Exact classical simulation of fault-tolerant quantum circuits remains limited by a tradeoff between exponential state vector scaling, exponential $T$-count scaling in stabilizer-rank approaches, and per-shot tracking overhead in sparse generalized stabilizer simulators. In this work, we introduce Clifft, an open-source simulator that shifts the dominant exponential cost from the total qubit count to a dynamic active subspace by factoring the quantum state into an offline Clifford frame, an online Pauli frame, and a dynamically sized active state vector. This architecture resolves deterministic Clifford coordinate transformations ahead of time, generalizing Stim's compile-once, sample-many execution model to circuits with non-Clifford operations. Consequently, exponential simulation costs are determined by the peak active virtual dimension, which expands during non-Clifford operations and contracts during measurements. Clifft remains within a constant factor of standard tools in the pure-Clifford and non-Clifford limits, while delivering up to orders-of-magnitude throughput gains over GPU-accelerated near-Clifford simulators on low-magic fault-tolerant benchmarks. Executing on commodity CPUs and exposing a Stim-like API, Clifft enables, to our knowledge, the first exact end-to-end simulation of magic state cultivation including the escape stage, over hundreds of billions of shots. These simulations show that escape-stage failures suppress the discrepancy between the true $T$-gate circuit and its $S$-proxy at low decoder-gap thresholds, while at high thresholds the full-protocol behavior approaches the larger discrepancy observed in the cultivation stages alone.

Combinatorial optimization is widely regarded as a primary application for near-term quantum processors, although a definitive demonstration of the practical quantum advantage remains elusive. Recent studies have reported that both gate-based quantum circuits and quantum annealers can outperform state-of-the-art classical heuristics on multi-objective optimization (MO-MaxCut) problems. However, these studies did not fully account for the substantial pre- and post-processing overheads intrinsic to quantum solvers, leading to incomplete comparisons between quantum and classical approaches. In this work, we re-examine the same benchmark suite using GPU-based quantum-annealing-inspired algorithms (QAIAs), which, analogously to quantum processors, generate probabilistic samples and thus serve as formidable classical contenders. Our results show that QAIAs can sample candidate solutions approximately two orders of magnitude faster than previously studied quantum processors. In terms of end-to-end runtime, QAIAs also surpass industry-leading classical solvers, thereby establishing themselves as the superior performers among the quantum and classical solvers evaluated thus far for the MO-MaxCut instances.

When studying massive stars and their life cycles, rotation plays a key role. Hence, understanding the rotation of these stars is crucial when determining their properties, or for constraining evolutionary models. We examine the reliability of the standard methods to derive projected rotation speeds vsini from photospheric spectra of hot, massive stars in the presence of large turbulent velocities. We include rotation in the spectral synthesis of O-stars by means of three-dimensional model atmospheres showing significant photospheric turbulent velocities. We then use these as mock-observations to back-test the Fourier Transform and goodness-of-fit methods commonly used for empirical determination of vsini when the turbulent velocity field is not known. When the expected vsini>v_mac, with v_mac the macroturbulent velocity, FT vsini determinations (most of the time) give reasonable results. However, if vsini < v_mac the method is no longer reliable. Results from the GOF method show that if one parameter is not significantly larger than the other, empirical best-fit values may be located in a large region of the vsini-v_mac parameter space, independent of the true values. The degenerate region follows well the empirical formula found by Howarth et al. (2007), sqrt(v_mac^2/2+vsini^2/4). In other words, only this sum can be constrained by GOF observational analysis. Our analysis shows clearly that, generally, only the sum sqrt(v_mac^2/2+vsini^2/4) can be constrained through the standard spectroscopic methods used to infer these parameters individually. Only in the case where one of the two clearly dominates, can good constraints on the dominating parameter be derived. This demonstrates that previously found empirical correlations between vsini and v_mac as well as derived statistical distributions of observed rotation rates for O-star populations will need to be re-analysed and interpreted.

We investigate a hierarchy of interacting dark energy (IDE) models featuring a non-gravitational coupling between dark matter and dark energy. Specifically, we examine scenarios where the background interaction kernel, $Q = 3H(δ+ ηa)ρ_\mathrm{de}$, allows for both constant and dynamical coupling parameters. Adopting the Chevallier-Polarski-Linder parametrization for the dark energy equation of state, $w_\mathrm{de} = w_0 + w_a(1-a)$, we derive closed analytical expressions for the energy densities of dark matter and dark energy. Afterwards, we obtain observational constraints using joint combinations of DESI DR2 baryon acoustic oscillations, Pantheon$+$ Type Ia supernovae, and Planck$+$ACT compressed cosmic microwave background likelihoods. For constant coupling models, we find parametric deviations from $Λ$ ranging from $2.7σ$ to $2.9σ$; however, for interactions with dynamical couplings, these significances are reduced to $1.3σ$--$1.5σ$. Ultimately, our Bayesian model comparison reveals that no investigated IDE scenario is statistically preferred over the concordance $Λ$CDM model. These results highlight the necessity of reporting Bayesian evidence alongside conventional frequentist maximum-likelihood analyses to ensure robust cosmological claims concerning dark energy evolution and interaction.

We study the out-of-equilibrium spinodal-like behavior of three-dimensional (3D) $q$-state Potts models (for $q\ge 3$), observed when the temperature is quenched across the first-order transition (FOT) point $β_{\rm fo}=T_{\rm fo}^{-1}$. We consider a standard quench protocol, in which high-temperature configurations, thermalized at $β_i<β_{\rm fo}$, are driven across the FOT by a purely relaxational dynamics at $β>β_{\rm fo}$. We focus on the emergence of spinodal-like behaviors in the thermodynamic limit, associated with the dynamic phase change. We argue that, if the nucleation of smooth droplets is the relevant mechanism of the post-quench phase change, for sufficiently small $β_{\rm fo}-β_i>0$, the time-dependent energy density should scale in terms of $ρ= (\ln t)^{3/2} δ$, where $δ= β/β_{\rm fo}-1$, with a discontinuity at a particular value $ρ=ρ_s>0$. This implies the emergence of a spinodal-like behavior, whose time scale $τ$ increases exponentially as $\ln τ\approx (ρ_s/δ)^{2/3}$ in the limit $δ\to 0^+$. We present a numerical analysis of the quench protocol in the 3D $q=6$ Potts model, which supports the above spinodal-like scenario.

Temporal metamaterials, created by modulating the refractive index in time, offer powerful means of controlling wave propagation but still lack a systematic design methodology. Here, we develop an analytic inverse-design framework rooted in space-time duality and the established theory of one-dimensional spatial inverse scattering. By prescribing reflection (backward-wave) and transmission (forward-wave) responses in rational-function form, we obtain closed-form refractive-index modulations that are guaranteed to be physically admissible. This approach avoids iterative optimization and provides direct analytic control of the modulation. We illustrate the method with syntheses of mathematical operators, such as derivatives and integrals, as well as Chebyshev- and Butterworth-type filters, and validate the results through finite-difference time-domain simulations. Our findings establish a general route to temporal media with tailored functional and spectral responses, enabling applications in wave-based information processing, programmable filtering, and amplification schemes inspired by photonic time crystals.

We analyze the filing-side legal infrastructure of eviction using 755,004 Philadelphia Municipal Court landlord-tenant records filed between 1969 and 2022, of which 747,125 are residential. Eviction in Philadelphia is organized upstream by a concentrated plaintiff-side bar, durable plaintiff-attorney dependence, repeated use of the same properties, and recurring tenant-name exposure. Between 1983 and 2022, the ten most active plaintiff attorneys handled 82.2% of represented plaintiff-side cases per year on average, compared with 14.8% for the ten most active plaintiffs. Large plaintiffs depend heavily on a single attorney: among plaintiffs filing at least 101 cases, 78.3% of each plaintiff's filings are handled by that plaintiff's most-used attorney, on average. Repetition is likewise central to the docket. Across the residential filing universe, 48.8% of cases occur at addresses with a prior filing in the preceding year, and 23.6% at addresses with six or more prior filings; these repeats are usually filed by the same plaintiff and follow a more default-heavy, less agreement-heavy pathway. We further examine a narrower mechanism: strict switches into specialist plaintiff-side counsel, defined as a plaintiff changing attorney to one in the prior-year top ten. Filing counts rise around the switch with non-flat pre-trends, indicating organizational reconfiguration rather than a clean exogenous shock. Within-plaintiff and within-plaintiff-property comparisons yield more stable estimates: judgment by agreement, fee share, waiver language, and corrected lockout-trigger language decline, while deadline language rises. We interpret eviction as a layered upstream process in which concentrated counsel, repeated places, and recurring tenants produce filings before any courtroom bargaining or adjudication occurs.

We conjecture, and show in a plethora of examples, that the sphere partition function of 3d $\mathcal{N}=4$ Chern-Simons-matter theories equals a sum of twisted traces on tensor products of Verma modules over the quantization of the moduli spaces of vacua. This extends a conjecture of Gaiotto-Okazaki to Chern-Simons-matter theories. We also show that the partition function of every Abelian gauge theory with higher charges has such twisted trace decomposition, and uncover new Abelian dualities between theories with and without Chern-Simons couplings.

Large language model (LLM)-based debugging systems can generate failure explanations, but these explanations may be incomplete or incorrect. Misleading explanations are harmful for downstream tasks (e.g., bug triage, bug fixing). We investigate how explanation quality is affected by various LLM context configurations. Existing work predominantly treats LLM-generated failure explanations as an ad hoc by-product of debugging or repair workflows, using generic prompting over undifferentiated artifacts such as code, tests, and error messages rather than targeting explanations as a first-class output with dedicated quality assessment. Consequently, existing approaches provide limited support for assessing whether these explanations capture the underlying fault-error-failure mechanism and for actionable next steps, and most techniques instead prioritize task success (e.g., patch correctness or review quality) over the explicit causal explanation quality. We systematically vary the debugging information to study how distinct context compositions affect the quality of LLM-generated failure explanations. Across 93 context configurations on real bugs and three economically viable models (gpt-5-mini, DeepSeek-V3.2, and Grok-4.1-fast), we evaluate explanations with six criteria and validate the LLM-as-a-judge scores against human ratings in a user study. Our results indicate that explanation quality is causally affected by context composition. Evidence-rich, failure-specific artifacts improve causal and action-oriented quality, whereas overly large contexts tend to yield vague explanations. Higher explanation-score quartiles are associated with higher downstream repair pass rates and, for some models, with fixes that are closer to the reference minimal fixes. In contrast, low-score quartiles can even underperform the no-explanation baseline. Reproduction package is publicly available.

In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and Rényi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis reveals several flaws in the use of these density-based descriptors. We demonstrate that for minimal-basis and different theoretical levels, the Shannon and Rényi entropies fail to encode the amount of static correlation conveyed by the underlying wavefunction. Conversely, shape-function Shannon entropies and Rényi entropies (for $α\neq 1$) violate extensivity. In larger basis sets, uncorrelated Hartree-Fock densities consistently overestimate entropy compared to sufficiently correlated (e.g., full-valence-CAS) densities. Moreover, the entropies for insufficiently correlated methods violate extensivity. These findings indicate that electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.

We test the standard Kardashev one-percent exponential conjecture against six decades of global primary-energy production data (1965-2024; Our World in Data). Markov Chain Monte Carlo inference yields a posterior growth rate of r = 2.01 +/- 0.03% per year (95% credible interval [1.94%, 2.08%]), placing the Kardashev 1% value well outside the credible interval. A linear OLS model fits the data with remarkably low dispersion (R^2 = 0.987) and is preferred over the free-rate exponential by the Widely Applicable Information Criterion (ΔWAIC = 5.5). Year-over-year increments are non-Gaussian (Shapiro-Wilk W = 0.925, p = 0.0014; skewness = -0.664) with identifiable crisis outliers (2008, 2020), rejecting the independent-increment multiplicative structure with positive drift required by Kardashev's (1+x)^t geometric series. Extrapolation of the linear model to the solar luminosity yields a Type II civilisational timescale of approximately 1.6E15 years -- approximately 1E5 times both the age of the Universe and the main-sequence lifetime of the Sun -- a physical reductio we term Kardashev's Conundrum. No functional form fitted to P(t) alone can simultaneously satisfy statistical adequacy and physical coherence: the Kardashev variable is dimensionally incomplete. We propose the Kardashev-Sagan-Nakamoto (KSN) renormalisation B(t) = P(t)/H(t) [J/Hash, the KarNak unit], where H(t) is the annual Bitcoin hashrate. The renormalisation adds no free parameters, is motivated by the Landauer limit, and fulfils Sagan's information-richness requirement. Over 2009-2024, B(t) spans 14 orders of magnitude.

Within the present noisy intermediate-scale quantum-computing era, hybrid quantum-classical-processor algorithms have emerged as promising avenues for tackling electronic-structure eigenproblems. Among them, the so-called ensemble-variational quantum eigensolver has been designed to treat ground and excited states on an equal footing and proven effective in capturing features such as conical intersections and avoided crossings between two electronic states, as we recently demonstrated for formaldimine. We also showed on that example how the underlying ensemble-variational principle was prone to provide a quasi-diabatic representation "for free". To date, this method has been limited to computing only two eigenstates of a Hamiltonian. The aim of the present paper is to show how and under what conditions this can be generalized to models that involve three coupled electronic states or more. Our approach relies on designing a parameterized basis transformation that can directly be implemented on a quantum computer for further post-treatment. This nontrivial step is accompanied by the development of quantum circuits specifically adapted to the several states of interest. An algebraic optimization strategy for the parameters of the basis transformation is formulated to obtain the target eigenstates as well as the optimally diabatic states under various objective flavors of the ensemble-variational principle. Our approach was tested for addressing the first three coupled electronic states of the H$_4^+$ molecular ion as a proof of principle, with three electrons in four spatial orbitals, along various geometries.

We theoretically study direct current generation in a quantum spin chain induced by spinon excitations by light irradiation. We consider a s=1/2 1D antiferromagnetic XXZ model with magnetoelectric coupling that describes multiferroics with broken inversion symmetry. We perform the real-time simulation using infinite time-evolving block decimation (iTEBD), and demonstrate the direct current generation under light irradiation. By comparing the second order nonlinear conductivity and the two-spinon excitation spectra of 1D XXZ model, we confirm that the spinon excitations are the origin for the direct current generation in the quantum spin chain. We find that the bulk photovoltaic effect is driven by electric polarization carried by the spinons through the shift current mechanism, and thus is regarded as ``the spinon shift current''.

To produce an operable quantum computer that is made with imperfect hardware, we must design and test scalable quantum error correcting codes that are suited for the devices we can build and, in unison, develop decoding strategies that accommodate device-specific noise characteristics. Here, we introduce the \emph{dynamic compass code}, a subsystem code with a novel syndrome extraction cycle, that has a competitive threshold while making efficient use of qubits arranged on a heavy-hex lattice. We use a superconducting qubit array to implement a distance-5 instance of this code, and demonstrate how detailed noise characterisation can boost decoder performance to yield significant improvements in logical error rates. We perform averaged circuit eigenvalue sampling (ACES) to acquire detailed context-dependent error information on all elements of the syndrome extraction process. Furthermore, we leverage soft information produced from measurement devices to augment the decoder with measurement error information and detect leakage errors for exclusion through post-selection. Our noise-informed approach yields up to 38.3\% improvement in the logical error rate of a distance-5 implementation of the dynamic compass code in experiment.

The reproduction of automobile components through additive manufacturing presents significant geometric challenges, as many automotive parts feature complex, organically shaped surfaces that are difficult to fabricate accurately using conventional 3D printing approaches without wasteful support structures. Multi-axis Digital Light Processing (DLP) 3D printing addresses this by orienting a robotic arm to cure resin layers at varying angles and positions, enabling the fabrication of geometries that fixed-axis systems cannot reliably reproduce. However, this flexibility introduces a key challenge: layers printed at non-orthogonal orientations exhibit non-uniform thickness across their cross-section, which traditional DLP systems cannot accommodate without subdividing the layer, increasing total layer count, print time, and the need for supporting structures. This paper introduces a variable exposure method to address this challenge. Rather than splitting a non-uniform layer into multiple uniform ones, our approach divides each layer into sublayers and modulates the UV illumination duration for each sublayer proportionally to its local thickness. This is governed by an established cure-depth equation relating exposure time to material penetration depth, allowing precise control over curing without additional hardware. The result is a meaningful reduction in total layer count for printed objects. Fewer layers directly translates to faster print times and a reduction in wasteful support structures. Our contribution is a practical and low-overhead extension to existing multi-axis DLP pipelines that improves print efficiency without sacrificing geometric accuracy, with clear applications in the rapid prototyping and reproduction of automotive components.

Planar cavity magnonics has been developed mainly for a single magnetic film, leaving multilayer behavior in spatially resolved cavity scattering largely unexplored. Here, we introduce a double layer planar cavity with two magnetic films embedded in the same microwave cavity to derive a full two-film scattering theory in the macrospin ($J = 0$) limit and recover the exact zero-gap half-thickness limit, thereby benchmarking the model against the known one-film result. We find that the double layer model actively enables geometry-controlled bright-channel enhancement, demonstrating that the magnon-photon coupling depends on spatial placement rather than just total magnetic volume. Antinode-compatible placements increase the coupling, while node-compatible placements suppress it. Weak symmetry breaking also transfers finite cavity weight to a mode dark in the symmetric limit, producing an additional branch without destroying the main avoided crossing. Finally, a reduced multimode theory for $J\neq 0$ predicts family-resolved bright and dark channels for odd standing-spin-wave modes.

We show that the wheel classes in the Kontsevich graph complex $GC_d$ admit representatives supported on graphs with only $3$- and $4$-valent vertices. This verifies that Merkulov's low-valence conjecture holds for the wheel classes. More precisely, for every $m \ge 2$, we prove that the wheel graph $W_{2m+1}$ is homologous to an explicit linear combination of $2^{m-2}$ graphs, each having only $3$- and $4$-valent vertices.

The precise location of the liquid-vapor critical point in aluminum has remained elusive for decades, with reported critical temperatures spanning nearly 4000 K. Here we resolve this long-standing uncertainty by combining deep potential molecular dynamics with large-scale simulations trained on high-fidelity electronic-structure data. We benchmark multiple exchange-correlation functionals against experimental liquid densities and identify PBEsol as providing the most consistent description. Using complementary approaches -- spinodal analysis of the equation of state and direct coexistence simulations with Gaussian mixture phase identification -- we converge on a critical temperature of 6531-6576 $^\circ$K, a critical density of $0.637$ g/cm$^{3}$, and a critical pressure of $1.6$ kbar. The precision of these values, with temperature uncertainties of $\sim$50 K, represents a marked improvement over previous estimates. Our framework establishes a transferable strategy for predicting critical phenomena in metals, with implications for laser ablation, shock compression, and planetary modeling under extreme conditions.

We introduce a holonomy-based geometric diagnostic for birefringence-derived director fields and apply it to stress-induced ferroelectric SrTiO$_3$. Treating the director as a line field in $\mathbb{R}P^2$, we define a holonomy angle $ω$ from residual rotations accumulated along closed loops in real space and compare it with a conventional local-gradient metric. Whereas the gradient quantifies local orientational variation, $ω$ probes the global compatibility of rotations along closed paths. The resulting $ω$ map cannot be reproduced by simple coarse-graining of local gradients, indicating sensitivity to loop-level orientational incompatibility. Analysis of alignment of holonomy rotation axes reveals a cooling-induced reorganization of the electromechanical response, consistent with strain- or stress-related inhomogeneity above the ferroelectric transition and additional ordering below it. These results demonstrate holonomy as a loop-based geometric diagnostic of strain compatibility in orientational fields derived from birefringence.

In a magnetically-dominated model of star formation, we expect to see alignments between the magnetic field orientation of star-forming dense cores and the cloud-scale magnetic field. Pandhi et al. (2023) showed instead, however, that the orientation of cores and their angular momentum vectors appear random with respect to the larger-scale magnetic field, implying that magnetic fields may play a diminished role in core formation and evolution. Here, we use higher-resolution dust polarization data from the B-Fields In Star-forming Region Observations (BISTRO) survey on the James Clerk Maxwell Telescope (JCMT) to investigate the change in the magnetic field orientation from cloud scales to core scales, and reassess any correlations between core-scale magnetic fields, core orientations and core velocity gradients. We produce a catalog of 79 cores over 14 star-forming regions with averaged core-scale magnetic field orientations. We find that the core-scale magnetic field is more disordered compared to the cloud-scale field, as measured by an increased standard deviation in the magnetic field vector orientations. Alignment between the core-scale and cloud-scale field varies greatly between regions. Our results are consistent with random alignments between the core-scale magnetic field, core orientation, and core velocity gradient, in agreement with the results by Pandhi et al. (2023) for the cloud-scale field. We conclude that there is a clear change in the magnetic field in the transition from cloud- to core-scales. Our results suggest that the magnetic field may not play a dominant role in the evolution of dense cores on core scales.

In this paper, we study half-densities enhancing the multiplication map on a symplectic groupoid and which satisfy a suitable associativity condition. This is structurally motivated by the expected complete semiclassical-analytic approximation to a star product for the underlying Poisson manifold. We show the existence and classification of such associative half-densities, and further apply this theory to the understanding of semiclassical factors in Kontsevich's quantization formula. In the particular case of a linear Poisson structure, we recover the factors appearing in the Duflo isomorphism and its Kashiwara-Vergne extensions as a canonical associative enhancement.

Network operators are often interested in verifying \emph{eventually-stable properties} of network control planes: properties of control plane states that hold eventually, and hold forever thereafter, provided the operating environment remains unchanged. Examples include eventually-stable reachability, access control, or path length properties. In this work, we introduce \textsc{CB-Ver}, a new framework for verifying such properties, based on the key idea of a \emph{converges-before graph} (CB-graph for short). When a user provides interfaces for each network component, \textsc{CB-Ver} checks the necessary component-by-component requirements in parallel using an SMT solver. In addition, the tool automatically synthesizes a CB-graph and checks whether it connects all nodes in a network -- if it does, the interfaces are valid and users can check whether additional eventually-stable properties are implied. Moreover, the CB-graph can then be used to determine fault tolerance properties of the network. We formalize our verification algorithm in the Lean theorem proving environment and prove its soundness. We evaluate the performance of \textsc{CB-Ver} on a range of benchmarks that demonstrate its ability to verify expressive properties in reasonable time. Finally, we demonstrate it is possible to automatically generate suitable interfaces by turning the problem around: Given a CB-graph, we use an off-the-shelf Constrained Horn Clause (CHC) solver to synthesize interfaces for every network component that together ensure the given correctness property.

This work presents the Parallelized Hierarchical Connectome (PHC), a general architectural framework that upgrades temporal-only State-Space Models (SSMs) into spatiotemporal recurrent networks. Conventional SSMs achieve parallel-scan training but are limited to temporal recurrence, lacking lateral or feedback interactions within a single timestep. PHC maps the diagonal SSM core to a shared Neuron Layer and inter-neuronal communication to a shared Synapse Layer of hierarchical regions, reconnected by a Multi-Transmission Loop iterating spatial recurrence within each temporal window, at parameter complexity Theta(D^2) versus Theta(D^2 L) of stacked SSMs. This spatiotemporal framework enables the seamless integration of neuro-physical priors typically intractable for standard SSMs, including adaptive LIF, synaptic delay, STP, Dale's Law with E/I-asymmetric topology, and STDP. The framework is instantiated as PHCSSM, the first spiking SSM that integrates all five biological priors and is evaluated on long-sequence data, achieving test accuracy competitive with state-of-the-art SSM baselines at 1,312 to 4,891 trainable parameters (1 to 4 orders of magnitude smaller than every baseline). PHCSSM further admits a sequential recurrent spiking neural network (RSNN) deployment mode that converges asymptotically to the parallel-scan training mode without artificial-neural-network-to-spiking-neural-network (ANN-to-SNN) conversion, with cross-backend reproducibility verified across four hardware backends (x86 CPU, H100 GPU, Cortex-A76, Cortex-M4F) including end-to-end deployment on the Cortex-M4F microcontroller (40 KB SRAM, 128 KB Flash). PHCSSM thereby bridges parallel-scan SSM and biologically grounded RSNN, two paradigms with previously incompatible training regimes, into a single architecture and trained weights.

No matter how much the world of computing changes, system design remains crucial. While most people try to learn it through quick tutorials or AI-generated summaries, there is no better way to master the field than by studying the original research papers. This book serves as a roadmap through those foundational texts, covering seminal papers in distributed systems, operating systems, and big data. It doesn't just look at what these systems do; it digs deep into why they were built that way. Built from years of notes taken during discussions at top universities and industry meetups, this guide helps readers understand how systems work under the hood. It is for those who are tired of surface-level content and want to develop the technical patience to wrestle with complex problem-solving. Readers will find the journey long and challenging but highly rewarding, as it enables them to elevate their engineering craft to a truly professional level.

We investigate the fate of a one-dimensional lattice superfluid formed by hard-core bosons, aka `atoms' (alternatively, a free spinless Fermi sea) subjected to nearest-neighbor attractive Hubbard-like interactions only in subgroups of two sites. The system, as expected, stabilizes a fluid of dimerized molecules at large attractive interactions. However, the composite molecules have an effective meek hopping scale and dominant repulsive interactions solely due to virtual quantum fluctuations. Interestingly, at an intermediate attractive potential, the system realizes a phase-separated region where the system is in an absorbing state. We show that this phase-separated region is due to an emergent attractive interaction between the dimers which leads to a local charge-density wave puddle where particles effectively cluster with local half-filling. Moreover the molecular superfluid gets spontaneously charge-ordered in the addition of an unpaired atom, reflecting the extreme sensitivity of the system to the existence of lone atoms. Using density-matrix renormalization group studies and effective low-energy Hamiltonians, we isolate the quantum processes to uncover the physics behind molecule formation in a strongly interacting one-dimensional system.

It is shown that the post-inflationary quantum chromodynamics (QCD) axion need not lead to a unique one-parameter prediction for the dark matter abundance whenever small explicit Peccei-Quinn symmetry breaking becomes dynamically relevant before the QCD transition. Although strongly constrained by the strong CP bound, such breaking remains phenomenologically viable and introduces a mass scale $μ$ that can control the early-time dynamics, as the QCD contribution to the axion mass is thermally suppressed at high temperatures. In this case, the axion string-wall network annihilates earlier, and the relic abundance is no longer primarily set by QCD dynamics alone, but instead depends on $μ$, in addition to $f_a$, the axion decay constant. This effect overlaps with the parameter space relevant for QCD axion dark matter and, depending on ultraviolet parameters and initial conditions, can extend across it entirely.

We present a protocol for actively suppressing Gauss law violations in quantum simulations of SU(2) lattice gauge theory. Mid-circuit measurements extract a syndrome $(J,M,N)$ characterising the gauge-violation sector at each vertex by resolving both the total angular momentum and the magnetic quantum numbers of the violation through a group quantum Fourier transform. A syndrome-conditional recovery operation maps the state back to the gauge-invariant subspace, and the procedure is iterated as a sweep over vertices in a process we call gauge cooling. We prove that every single-qubit Pauli error at a coordination-four vertex with four spin-$1/2$ edges is detected by the gauge syndrome, and we show that the Knill--Laflamme conditions fail for syndrome-based recovery alone whenever the singlet multiplicity exceeds one. The residual physical-subspace errors carry a structured Pauli decomposition with vanishing $Y$ component, which suggests compatibility with concatenation by a CSS stabilizer code. We demonstrate the protocol on a single-plaquette simulation of the Kogut--Susskind Hamiltonian truncated to the spin-$1/2$ representation under depolarising and amplitude damping noise, and we observe that gauge cooling restores approximate gauge invariance and improves fidelity at noise rates representative of current superconducting hardware.

Net benefit is widely used and reported to evaluate the clinical utility of prediction models, yet its interpretation often remains difficult in practice. In this didactical note, we develop two complementary interpretations that make net benefit easier to understand for clinical audiences. We show that comparisons with treat-none and treat-all can be expressed through threshold-specific observed risk in patients above and below the decision threshold, linking decision-curve performance to calibration in clinically relevant subgroups. We also show how net benefit relates to positive predictive value, offering a more intuitive explanation of when acting on model predictions is justified. We derive and illustrate these results and propose positive predictive value curves as a practical complement to decision curves.

In this article, we analyze the quantum and topological properties of graphene-based plasmonic systems. We consider the following plasmonic materials: single-layer graphene, twisted bilayer graphene, and other graphene stackings, as well as the following architectures: graphene-based gratings, grids, chains of graphene disks, and the kagomé lattice.

The Hubble Missing Globular Cluster Survey (MGCS) has taken one of the last opportunities to complete the census of Galactic globular clusters (GCs) started by past Hubble Space Telescope (HST) programs, securing high-resolution data for 34 GCs never observed before by HST. The previous papers in the series have highlighted the astrometric and photometric potential of the project by analyzing a subsample of targets. We present, and release to the community, the official astro-photometric catalogs of the MGCS for all GCs imaged by this project. We describe the data reduction using state-of-the-art techniques designed for HST. We discuss the photometric calibration and show, for the first time, the synergy with the Gaia catalog to ensure homogeneous photometry across our data set. We compute artificial-star tests that can be used to assess systematics and the completeness level of our data. We combined HST and Gaia data to refine the absolute proper motions of our GCs, reaching a precision $\sim$3 times better than that of Gaia alone. We used these new proper motions to update (and to determine for the first time for five systems) the associations between GCs and their putative galaxy progenitors. This work continues decades-long efforts of large Treasury programs in sharing precise and accurate atlases to the community for studying GCs across a wide range of scientific endeavors.