The inherent compositional heterogeneity of multi-principal element alloys (MPEAs) gives rise to complex, spatially varying mechanical fields that cannot be uniquely determined from coarse-grained composition descriptors. This non-uniqueness introduces intrinsically probabilistic structure-property relationships, posing a fundamental challenge to conventional deterministic modeling and machine learning approaches that collapse such mappings into average predictions. Here, we present AlloyVAE, a physics-informed generative framework that learns the full conditional distribution of mechanical fields from microstructural inputs. Built upon a conditional variational autoencoder architecture, the model incorporates learned smoothing operators to enhance functional regularity and a self-consistency mechanism to enforce physical plausibility. Trained on atomistic simulation data, AlloyVAE accurately predicts distributions of residual stress fields from composition and short-range order, and enables the generation of multiple physically consistent realizations under identical input conditions. Beyond forward prediction, the framework supports inverse design by optimizing composition fields to achieve targeted mechanical responses, and is extensible to coupled mappings involving eigenstrain. By capturing one-to-many structure-property relationships in heterogeneous materials, this work establishes a probabilistic paradigm for materials modeling and design, providing a scalable alternative to conventional simulations for navigating high-dimensional compositional spaces.

Translating machine code into human-readable high-level languages is an open research problem in reverse engineering. Despite recent advancements in LLM-based decompilation to C, modern languages like Dart and Swift are unexplored. In this paper, we study the use of small specialized LLMs as an idiomatic decompiler for such languages. Additionally, we investigate the augmentation of training data using synthetic same-language examples, and compare it against adding human-written examples using related-language (Swift -> Dart). We apply CODEBLEU to evaluate the decompiled code readability and compile@k to measure the syntax correctness. Our experimental results show that on a 73-function Dart test dataset (representing diverse complexity levels), our 4B specialized model achieves 71.3 CODEBLEU (95% CI 65.5-77.1), approximately comparable to a ~480B code model (73.1; 67.4-78.8). On a subset of 34 natural Dart functions, it reaches compile@k5 = 79.4% (Wilson 95% CI 63.2-89.7), vs. 64.7% (47.9-78.5) for the base model; the difference is suggestive but not statistically significant at 0.05. Our results indicate that adding Swift training data helps at 8B but not at 4B, suggesting a capacity threshold for effective cross-lingual transfer. Our experimental results show that small specialized models can generate readable, idiomatic Dart with meaningful identifiers while using minimal compute.

Magboltz is widely used to compute electron transport properties in gas mixtures for detector applications. Its text-based workflow, however, can be a barrier for routine use, especially for users who are not already familiar with the program. We present Magboltz-GUI, a Python-based graphical user interface for defining gas mixtures, configuring simulation parameters, running Magboltz, and visualizing or exporting the resulting. The tool is designed as a lightweight frontend for common tasks in research and teaching environments involving gaseous detectors, including micropattern technologies such as Micromegas. This paper describes the software implementation, main interface components, and its availability as an open-source distributed package via Python tools.

We consider a secret sharing setting with a monotone access structure involving a control node and $L$ users, connected via a classical-quantum broadcast channel whose input is controlled by the control node, referred to as the dealer. Unlike traditional secret sharing settings, where the dealer fully controls the shares given to each user, in our model, the dealer encodes the secret for transmission over the broadcast channel. This means that the shares received by users are perturbed by the channel and are not fully controlled by the dealer. Our main results are achievable one-shot secret sharing rates, as well as converse bounds for arbitrary monotone access structures. We further derive second-order and asymptotic achievable rates for arbitrary monotone access structures. In the special case where all shares are required to recover the secret, we show that our result coincides with the existing secret sharing capacity over classical channels.

We demonstrate temporal pattern formation in a coherently driven fiber ring cavity whose effective finesse is continuously reconfigured using distributed Raman amplification. We achieve an effective finesse of up to $\mathcal{F}_{\mathrm{eff}}\approx800$, corresponding to a linewidth of approximately 725 Hz ($Q\approx2.7\times10^{11}$) at 1555 nm. By exploiting the resulting increase in effective photon lifetime, we excite stable temporal cavity solitons and generate a low-repetition-rate frequency comb with a spacing of 580~kHz. Finally, we analyze the impact of the Raman loss-compensation mechanism, particularly its associated noise and show that a trade-off exists between soliton excitation threshold and stability.

Distribution System State Estimation (DSSE) plays an increasingly-important role in modern power grids due to the integration of distributed energy resources (DERs). The inherent characteristics of distribution systems make classical estimation methods struggle, and recent advancements in data-driven learning methods, although promising, exhibit systematic failure in generalization and scalability that limits their applicability. In this work, we propose MambaDSSE, a model-free data-driven framework that incorporates Koopman-theoretic probabilistic filtering with a selective state-space model that learn to infer the underlying time-varying behavior of the system from data. We evaluate the model across a variety of test systems and scenarios, and demonstrate that the proposed method outperforms machine learning baselines on scalability, resilience to DER penetration levels, and robustness to data sampling rate irregularities. We further highlight the Mamba-based SSM's ability to capture long range dependencies from data, improving performance on the DSSE task.

Advances in intensity-based microscopy techniques have improved our ability to quantify particle motion at microscopic scales, enabling insight into diffusion and collective dynamics. Building on this foundation, we introduce a novel real-space approach that analyses intensity fluctuations within virtual observation boxes of variable size on microscopy images. By correlating these signals, we uncover distinct temporal regimes in the mean square changes of intensity, $\langle ΔI^2(t) \rangle$, which are strongly dependent on the box size compared to the particle width. For small boxes or short timescales, $\langle ΔI^2(t) \rangle$ scales with the mean-square displacement, while for longer timescales and larger boxes, it scales with its square root. We develop a general theoretical framework that captures these regimes and explicitly apply it to a dilute colloidal suspension imaged with confocal microscopy as an experimental model system. This allows for a robust extraction of diffusion coefficients and physical insights into particle dynamics. Our method complements intensity-based and real-space analysis, offering a tool for studying individual and potentially collective behaviour directly from image intensities, even in systems where individual particles cannot be resolved.

Organising the space of entanglement structures of a multipartite quantum system is a much more challenging task than its bipartite version: while the local unitary (LU) orbit of a bipartite pure state can be conveniently characterized by its entanglement spectrum, invariants of multipartite entanglement structures are comparatively difficult to define and work with. The root cause of this difference is that the bipartite problem can be reduced to the analysis of matrix invariants, while its multipartite version is governed by a much richer space of tensor invariants. The present work explores the latter through the lens of so-called trace-invariants, which are in one-to-one correspondence with combinatorial objects known as colored graphs. We first explain why trace-invariant evaluations can serve as labels of LU-orbits of multipartite pure states, how this strategy extends to random states, and how the effect of local operations (LO) can be analyzed through such data. We then focus on entanglement classification within an (infinite-dimensional) subspace of reference states, whose basic building blocks are GHZ states of various dimensions. We show that relatively simple subclasses of trace-invariants are sufficient to separate the LU-orbits of reference states, and enable a complete (resp. an incomplete) characterization of their relations in the LO (resp. LOCC) resource theory of entanglement. Finally, we investigate how a (still infinite) subclass of reference states of local dimension N can be efficiently distinguished at leading and subleading orders in an asymptotic large-N expansion (among themselves, or from Haar-random states). This analysis relies crucially on combinatorial quantities associated to colored graphs, some of which have already played instrumental roles in the recent literature on random tensors. Results of broader relevance are reported along the way.

Let $S=(s_1,s_2,\ldots)$ be a non-decreasing sequence of positive integers. For a graph $G$ with vertex set $V(G)$, a labeling $ϕ\colon V(G)\to \{1,\ldots,k\}$ is an $S$-packing $k$-coloring if, whenever two distinct vertices $u,v\in V(G)$ are assigned the same color $i$, their distance in $G$ is greater than $s_i$. The minimum $k$ for which $G$ admits such a coloring is the $S$-packing chromatic number of $G$. A graph $G$ is $χ_S$-vertex-critical if $χ_S(G-v) < χ_S(G)$ for every $v \in V(G)$, and it is $χ_S$-critical if $χ_S(H) < χ_S(G)$ holds for every proper subgraph $H$ of $G$. In this paper, the exact value of $χ_S(P_n)$ is determined for every path of order $n$ and for every packing sequence $S$ where $s_i < 2^i$ holds for each entry $s_i$. As a consequence, $χ_S$-critical and $χ_S$-vertex-critical paths are identified for each such sequence $S$. In addition, we extend earlier results on $χ_S$-critical cycles and provide a complete characterization of $χ_S$-critical and $χ_S$-vertex-critical cycles for packing sequences $S= (1, s_2, \dots )$ with $s_2 \in \{2,3\}$ and $s_3,s_4 \in \{4,5,6,7\}$.

Orthogonal time frequency space (OTFS) modulation offers superior robustness to high-mobility channels compared to conventional orthogonal frequency-division multiplexing (OFDM) waveforms. However, its explicit delay-Doppler (DD) domain representation incurs substantial signal processing complexity, especially with increased DD domain grid sizes. To address this challenge, we present a scalable, real-time Zak-OTFS receiver architecture on GPUs through hardware--algorithm co-design that exploits DD-domain channel sparsity. Our design leverages compact matrix operations for key processing stages, a branchless iterative equalizer, and a structured sparse channel matrix of the DD domain channel matrix to significantly reduce computational and memory overhead. These optimizations enable low-latency processing that consistently meets the 99.9-th percentile real-time processing deadline. The proposed system achieves up to 906.52 Mbps throughput with a DD grid size of (16384,32) using 16QAM modulation over 245.76 MHz bandwidth. Extensive evaluations under a Vehicular-A channel model demonstrate strong scalability and robust performance across CPU (Intel Xeon) and multiple GPU platforms (NVIDIA Jetson Orin, RTX 6000 Ada, A100, and H200), highlighting the effectiveness of compute-aware Zak-OTFS receiver design for next-generation (NextG) high-mobility communication systems.

Given a graph $F$, the random Turán problem asks to determine the maximum number of edges in an $F$-free subgraph of $G_{n,p}$. Prior to this work, the only bipartite graphs $F$ with known tight bounds included certain classes of complete bipartite graphs and theta graphs. We greatly expand upon these examples by proving tight bounds for a number of bipartite graphs which have a vertex complete to one part. We also prove new general upper bounds for this problem which in many cases do significantly better than the only previous known general upper bound due to Jiang and Longbrake. Our proofs utilize dependent random choice together with the recent technique of balanced vertex supersaturation in conjunction with hypergraph containers.

We demonstrate that wave amplification enables even weak nonlinearities to reshape linear wave-packet transport in nonreciprocal systems. We study the dynamics of bulk Gaussian wave packets in the Hatano--Nelson model with onsite cubic nonlinearity. We show that the interplay between nonlinearity and amplification generates growing frequency shifts that drive the wave packet through three successive dynamical regimes: an early nonlinear-skin regime with coherent propagation, an intermediate wave-mixing regime driven by mode resonances, and a self-trapping regime in which part of the packet localizes while the remainder ballistically spreads along the system favored direction. The crossover time scales are set by the width and average spacing of the eigen-frequency spectrum. Crucially, within the nonlinear-skin regime, we derive analytical predictions for the wave-packet dynamics and show that nonlinearity couples amplification, dispersion, and nonreciprocity, thereby modifying the magnitude of the wave-packet acceleration and introducing an explicit time dependence into its evolution. Focusing nonlinearities suppress the acceleration and cause it to decrease in time, whereas defocusing nonlinearities enhance it and cause it to increase. We further show that nonlinear interactions typically break down the wave packet before the non-Hermitian jump can occur. Our results provide a route toward accurate control of waves in nonreciprocal metamaterials.

This paper presents lineshapes for molecular Optical-Optical Double Resonance (DR) Spectroscopy with arbitrary strength for both pump and probe field using the steady-state solutions for the 3-level density matrix. When the Doppler broadening can be neglected, the results are analytical, and the probe spectrum is a pair of Lorentzian lines that display Autler-Townes splitting, and each has an angular frequency half-width half maximum equal to the relaxation rates, which are all assumed equal. When Doppler broadening is introduced, one must resort to numerical integration except for the limit of weak pump and probe fields. When the Doppler width is assumed much larger than the pump and probe Rabi Frequencies, the calculated DR lineshapes are found to be Lorentzian with a strong pump field limit that is proportional to the pump Rabi frequency, what is commonly known as power broadening. However, the width does not equal the Rabi frequency and is different for co- and counter-propagating pump and probe fields. Furthermore, that broadening is largely inhomogeneous, despite the Lorentzian shape. The saturation power is found to be about 4 times higher than for the bare probe transition with the same relaxation rate, dramatically lower than that expected if the width is interpreted as homogeneous.

Fast radio bursts (FRBs) are enigmatic cosmic transients of millisecond duration observed in the radio band. The identification of FRB-associated magnetar X-ray bursts (MXBs) from galactic magnetar SGR J1935+2154 suggests that at least a fraction of FRBs can be produced from magnetar activity. However, the sample size of FRB-associated MXBs is still very small. Here we report a bright and peculiar FRB-associated MXB from SGR J1935+2154 detected by GECAM on November 20, 2022, dubbed MXB 221120. We find that both temporal and spectral properties of MXB 221120 exhibit distinctive features. Its light curve could be generally described by a single FRED function with superposition of several narrow pulses. Interestingly, we identify a possible QPO feature with center frequency of ~18 Hz in this MXB. The time-integrated spectrum is best fitted by a blackbody model with temperature (kT ) of 18.6 keV, rendering it the first thermal spectrum FRB-associated MXB from SGR J1935+2154. Compared to other MXBs with single emission episode, MXB 221120 has longer duration and higher blackbody temperature, making it an outlier in the burst sample. These results indicate that MXB 221120 may be produced by a special mechanism with extreme physical conditions.

As quick commerce (Q-Commerce) platforms in India redefine urban consumption, the use of deceptive design dark patterns to inflate order values has become a systemic concern. This paper investigates the 'Awareness-Action Gap' among Indian university students, a demographic characterized by high digital fluency yet significant financial constraints. Using a qualitative approach with 16 participants, we explore how temporal pressures and convenience-driven architectures override price sensitivity. Our findings reveal that while students recognize manipulative UI tactics, they frequently succumb to them due to induced cognitive load and the normalization of deceptive marketing as a price of capitalism. We conclude by suggesting value-sensitive design alternatives to align commercial incentives with user autonomy in the Global South.

For a (molecular) graph $G$ and any real number $α\ne 0$ , the zero-order general Randić index , denote by $^0R_α$, is defined by the following equation: \begin{align*} {^0R_α} (G) =\sum_{v\in G}d_G (v) ^α (α\in \mathbb{R}-\left\{0\right\}) . \end{align*} In this paper, we use this index to give sufficient conditions for a graph $G$ to satisfy the Hamiltonian (or $k$-Hamiltonian) property, and show that none of these conditions can be dropped. Finally we give similar results for the case when $G$ is a balanced bipartite graph.

Large-scale optimization problems are ubiquitous in the physical sciences; yet, high-fidelity models can often be complex and computationally prohibitive for optimization. A practical alternative is to use a low-fidelity model to facilitate optimization. However, the discrepancy between the high- and low-fidelity models can lead to suboptimal solutions. To address this, we build on recent work in Hyper-Differential Sensitivity Analysis to leverage limited high-fidelity simulations to update the optimization solution. Our contributions in this article include: (i) incorporating pseudo-time continuation techniques to efficiently compute higher-accuracy optimal solution updates, and (ii) proposing a Bayesian framework for sequential data acquisition that strategically guides high-fidelity evaluations and reduces uncertainty in the model discrepancy estimation. Numerical results demonstrate that our framework delivers significant improvements to optimization solutions with only a few high-fidelity evaluations.

Model uncertainty of inverter-based resources (IBRs) presents significant challenges for power system control and stability. This work studies secondary frequency regulation in inverter-based power systems using a Data-driven Koopman Predictive Control (DKPC) framework. The method employs Koopman theory to lift the nonlinear system dynamics into a higher-dimensional space where they can be approximated as linear. Based on Willems' fundamental lemma, a behavioral model is constructed directly from lifted input-output data. A receding-horizon predictive control formulation is then provided that operates entirely using observed data, without requiring a parametric model, while satisfying explicit constraints on the control input and system output. The proposed approach is particularly suited for IBRs with complex or uncertain dynamics. Numerical results demonstrate its effectiveness for frequency control as benchmarked against the Data-enabled Predictive Control (DeePC). The trade-off between tracking performance and control effort is illustrated through tuning of the weighting parameters.

Transitioning to a Circular Economy requires policies to drive sustainable practices. This study proposes a bilevel optimization framework to evaluate the combined use of carbon taxes and subsidies in promoting circular supply chains under varying budget levels. A case study of the coffee packaging supply chain with an Extended Producer Responsibility scenario is used to demonstrate this approach. The framework captures the hierarchical interaction between a regional government (upper level), which aims to minimize environmental impacts, and coffee companies (lower level), which seek to minimize costs. Two bilevel optimization problems are formulated based on two environmental objectives: (1) minimization of greenhouse gas (GHG) emissions, and (2) maximization of circularity. The model integrates mixed-integer linear programming (MILP) with life cycle assessment (LCA), techno-economic assessment (TEA) and circularity assessment. Results demonstrate that subsidies effectively drive supply chain shifts toward low-emission and high-circularity configurations, while carbon taxes alone have a more limited impact. Sensitivity analyses highlight the influence of key parameters, such as glass washing distance and loss rates, on policy effectiveness. Overall, the study provides a bilevel optimization framework with quantitative insights to support policy design for sustainable circular supply chains.

In a class of theories, dark matter is explained by postulating the existence of a `dark sector', which interacts gravitationally with ordinary matter. If this dark sector contains a U(1) symmetry, and a corresponding `dark' photon ($A_{D}$) , it is natural to expect that this particle kineticly mix with the ordinary photon, and hence become a `portal' through which the dark sector can be studied. The strength of the mixing is given by a mixing parameter $(ε)$. This same parameter governs both the production and the decay of the $A_{D}$ back to SM particles, and for values of $ε$ not already excluded, the signal would be a quite small, and quite narrow resonance: If $ε$ is large enough to yield a detectable signal, its decay width will be smaller than the detector resolution, but so large that the decay back to SM particles is prompt. For masses of the dark photon above the reach of Belle II, future high energy e$^+$e$^-$ colliders are ideal for searches for such a signal, due to the low and well-known backgrounds, and the excellent momentum resolution and equally excellent track-finding efficiency of the detectors at such colliders. This contribution will discuss a study investigating the dependency of the limit on the mixing parameter and the mass of the $A_{D}$ using the $A_{D}\rightarrowμ^{+}μ^{-}$ decay mode in the presence of standard model background, using fully simulated signal and background events in the ILD detector at the ILC Higgs factory. In addition, a more general discussion about the capabilities expected for generic detectors at e$^+$e$^-$ colliders operating at other energies will be given.

We define compatible Finsler distances on $1/n$-translation surfaces, we study their geodesics, and construct a Liouville current for each such metric, that is a geodesic current that encodes the information of the length of the closed curves. The construction is based on multi-foliations, a generalization of measured foliations of independent interest.

This roadmap outlines research pathways to determine whether Mars could be warmed with non-biological methods. It does not presuppose that warming Mars is desirable; its purpose is to identify what would need to be true for Mars to be warmed, what it would cost, and what could go wrong. Three complementary research tracks appear promising. Solid-state greenhouse membranes offer local warming, aiding water harvesting, food production, and oxygen supply near human bases. Orbiting reflectors can warm key sites such as bases and CO$_2$-ice reservoirs, although a large combined area would be required. Strengthening Mars' natural greenhouse effect might warm large regions or the globe, although many aspects remain to be worked out. Each approach carries scientific and technical risks that research must address. Near-term priorities are on-Earth testing of key parameters that will determine whether engineered aerosol warming is realistically possible, assessing whether exponential production of bioplastic habitats is possible, and designing at-Mars process experiments. In the near term, the research proposed here is closely aligned with and supports research needed to understand Mars' atmosphere and volatile evolution and hazards to human explorers. The main external uncertainty is whether or not launch costs continue to fall. This is early-stage research, and we discuss key near-term decision points, alternative pathways, and payoffs if research outcomes are negative. We also outline build-out pathways if research succeeds and demand exists. Relatively modest research investments would keep open the option of extending life beyond Earth as Mars' scientific exploration continues.

We study the power spectrum of the velocity field induced during a first-order phase transition occurring in the radiation-dominated era. We focus on the phase of bubble expansion, assuming that it ends with the onset of the sound-wave regime. The main result we present is a refined template for the velocity spectrum at the beginning of the sound-wave phase, which can be used for studying the resulting anisotropic stresses and gravitational wave production. In particular, we find that the breaks in the velocity spectrum are not associated to the bubble size and the sound shell thickness, as previously proposed, but to the position of the discontinuities. This distinction is particularly relevant for supersonic deflagrations, as it implies that the intermediate slope is more pronounced and the two breaks are more separated when the wall velocity approaches the Chapman-Jouget speed, instead of the sound speed. We also show that the asymptotic branches of the velocity power spectrum are determined by the integral over the single-bubble profiles at large scales, and by the discontinuities of the velocity profiles at small scales. Furthermore, we study the dependence of the two breaks and the intermediate slope on the distribution function of the times of bubble nucleation (exponential and simultaneous). All the results presented in this work have been included in the public Python package CosmoGW.

Andrews and the third author recently studied congruences for certain restricted two-color partitions. They made two conjectures for Ramanujan-type congruences and a vanishing identity for the limiting sequence. In this paper, we settle these conjectures by relating the corresponding generating function to modular forms and mock theta functions.

A formal and systematic framework is proposed to quantify the intrinsic collectivity of resonance states in the continuum, independent of their extrinsic manifestation in the strength function. By integrating Takagi factorization into the Jost-RPA framework, we utilize the rank-1 property of the S-matrix residue at a resonance pole to uniquely decompose it into microscopic transition amplitudes for each configuration. To evaluate the nature of these modes, we introduce the Intrinsic Coherence Index ($C^{(n)}$) and the Collective Phase ($Θ^{(n)}$), which characterize the dynamical phase synchronization and the line-shape orientation, respectively. Furthermore, a unified Total Collectivity Index ($R^{(n)}$) is defined by combining the coherence index with the Normalized Participation Ratio ($η^{(n)}$). Applying this framework to the isoscalar $2^+$, isovector $2^+$, and $E1$ excitations in $^{16}$O, we demonstrate that the intrinsic collectivity is decoupled from the observable line shape. Our analysis identifies "hidden" collective modes -- states with high internal synchronization that do not appear as prominent peaks -- and clarifies that distorted structures or dips can either be highly collective or non-collective depending on their microscopic phase alignment. This approach provides a well-defined structural basis for investigating many-body excitations in open quantum systems and nuclei near the drip lines.

We study the computational complexity of approximately computing the partition function of a spin system. Techniques based on standard counting-to-sampling reductions yield $\tilde{O}(n^2)$-time algorithms, where $n$ is the size of the input graph. We present new counting algorithms that break the quadratic-time barrier in a wide range of settings. For example, for the hardcore model of $λ$-weighted independent sets in graphs of maximum degree $Δ$, we obtain a $\tilde{O}(n^{2-δ})$-time approximate counting algorithm, for some constant $δ> 0$, when the fugacity $λ< \frac{1}{Δ-1}$, improving over the previous regime of $λ= o(Δ^{-3/2})$ by Anand, Feng, Freifeld, Guo, and Wang (2025). Our results apply broadly to many other spin systems, such as the Ising model, hypergraph independent sets, and vertex colorings. Interestingly, our work reveals a deep connection between $\textit{subquadratic}$ counting and $\textit{perfect}$ marginal sampling. For two-spin systems such as the hardcore and Ising models, we show that the existence of perfect marginal samplers directly yields subquadratic counting algorithms in a $\textit{black-box}$ fashion. For general spin systems, we show that almost all existing perfect marginal samplers can be adapted to produce a sufficiently low-variance marginal estimator in sublinear time, leading to subquadratic counting algorithms.

We present a detailed computational and algebraic study of Mutually Unbiased Bases (MUBs) in finite-dimensional Hilbert spaces, with a particular focus on dimensions 2, 3, 4, and the challenging case of 6. Starting from the Hadamard-phase parametrization, we derive explicit analytical conditions for mutual unbiasedness in dimension 4, providing a tractable system of trigonometric constraints on the phase parameters. We then explore a tensor-product construction via Pauli operators, highlighting the algebraic and group-theoretical origin of MUBs in two-qubit systems, and demonstrating how these constructions yield a complete set of 5 MUBs in dimension 4. Extending our approach, we investigate the Fourier-family method in dimension 6, where the absence of a prime-power structure imposes strong rigidity constraints and limits the known constructions to sets of 3 MUBs. We provide a systematic computational framework for testing candidate phase vectors, bridging the gap between analytical insight and numerical exploration. Finally, we generalize the discussion to arbitrary prime-power dimensions, emphasizing the role of finite-field structures, Heisenberg-Weyl operators, and discrete symmetries in generating complete sets of MUBs. Our work offers a transparent, line-by-line verification methodology, highlighting both the geometric and algebraic richness of MUBs, and clarifying why certain dimensions resist full analytical constructions. This study serves as a comprehensive resource for researchers seeking both theoretical understanding and practical construction of MUBs in quantum information science.

We investigate the quantum algorithms for dynamic programming by Ambainis et al. (SODA'19). While giving provable complexity speedups and applicable to a variety of NP-hard problems, these algorithms have a notable drawback: they require a large amount of Quantum Random Access Memory (QRAM), which potentially could be very challenging to implement in a physical quantum computer. In this work, we study how we can improve the space complexity by trading it for time, while still retaining a speedup over the classical algorithms. We show novel quantum time-space tradeoffs, which we obtain by adjusting the parameters of these algorithms and combining them with "quantized" classical strategies.

We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to spectra are symmetric monoidally equivalent to the corresponding variants of spectral Mackey functors. The symmetric monoidal structures appearing here are the Day convolutions on both sides, and the Mackey functors we consider involve variations on the category of finite sets and surjections. The method is first to introduce certain multivariable functors we call subdiagonal functors. By considering them all at once using parametrised category theory, we prove inductively that they all admit Mackey functor descriptions as symmetric monoidal categories, endowing them with a universal property along the way. In particular, specialising this to univariate functors gives a new proof and strengthening of Glasman's result about d-excisive endofunctors on spectra. As application of our perspective, we prove a ``Segal conjecture'' in the context of Goodwillie calculus when d is a prime number.

This paper investigates the convexity of the solution set of the linear complementarity problems over tensor spaces (TLCPs). We introduce the notion of a $T$-column sufficient tensor and study its properties and relationships with several structured tensors. An equivalent condition for the convexity of the solution set of the $\mathrm{TLCP}$ is established. In addition, sufficient conditions for uniqueness and for feasibility implying solvability are derived.