of EEG dynamics. Rather than analyzing raw EEG signals, we focus on the principal mode of EEG phase dynamics, reflecting anterior-posterior information flow, and quantify disorder using permutation entropy. We apply this to two datasets: (i) EEG recordings from a general anesthesia protocol, and (ii) EEG recordings acquired in the resting state from healthy control subjects and individuals with inattentive-type attention deficit hyperactivity disorder (ADHD), including eyes-open and eyes-closed conditions. We find that the permutation entropy distributions exhibit a clear dependence on brain state. In particular, conscious, inattentive-type ADHD, and eyes closed conditions show lower mean values and larger standard deviations of permutation entropy. To evaluate the discriminative power of permutation entropy, we train classification models using permutation entropy as an input feature. The results show that the distinction between conscious and unconscious states can be reliably captured in the general-anesthesia dataset. In the resting-state dataset, eyes-open and eyes-closed conditions are distinguishable, whereas classification between control and inattentive-type ADHD groups does not show clear separability. This indicates that information not captured in ordinal patterns, such as the original time-series values, may play a more crucial role in detecting inattentive-type ADHD. Our findings demonstrate that permutation entropy derived from EEG phase dynamics provides an effective indicator of brain states, particularly in relation to consciousness, while also highlighting its limitations for identifying individuals with inattentive-type ADHD.

Dual methods are useful for distributed optimization because they allow agent-level subproblems to be solved in parallel. However, achieving primal feasibility with dual methods is a challenge; it can take many iterations to find prices that recover primal feasibility, and even with optimal dual prices primal feasibility is not guaranteed unless special conditions like strict convexity hold. To address this limitation, we propose a simple primal recovery method, multiple approximate-response agents (MARA), that is able to rapidly reduce primal infeasibility, tolerating some degree of suboptimality. The method is agnostic to how dual prices are computed, so MARA can be applied to enhance any dual algorithm. Rather than returning a single primal response to each price query, MARA requires agents to generate multiple primal responses, each of which has bounded suboptimality. Because these multiple responses can be computed in parallel, there is no increase in the wall-clock time of the underlying dual algorithm. MARA then constructs a convex combination of the multiple responses by minimizing the sum of the primal and complementary slackness residuals to produce a high-quality primal solution. Tests of MARA using both a price localization method and a dual subgradient method show that it typically converges to a feasible, near-optimal solution in a few tens of iterations. Moreover, hyperparameters of MARA can be flexibly tuned to control the trade-off among speed, computational budget, and degree of suboptimality of the feasible solutions.

In this paper, we investigate the computational complexity of the knapsack problem and subset sum problem for the following tropical algebraic structures. We consider the semigroup of square matrices of size $k \times k$ with non-negative entries over the max-plus algebra and the semigroup square matrices of size $k \times k$ with positive entries over the max-times algebra. We prove that the knapsack problem and subset sum problem for these structures are $\textsf{NP}$-complete. We demonstrate that there are pseudo-polynomial algorithms to solve these problems. Also, we show that for the latter semigroup, there are polynomial generic algorithms to solve the knapsack problem and the subset sum problem.

Quantum squeezed states, with reduced quantum noise, have been widely utilized in quantum sensing and quantum error correction applications. However, generating and manipulating these nonclassical states with a large squeezing degree typically requires strong nonlinearity, which inevitably induces additional decoherence that diminishes the overall performance. Here, we demonstrate the generation and amplification of squeezed states in a superconducting microwave cavity with weak Kerr nonlinearity. By subtly engineering an off-resonant microwave drive, we observe cyclic dynamics of the quantum squeezing evolution for various Fock states |N> with N up to 6 in displaced frame of the cavity. Furthermore, we deterministically realize quantum squeezing amplification by alternately displacing the Kerr oscillator using the Trotterization technique, achieving a maximum squeezing degree of 14.6 dB and squeezing rate of 0.28 MHz. Our hardware-efficient displacement-enhanced squeezing operations provide an alternative pathway for generating large squeezed states, promising potential applications in quantum-enhanced sensing and quantum information processing.

We study uncertainty quantification for partial differential equations subject to domain uncertainty. We parameterize the random domain using the model recently considered by Chernov and Le (2024) as well as Harbrecht, Schmidlin, and Schwab (2024) in which the input random field is assumed to belong to a Gevrey smoothness class. This approach has the advantage of being substantially more general than models which assume a particular parametric representation of the input random field such as a Karhunen-Loeve series expansion. We consider both the Poisson equation as well as the heat equation and design randomly shifted lattice quasi-Monte Carlo (QMC) cubature rules for the computation of the expected solution under domain uncertainty. We show that these QMC rules exhibit dimension-independent, essentially linear cubature convergence rates in this framework. In addition, we complete the error analysis by taking into account the approximation errors incurred by dimension truncation of the random input field and finite element discretization. Numerical experiments are presented to confirm the theoretical rates.

We study memory-bounded algorithms for the $k$-secretary problem. The algorithm of Kleinberg (SODA 2005) achieves an optimal competitive ratio of $1 - O(1/\sqrt{k})$, yet a straightforward implementation requires $Ω(k)$ memory. Our main result is a $k$-secretary algorithm that matches the optimal competitive ratio using $O(\log k)$ words of memory. We prove this result by establishing a general reduction from $k$-secretary to (random-order) quantile estimation, the problem of finding the $k$-th largest element in a stream. We show that a quantile estimation algorithm with an $O(k^α)$ expected error (in terms of the rank) gives a $(1 - O(1/k^{1-α}))$-competitive $k$-secretary algorithm with $O(1)$ extra words. We then introduce a new quantile estimation algorithm that achieves an $O(\sqrt{k})$ expected error bound using $O(\log k)$ memory. Of independent interest, we give a different algorithm that uses $O(\sqrt{k})$ words and finds the $k$-th largest element exactly with high probability, generalizing a result of Munro and Paterson (1980).

We propose a unified model for the three Standard Model (SM) gauge symmetries and $SU(3)$ family symmetry based on $SO(16)$ grand unified gauge symmetry on six-dimensional (6D) spacetime. In this model, three chiral generations of quarks and leptons are unified into a 6D Weyl fermion in the spinor representation of $SO(16)$. The 6D $SO(16)$ gauge anomaly is canceled by the vectorlike nature of the model, and the 4D gauge anomalies are canceled by introducing suitable 4D localized fermions at the fixed point. The 4D gauge coupling constant of $SO(16)$ has the property of becoming weaker at high energies.

In this paper, we explore a taxonomy of connectivity for space-like structures. It is inspired by isolating posets of connected pieces of a space and examining its embedding in the ambient space. The taxonomy includes in its scope all standard notions of connectivity in point-set and point-free contexts, such as connectivity in graphs and hypergraphs (as well as k-connectivity in graphs), connectivity and path-connectivity in topology, and connectivity of elements in a frame.

We have newly developed a Cockcroft-Walton (CW) multiplier that can be used in a gas time projection chamber (TPC). A TPC requires a high voltage to form an electric field that drifts ionization electrons. Supplying the high voltage from outside the pressure vessel requires a dedicated high-voltage feedthrough. An alternative approach is to generate the high voltage inside the pressure vessel with a relatively low voltage introduced from outside. A CW multiplier can convert a low AC voltage input to a high DC voltage output, making it suitable for this purpose. We have integrated a CW multiplier into the AXEL (A Xenon ElectroLuminescence detector), a high pressure xenon gas TPC to search for neutrinoless double beta decay of $^{136}$Xe. It uses silicon photomultipliers to detect the ionization electrons through elecrtoluminescence, making it strong against electronic noise. Operation of the CW multiplier was successfully demonstrated; the TPC was operated for 40 days at 6.8 bar, and an energy resolution as high as (0.67 $\pm$ 0.08) % (FWHM) at 2615 keV was obtained.

In this paper, we study involutive non-degenerate set-theoretic solutions of the Yang-Baxter equation with regular displacement group. In particular, we completely describe the blocks of imprimitivity and the congruences of the irretractable ones, that we show belonging to the class of the latin solutions. Among these solutions, we characterise the simple ones having nilpotent permutation group. A more precise description involving the First Weyl Algebra will be provided when the displacement group is abelian and normal in the total permutation group, and we enumerate and classify the simple ones having minimal size $p^p$, for an arbitrary prime number $p$. Finally, we illustrate our results by some examples.

Gamma-Ray Bursts (GRBs), observed at high-z, are probes of the evolution of the Universe and can be used as cosmological tools. Thus, we need correlations with small dispersion among key parameters. To reduce such a dispersion, we mitigate gaps in light curves (LCs), including the plateau region, key to building the two-dimensional Dainotti relation between the end time of plateau emission (Ta) and its luminosity (La). We reconstruct LCs using nine models: Multi-Layer Perceptron (MLP), Bi-Mamba, Fourier Transform, Gaussian Process-Random Forest Hybrid (GP-RF), Bidirectional Long Short-Term Memory (Bi-LSTM), Conditional GAN (CGAN), SARIMAX-based Kalman filter, Kolmogorov-Arnold Networks (KANs), and Attention U-Net. These methods are compared to the Willingale model (W07) over a sample of 521 GRBs. MLP and Attention U-Net outperform other methods, with MLP reducing the plateau parameter uncertainties by 37.2% for log Ta, 38.0% for log Fa, and 41.2% for alpha (the post-plateau slope in the W07 model), achieving the lowest 5-fold cross-validation (CV) mean squared error (MSE) of 0.0275. Attention U-Net achieved the lowest uncertainty of parameters, a 37.9% reduction in log Ta, a 38.5% reduction in log Fa and a 41.4% reduction in alpha, but with a higher MSE of 0.134. Although Attention U-Net achieves the largest uncertainty reduction, the MLP attains the lowest test MSE while maintaining comparable uncertainty performance, making it the more reliable model. The other methods yield MSE values ranging from 0.0339 to 0.174. These improvements in parameter precision are needed to use GRBs as standard candles, investigate theoretical models, and predict GRB redshifts through machine learning.

We identify several classes of monomial ideals that possess minimal generalized Barile-Macchia resolutions. These classes of ideals include generic monomial ideals, monomial ideals with linear quotients, and edge ideals of hypertrees. We also characterize connected unicyclic graphs whose edge ideals are bridge-friendly and, in particular, have minimal Barile-Macchia resolutions. Barile-Macchia and generalized Barile-Macchia resolutions are cellular resolutions and special types of Morse resolutions.

This paper presents a learning-based current calculation model to achieve power-optimal magnetic-field interaction for multi-agent formation and attitude control. In aerospace engineering, electromagnetic coils are referred to as magnetorquer (MTQ) coils and used as satellite attitude actuators in Earth's orbit and for long-term formation and attitude control. This study derives a unique, continuous, and power-optimal current solution via sequential convex programming and approximates it using a multilayer perceptron model. The effectiveness of our strategy was demonstrated through numerical simulations and experimental trials on the formation and attitude control.

So far, the striking sign reversal in the near-ambient slope of the gap temperature dependence of colloidal CsPbCl3 perovskite nanocrystals (NCs) compared to its Br counterpart, remains unresolved. Pure bromide NCs exhibit a linear gap increase with increasing temperature, to which thermal expansion and electron-phonon interaction equally contribute. In contrast, the temperature slope for the chlorine compound gap is outspoken negative. By combining temperature and pressure-dependent photoluminescence on a series of CsPb(Br1-xClx)3 NCs, we unravel the origin of such inversion. Responsible is solely the electron-phonon interaction, undergoing a sudden change in sign and magnitude due to activation of an anomalous electron-phonon coupling mechanism linked to vibrational modes characterized by synchronous octahedral tilting and Cs rattling. This takes place in the shrunken orthorhombic NC lattice for Cl concentrations exceeding ca. 40%. We have thus clarified a puzzling result directly impacting the optoelectronic properties of lead halide perovskite NCs.

A strong $s$-blocking set in a projective space is a set of points that intersects each codimension-$s$ subspace in a spanning set of the subspace. We present an explicit construction of such sets in a $(k - 1)$-dimensional projective space over $\mathbb{F}_q$ of size $O_s(q^s k)$, which is optimal up to the constant factor depending on $s$. This also yields an optimal explicit construction of affine blocking sets in $\mathbb{F}_q^k$ with respect to codimension-$(s+1)$ affine subspaces, and of $s$-minimal codes. Our approach is motivated by a recent construction of Alon, Bishnoi, Das, and Neri of strong $1$-blocking sets, which uses expander graphs with a carefully chosen set of vectors as their vertex set. The main novelty of our work lies in constructing specific hypergraphs on top of these expander graphs, where tree-like configurations correspond to strong $s$-blocking sets. We also discuss some connections to size-Ramsey numbers of hypergraphs, which might be of independent interest.

In this research, we quantify an inflow of women into science in the past three decades. Structured Big Data allow us to estimate the contribution of women scientists to the growth of science by disciplines (N = STEMM 14 disciplines) and over time (1990-2023). A monolithic segment of STEMM science emerges from this research as divided between the disciplines in which the growth was powerfully driven by women - and the disciplines in which the role of women was marginal. There are four disciplines in which 50% of currently publishing scientists are women; and five disciplines in which more than 50% of currently young scientists are women. But there is also a cluster of four highly mathematized disciplines (MATH, COMP, PHYS, and ENG) in which the growth of science is only marginally driven by women. Digital traces left by scientists in their publications indexed in global datasets open two new dimensions in large-scale academic profession studies: time and gender. The growth of science in Europe was accompanied by growth in the number of women scientists, but with powerful cross-disciplinary and cross-generational differentiations. We examined the share of women scientists coming from ten different age cohorts for 32 European and four comparator countries (the USA, Canada, Australia, and Japan). Our study sample was N = 1,740,985 scientists (including 39.40% women scientists). Three critical methodological challenges of using structured Big Data of the bibliometric type were discussed: gender determination, academic age determination, and discipline determination.

Marine Protected Areas (MPAs) have been established globally to conserve marine resources. Given their maintenance costs and impact on commercial fishing, it is critical to evaluate their effectiveness to support future conservation. In this paper, we use data collected from the Australian coast to estimate the effect of MPAs on biodiversity. Environmental studies such as these are often observational, and processes of interest exhibit spatial dependence, which presents challenges in estimating the causal effects. Spatial data can also be subject to preferential sampling, where the sampling locations are related to the policy and the response variable, further complicating inference and prediction. To address these challenges, we propose a spatial causal inference method that simultaneously accounts for unmeasured spatial confounders in both the sampling process and the treatment allocation. We prove the identifiability of key parameters in the model and the consistency of the posterior distributions of those parameters. We show via simulation studies that the causal effect of interest can be reliably estimated under the proposed model. The proposed method is applied to assess the effect of MPAs on fish biomass. We find evidence of preferential sampling and that properly accounting for this source of bias impacts the estimate of the causal effect.

This paper is concerned with a comparison principle for viscosity solutions to Hamilton-Jacobi (HJ), -Bellman (HJB), and -Isaacs (HJI) equations for general classes of partial integro-differential operators. Our approach innovates in three ways: (1) We reinterpret the classical doubling-of-variables method in the context of second-order equations by casting the Ishii-Crandall Lemma into a test function framework. This adaptation allows us to effectively handle non-local integral operators, such as those associated with Lévy processes. (2) We translate the key estimate on the difference of Hamiltonians in terms of an adaptation of the probabilistic notion of couplings, providing a unified approach that applies to differential, difference, and integral operators. (3) We strengthen the sup-norm contractivity resulting from the comparison principle to one that encodes continuity in the strict topology. We apply our theory to a variety of examples, in particular, to second-order differential operators and, more generally, generators of spatially inhomogeneous Lévy processes.

Confidence estimates are often "detection-like" - driven by positive evidence in favour of a decision. This empirical observation has been interpreted as showing that human metacognition is limited by biases or heuristics. Here, we show that Bayesian confidence estimates also exhibit heightened sensitivity to decision-congruent evidence in higher-dimensional signal detection theoretic spaces, leading to detection-like confidence criteria. This effect is due to a nonlinearity induced by normalisation of confidence by a large number of unchosen alternatives. Our analysis suggests that detection-like confidence is rational when participants consider a greater number of hypotheses than assumed by the experimenter. Further, we show that a similar dimensionality-driven mechanism can give rise to and modulate the strength of the positive evidence biases in convolutional neural networks, linking our signal detection theoretic analysis to confidence behaviour in artificial systems.

All-Solution Satisfiability (AllSAT) and its extension, All-Solution Satisfiability Modulo Theories (AllSMT), have become more relevant in recent years, mainly in formal verification and artificial intelligence applications. The goal of these problems is the enumeration of all satisfying assignments of a formula (for SAT and SMT problems, respectively), making them useful for test generation, model checking, and probabilistic inference. Nevertheless, traditional AllSAT algorithms face significant computational challenges due to the exponential growth of the search space and inefficiencies caused by blocking clauses, which cause memory blowups and degrade unit propagation performances in the long term. This paper presents two novel solvers: tabularAllSAT, a projected AllSAT solver, and tabularAllSMT, a projected AllSMT solver. Both solvers combine Conflict-Driven Clause Learning (CDCL) with chronological backtracking to improve efficiency while ensuring disjoint enumeration. To retrieve compact partial assignments we propose a novel aggressive implicant shrinking algorithm, compatible with chronological backtracking, to minimize the number of partial assignments, reducing overall search complexity. Furthermore, we extend the solver framework to handle projected enumeration and SMT formulas effectively and efficiently, adapting the baseline framework to integrate theory reasoning and the distinction between important and non-important variables. An extensive experimental evaluation demonstrates the superiority of our approach compared to state-of-the-art solvers, particularly in scenarios requiring projection and SMT-based reasoning.

A problem by Feichtinger, Heil, and Larson asks whether every infinite matrix $A$ with $\sum_{k,l}|A_{kl}| < \infty$ (an equivalent substitute for the Feichtinger algebra) that is positive-semidefinite admits a symmetric rank-one decomposition $A = \sum_k f_k^*\otimes f_k$ with $\sum_k \|f_k\|_{1}^2 < \infty$. In the finite-dimensional setting, we analyze the corresponding quantitative $\ell_1^n$ optimization problem by an exact reformulation as a linear program over measures, derive its dual, and prove strong duality. We then obtain an equivalent adjoint formulation regarding the quality of a convex relaxation. In the infinite-dimensional setting, we first provide a negative answer to this question using a concurrent finite-dimensional result by Bandeira-Mixon-Steinerberger. We further study the collection of operators for which such decomposition exists, showing that they are dense in a suitable topology and invariant under the action of the positive-coefficient analytic Wiener subalgebra. In addition, we give a sufficient condition for successful rank-one decomposition in terms of $2$-summing factorization, and we characterize exactly when $A^{1/2}$ is $2$-summing.