We provide a transformation rule for adjoint test modules along Cohen--Macaulay maps between Cohen--Macaulay varieties that have $F$-rational geometric fibers. This is, in part, an effective version of Enescu's theorem on the ascent of $F$-rationality under local maps with $F$-rational geometric fibers.

Stencil computations are a fundamental kernel in scientific computing, critical for simulations in domains such as fluid dynamics and climate modeling. However, these computations are often memory-bound on traditional High-Performance Computing architectures like GPUs, struggling against the "Memory Wall". Simultaneously, the rise of AI-oriented hardware, such as the Cerebras Wafer-Scale Engine, offers massive core parallelism and high-bandwidth on-chip memory, though typically optimized for lower-precision workloads. This work investigates the viability of bridging this divergence by mapping stencil algorithms onto the Cerebras WSE-3. The study introduces CStencil, a novel framework designed to implement two-dimensional stencil computations on the WSE-3. To ensure a rigorous and fair performance evaluation, the research also adapts ConvStencil, a state-of-the-art GPU stencil solver, porting it from its original double-precision design to single-precision for execution on an NVIDIA A100 GPU. Experimental results show that the WSE-3's distributed SRAM and mesh interconnect effectively eliminate the off-chip memory bottlenecks common in GPU implementations. CStencil achieves speedups of up to 342x over the adapted ConvStencil version. A roofline model analysis further confirms that CStencil saturates the available compute and memory resources, demonstrating that the WSE dataflow architecture can be successfully repurposed for traditional scientific algorithms. These findings highlight the potential of the WSE-3 to deliver hardware utilization levels unattainable on conventional systems, offering a promising path toward overcoming the memory limitations of current HPC architectures.

A stochastic free-boundary problem for the three-dimensional barotropic compressible Navier--Stokes equations is studied. The main feature of the model is that the free boundary is transported by a Stratonovich stochastic flow, so that the noise enters the kinematic boundary condition and hence the evolution of the moving domain. An additional Itô forcing in the momentum equation is also allowed. The problem is transformed by a stochastic Lagrangian map generated by the velocity and the transport vector fields. In these coordinates the density is represented through the Jacobian of the flow, and the remaining system is solved by combining stochastic maximal regularity, deterministic %\rL^p%-%\rL^q$ estimates, and a localized contraction argument. Local pathwise well-posedness is obtained up to an a.s. positive stopping time, with strictly positive density and pathwise uniqueness.

We investigate the classical reducibility of random unit-disk graph (UDG) instances of the maximum independent set (MIS) and maximum weighted independent set (MWIS) problems, which can be natively realised in Rydberg atom quantum processors. Using state-of-the-art kernelisation techniques, we systematically probe how far classical preprocessing can simplify such native optimisation problems of varying size and connectivity. While many small or sparse instances can be fully reduced, dense graphs often retain finite irreducible kernels even after extensive reductions. Introducing vertex weights tends to increase reducibility, whereas extending the interaction range in the underlying UDG connectivity suppresses the reduction efficiency. By exploring where classical reductions cease to be effective, we aim to delineate the regime of problem instances that remain computationally demanding - those most relevant for testing and benchmarking near-term quantum optimisation hardware. We find that for the remaining finite kernels, quantum execution would require non-native embeddings with substantial resource overheads, suggesting that directly running native instances may be more practical than embedding a reduced kernel.

We explore the quasiparticle properties of a single $Λ$ hyperon propagating through symmetric nuclear matter using the Green's function formalism. The $NΛ$ interaction is described by a non-local regulated low-momentum contact potential with a leading-order constant term and a next-to-leading-order derivative correction. The two coupling constants in the ${}^1S_0$ and ${}^3S_1$ channels are fixed by matching the vacuum on-shell $T$ matrix to the scattering length and effective range obtained from modern next-to-next-to-leading-order chiral effective field theory. Using this effective interaction, we calculate the retarded $Λ$ self-energy from the in-medium $NΛ$ ladder $T$ matrix, which sums repeated $NΛ$ scattering in the nucleonic medium. At saturation density, the zero-momentum quasiparticle pole is found at $E_{\rm qp}(0,ρ_{\rm sat})=-29.55~{\rm MeV}$, in good agreement with the empirical depth of the single $Λ$ potential in nuclear matter. The self-energy decomposition gives a static Born contribution $Σ_Λ^{\rm Born}(0)=-26.36~{\rm MeV}$ and a dynamical correlation contribution ${\rm Re}\,Σ_Λ^{\rm corr,R}(0,E_{\rm qp})=-3.19~{\rm MeV}$, showing that repeated in-medium $NΛ$ scattering is needed to reproduce the empirical binding scale. The quasiparticle remains narrow and well defined, with a large residue $Z(0)=0.98$, a small damping width $Γ(0)=0.023~{\rm MeV}$, and a sharp spectral peak near the quasiparticle energy. At finite momentum, the $Λ$ quasiparticle becomes less bound, with $E_{\rm qp}(k,ρ_{\rm sat})$ increasing from $-29.55~{\rm MeV}$ at $k=0$ to $-6.49~{\rm MeV}$ at $k=1~{\rm fm}^{-1}$, while the residue and width change only weakly. A low-momentum fit gives $m_Λ^*/m_Λ=0.747$, consistent with the range obtained in Brueckner calculations with Nijmegen hyperon--nucleon potentials.

Understanding how nonequilibrium systems respond to perturbations is a central challenge in physics. In this work, we establish mutual linearity in nonequilibrium overdamped Langevin systems. This theory provides a framework for controlling and designing nonequilibrium responses in continuous systems. When a dynamical parameter is locally perturbed at a single position, the stationary densities at any two positions are linearly related. It further leads to mutual linearity among different stationary state-current observables. We also extend the mutual linearity to non-stationary relaxation processes in the Laplace domain. Our theory reveals that mutual linearity in both discrete and continuous systems originates from the same one-dimensional response structure. We further show that mutual linearity is robust under finite-width perturbations. As an application, we demonstrate the mutual linearity and its finite-width robustness in the F$_1$-ATPase rotary motor model.

The Středa formula links the Hall conductivity of an insulator to the magnetic-field response of its particle density, providing a local and universal probe of the topological Chern number. Beyond this quantized response, an energy-resolved Středa marker can be defined from the magnetic response of the density of states, revealing detailed features of the quantum geometry of Bloch bands. We show that driven-dissipative bosonic lattices provide direct access to both the integrated and energy-resolved Středa responses. Our scheme uses controlled pumping with uniform strength and random phases across the lattice, together with uniform loss, to yield a Lorentzian filter of eigenmode occupations. For generic dispersive bands, this enables reconstruction of a coarse-grained energy-resolved Středa response, establishing these platforms as versatile probes of anomalous spectral flow and energy-resolved quantum geometry. As a striking application, we show that this marker elucidates the fate of topological bands under strong disorder, capturing the quantum-geometric structure underlying topological Anderson insulators.

We report a comprehensive NMR study of the chiral square-cupola antiferromagnet Pb(TiO)Cu$_4$(PO$_4$)$_4$ and compare its microscopic hyperfine and local-field parameters with the Ba/Sr analogues in the $A$(TiO)Cu$_4$(PO$_4$)$_4$ family. Above $T_{\rm N}\simeq 6.7$ K, the $^{31}$P Knight shift tracks the bulk susceptibility and yields nearly isotropic transferred hyperfine couplings $H_{\rm hf}^{[010]}=6.77(3)$ and $H_{\rm hf}^{[001]}=6.19(3)$ kOe/$μ_{\rm B}$. Below $T_{\rm N}$, the frequency-swept $^{31}$P spectrum splits into three lines, in contrast to the four-line pattern reported for BaTCPO. The line separation tracks the onset of the static $^{31}$P internal field with a power-law exponent $β\simeq 0.23$, consistent with quasi-two-dimensional criticality. Crystal-rotation $^{31}$P NMR in the ordered state resolves all eight symmetry-related P sites and their site-dependent anisotropy. In the ordered state, zero-field $^{63,65}$Cu NMR gives a Cu-site internal field $B_{\rm int}=14.50(6)$ T and a quadrupole frequency $ν_Q=32.72(5)$ MHz, while point-charge electric-field-gradient calculations including Sternheimer corrections yield an on-site Cu hole occupancy $n_d=0.20(4)$, consistent with a ligand-hole-dominated charge-transfer character. Comparing PbTCPO with BaTCPO and SrTCPO, we find that the transferred hyperfine coupling $H_{\rm hf}$ varies across the series, reflecting changes in local Cu-O-P covalency, whereas the ordered-state $^{31}$P internal field in PbTCPO is $69.5$ mT, considerably higher than in BaTCPO ($35.6$ mT) and SrTCPO ($34.6$ mT). This enhancement is not captured by dipolar terms alone and points to the combined effects of transferred contributions and stacking-dependent cancellation.

We classify, up to projective automorphism, all homogeneous pre-foliations of co-degree one and degree four on the complex projective plane $\Ptwo$ whose Legendre transform defines a flat $4$-web. The classification is organized according to the type of the underlying homogeneous foliation $\Hcal$ of degree~$3$, distinguishing the cases $°(\Tcal_{\Hcal})=2$, $3$, and~$4$. The case $°(\Tcal_{\Hcal})=2$ was treated by Bedrouni, while the cases $°(\Tcal_{\Hcal})=3$ and $°(\Tcal_{\Hcal})=4$ are completed here. The proof combines Bedrouni's curvature-holomorphy criteria with explicit normal forms and symbolic computation; the result yields a finite list of explicit one-forms, parametrised by the ramification data of the Gauss map of~$\Hcal$.

For a single trapped ion, the excitation spectrum of a narrow optical transition consists of a Doppler- and recoil-free carrier accompanied by motional sidebands, which are equally spaced by the trap secular frequency and lie under a Doppler-broadened envelope that is shifted by the photon recoil. Outside the Lamb-Dicke regime, the large photon recoil distributes the line strength across many sidebands and suppresses excitation of the carrier. With multiple ions, the motional spectrum becomes dense, and the carrier is further weakened. Here, we predict a counterintuitive revival effect: increasing the number of ions in a linear chain can restore strong carrier excitation even under trapping conditions far from the single-ion Lamb-Dicke regime. Using a quantum-mechanical model of the excitation dynamics in linear ion chains, we find that sufficiently long chains concentrate the spectrum into the carrier. This effect enables efficient excitation of light ions at short wavelengths. It may also benefit multi-ion optical clocks and mixed-species quantum-logic spectroscopy.

A vertex set $W$ in a graph $G$ is a valid $k$-swap for a vertex cover $S$ of $G$ if $W$ has size at most $k$ and $S'=(S \setminus W) \cup (W \setminus S)$, the symmetric difference of $S$ and $W$, is a vertex cover of $G$. If $|S'| < |S|$, then $W$ is improving. In LS Vertex Cover, one is given a vertex cover $S$ of a graph $G$ and wants to know if there is a valid improving $k$-swap for $S$ in $G$. In applications of LS Vertex Cover, $k$ is a very small parameter that can be set by a user to determine the trade-off between running time and solution quality. Consequently, $k$ can be considered to be a constant. Motivated by this and the fact that LS Vertex Cover is W[1]-hard with respect to $k$, we aim for algorithms with running time $\ell^{f(k)}\cdot n^{\mathcal{O}(1)}$ where $\ell$ is a structural graph parameter upper-bounded by $n$. We say that such a running time grows mildly with respect to $\ell$ and strongly with respect to $k$. We obtain algorithms with such a running time for $\ell$ being the $h$-index of $G$, the treewidth of $G$, or the modular-width of $G$. In addition, we consider a novel parameter, the maximum degree over all quotient graphs in a modular decomposition of $G$. Moreover, we adapt these algorithms to the more general problem where each vertex is assigned a weight and where we want to find a valid $d$-improving $k$-swap, that is, a valid $k$-swap which decreases the weight of the vertex cover by at least $d$.

Sampling from a high-dimensional probability distribution is a fundamental algorithmic task arising in wide-ranging applications across multiple disciplines, including scientific computing, computational statistics and machine learning. Langevin Monte Carlo (LMC) algorithms are among the most widely used sampling methods in high-dimensional settings. This paper introduces a novel higher-order and Hessian-free LMC sampling algorithm based on an efficient stochastic Runge--Kutta method of strong order $1.5$ for the overdamped Langevin dynamics. In contrast to the existing Runge--Kutta type LMC (Li et al., 2019) involved with three gradient evaluations, the newly proposed algorithm is computationally cheaper and requires only two gradient evaluations for one iteration. Under certain log-smooth conditions, non-asymptotic error bounds of the proposed algorithms are analyzed in $\mathcal{W}_2$-distance. In particular, a uniform-in-time convergence rate of order $O(d ^{\frac32} h^{\frac32})$ is derived in a non-log-concave setting, matching the convergence rate proved in the aforementioned work but under the log-concavity condition. Numerical experiments are finally presented to demonstrate the effectiveness of the new sampling algorithm.

Eugenio Beltrami published his seminal 'Essay on the Interpretation of Non-Euclidean Geometry' in 1868, where he showed that geodesics on a surface of constant negative curvature can be mapped as straight lines on a Euclidean disc. More importantly he showed that figures on the disc would satisfy the identities of hyperbolic geometry characteristic of a surface of negative curvature. However Beltrami did not always give a full explanation of the equations which he used. These notes are an attempt to provide a derivation of some of his principal results, including his formula for hyperbolic distance on the disc, his proof that the sum of the (hyperbolic) angles of a triangle on the disc is less than two right angles and his equations for circles, equidistants and horocycles.

We describe an electron bunch injector scheme based on proton-driven plasma wakefield acceleration for the Electron-Ion Collider. The proton bunches needed to drive the plasma wake are taken from the existing Blue-Ring of RHIC. The polarized electron source is taken from the current EIC design. We describe the different elements making up the injection scheme and give an estimate for the performance. Our initial study indicates that the design parameters of the EIC are within reach when accelerating the electron bunches in the proton-driven plasma wake, with average polarization of ~70% and a luminosity of 1e34 cm$^{-2}$s$^{-1}$.

Magnetohydrodynamic (MHD) simulations are indispensable research infrastructure in astrophysics today. In order to satisfy the solenoidal constraint of the MHD equations on discretized grids, modern simulation codes often employ either constrained transport (CT) with a staggered grid or divergence cleaning using an additional variable. We compare CT and Dedner's mixed divergence cleaning schemes systematically, and find that the divergence cleaning scheme can produce substantial artifacts in certain situations. Through numerical experiments including both idealized tests and practical applications, we show that the original implementation of Dedner's scheme becomes inaccurate when magnetic fields are strongly localized or when the timestep suddenly changes. We find that some previous results, such as the extremely rapid growth of magnetic fields during star formation in the early Universe, may be affected by the spurious behavior of the divergence cleaning scheme. We propose a few modifications to improve the robustness of the divergence cleaning method. Nevertheless, we find that the CT scheme is more accurate and reliable in many situations.

We study connected graphs with a fixed degree sequence, in the sparse setting where the number of edges grows linearly in the number of vertices. Using the relation to the configuration model, we identify the number of such connected graphs up to the exponential order. We do this by viewing a connected graph with a given degree distribution as the realization of the giant component in a larger configuration model, and carefully choosing the degree distribution of the larger graph so that it is likely that its giant component has the required degree distribution. To ensure that the connected graph has exactly the correct degrees, we use a switching argument. Additionally, we obtain results on rare event probabilities and describe the local structure of a uniform connected graph with a fixed degree sequence.

Two-dimensional transition metal dichalcogenides (TMDCs) are promising materials for next-generation optoelectronic devices, yet their implementation is hindered by limited sample stability and challenges in forming reliable electrical contacts. Here, by utilizing time-domain THz emission spectroscopy we directly probe charge carrier dynamics in monolayer WS2 on gold (Au) and fused silica (SiO2) as a function of interface morphology. For laser excitation above the band gap of WS2, we independently extract effective transport times for both electrons and holes and find that discontinuous WS2 contacts on rough Au generate larger net photocurrents than uniform, strongly coupled interfaces - a counterintuitive observation attributed to imbalanced electron and hole transfer from WS2 to Au. Crucially, we demonstrate that ultrafast charge extraction and separation suppress recombination-driven energy release and thereby prevent photo-induced degradation under ambient conditions, eliminating the need for encapsulation. These findings redefine interfacial design as a central control parameter for both performance and stability in 2D optoelectronic devices.

We introduce a sequence representation of a random variable $X$ supported on a compact interval $[a,b]$, which we call a primitive sequence. We construct this sequence by repeatedly antidifferentiating the associated cumulative distribution function of $X$ and evaluating the antiderivatives at the endpoint $b$. We show that the primitive sequence of $X$ can be identified as a factorially rescaled moment sequence of the reflected random variable $b-X$. Through this identification, we show that the primitive sequence transparently captures qualitative features of the distribution of $X$. We then connect primitive sequences directly to classical moment theory and exploit this connection to characterize admissible primitive sequences and to show that under natural topologies, the map from probability measures to primitive sequences is a homeomorphism. We end by examining the set of probability measures whose first $m$ primitive sequence terms are fixed, and thereby obtaining sharp upper and lower bounds on two functionals of those measures.

Stellar streams are excellent probes of the gravitational potential in which they evolve. In the Milky Way (MW), globular cluster (GC) streams are routinely used to infer properties about time-dependent perturbations of the underlying potential. This implies that streams with Galactocentric radii small enough to be perturbed by the MW bar should offer constraints on it, such as its pattern speed, which currently has a wide range of values reported in the literature and is important when studying stellar kinematics. The GC M92 has a small pericentre and should be affected by the bar. It has a diffuse stellar stream, but confirming stream members has previously been hindered by a lack of spectroscopic data. In this paper, we use Dark Energy Spectroscopic Instrument (DESI) observations together with photometric and astrometric data to obtain spectroscopic members of the M92 stream for the first time. We identify a clear spatial distribution and gradients in distance moduli, proper motions, and radial velocities that confirm the stream's existence. We compare the observed stream to mock streams generated in different barred potentials and estimate the MW bar's pattern speed $Ω= 29.1^{+0.7}_{-0.4}$ km s$^{-1}$ kpc$^{-1}$ and $\dot Ω= 0.7^{+3.5}_{-2.3}$ km s$^{-1}$ kpc$^{-1}$ Gyr$^{-1}$. This is the first time a stellar stream is used to probabilistically infer these bar properties, and it opens up an exciting realm of inner Galactic potential characterisation using stellar streams.

We construct and analyze the logarithmic sector of chiral Topologically Massive Gravity (TMG) at the critical point $μ\ell = 1$ from the perspective of Virasoro evolution and radial monodromy in $\mathrm{AdS}_3$. We show that the logarithmic graviton arises naturally as a generalized eigenstate of $L_0$, with its Jordan structure persisting uniformly across the full $SL(2,\mathbb{R})_L$ descendant tower generated by $L_{-1}$. A central result is that the logarithmic mixing of primary and descendant states can be equivalently interpreted as unipotent monodromy under analytic continuation of the radial coordinate $r \to e^{2πi} r$. This establishes a direct identification between the LCFT Jordan cell structure and a geometric monodromy operator acting in the bulk. We demonstrate that requiring monodromy-compatible Virasoro flow uniquely reconstructs the full indecomposable logarithmic module, including all descendant levels, and show explicit equivalence with the logarithmic graviton module previously obtained in the linearized analysis of chiral TMG. This provides a unified representation-theoretic and geometric characterization of logarithmic gravity in $\mathrm{AdS}_3$.

We prove a strengthening of Chang's lemma for subsets of $\mathbb F_p^n$. The classical conclusion that the large spectrum is contained in a subspace of dimension at most $2\varepsilon^{-2}\log(1/α)$ is refined to show that every character outside this subspace has small correlation with the set not only globally, but also on average over the cosets of the orthogonal complement, in a natural cosetwise $\ell^1$ norm. As a consequence, we obtain a localized counting lemma. We also give an extension of the argument to arbitrary finite abelian groups.

We show that every entire solution to the Bernoulli (or one-phase) free boundary problem with finite Morse index in $\mathbb{R}^3$ is axially symmetric. In fact, we additionally prove that the same result would follow in any dimension $4 \le n \le 6$ in which stable entire solutions are shown to be flat.

We investigate finite-time blow-up for nonnegative solutions to the Cauchy problem associated with semilinear parabolic equations driven by a mixed local--nonlocal operator. The reaction term is assumed to satisfy suitable structural hypotheses, the prototype being $f(u)=u^p$ with $p>1$. By adapting the Kaplan method to the present framework, we prove that solutions blow up in finite time whenever the initial datum is sufficiently large. In the prototype case $f(u)=u^p$, this conclusion holds for every $p>1$. As a particular case of our operator, we also include the fractional Laplacian; to the best of our knowledge, this type of result is new even in that special case.

The design of a system and its implementation are two tasks often carried out by different individuals on a development team, and can occur weeks or months apart. This creates a potential for divergence between real behavior and the designed model that an implementation is intended to match. Particularly as time passes and individuals who were present for the original conception of the design leave, a system can lose coherence and drift from intended design principles. Even with a robust system design, more is needed to ensure that the key implementation details match the design and that adherence to a particular strategy is not lost over time. This paper proposes an approach to address that concern for distributed systems using conformance checking, a methodology borrowed from process mining. Distributed traces produced by instrumented applications are evaluated for conformance by comparison to design traces. The resulting conformance percentage is a quantitative metric that can be tracked over time to determine how closely a concrete implementation corresponds to the key attributes of the expected design model. This analysis is done using the dominant industry standard, OpenTelemetry, and so should apply to a wide range of distributed systems.

Adding a sublattice bias to the two dimensional Bose Hubbard model greatly enriches the available physics, and introduces knobs which can be used to control and interrogate the quantum state. We describe the physics of this checkerboard Bose Hubbard model and how it can be explored using transmon arrays. We show that the sublattice bias brings the commensurate superfluid phase into an experimentally accessible regime, and gives new probes. We characterize the superfluid and insulating phases, with careful attention to finite size effects.

Magnetic kagome metals provide a fertile platform for exploring unusual magnetotransport phenomena arising from the intricate interplay between electronic topology, electron correlations, and magnetic order. MgMn6Sn6 is a room-temperature kagome ferromagnet with strong in-plane magnetic anisotropy. Here, we report a combined study of single-crystal neutron diffraction (SCND) and magnetotransport properties of MgMn6Sn6, supported by first-principles calculations. Our SCND measurements reveal a non-collinear arrangement of Mn magnetic moments within the basal plane of the kagome bilayer. The Hall conductivity shows a substantial intrinsic contribution of approximately 0.29 e^2/h per kagome layer, which is nearly isotropic with respect to the field orientation. At low temperatures, the anomalous Hall conductivity develops a pronounced anisotropic extrinsic component, highlighting the directional sensitivity of scattering processes. The significantly large value of the Sommerfeld coefficient, in the absence of f-electrons, underscores enhanced electron correlation. Therefore, the non-collinear kagome ferromagnet MgMn6Sn6 is a promising candidate for studying the effects of electron correlation on magnetotransport properties.

We study vortex ring formation arising from the interaction between a cavitation bubble and a confined air bubble in a cylindrical blind hole, using high-speed shadowgraphy imaging. As the cavitation bubble grows above the hole, it drives a downward flow that compresses the air bubble at the base. The air bubble subsequently expands, expelling the overlying liquid column upward as a coherent slug; impact of this slug on the far boundary of the collapsing cavitation bubble produces a vortex ring. Parametric experiments across the dimensionless stand-off distance $\mathcal{H} = h/R_{\max}$ and the air bubble fill fraction $\mathcal{B} = (d_\text{hole} - d_\text{top})/d_\text{hole}$ identify three regimes: (i) liquid column impact during collapse, producing a vortex ring ($\mathcal{H} \lesssim 0.5$, $\mathcal{B} \lesssim 0.5$); (ii) late impact near the end of collapse (large $\mathcal{H}$); and (iii) direct air bubble impact after bypassing the liquid column (large $\mathcal{B}$), with neither (ii) nor (iii) producing a ring. Two one-dimensional models, based on the Rayleigh-Plesset equation and isentropic air bubble expansion, predict the liquid column impact location and its speed $U_\text{lc}$, respectively. A dimensionless timing parameter $Π= (h + R_{\max}) / (U_\text{lc} \cdot t_\text{cav}/2)$, comparing the liquid column travel time to the cavitation collapse half-period, distinguishes the three regimes: ring formation occurs for $1 \lesssim Π\lesssim 1.5$. The ring propagates from the hole at an initial speed of $5$ m/s, decelerating quadratically, and breaks apart via azimuthal instabilities at $Re \approx 4500$.

Open-source software (OSS) pipelines rely on automated static analysis tools to prevent the introduction of vulnerabilities in code. However, there is limited understanding of the efficacy of these tools across the OSS ecosystem over time. In this paper, we introduce a novel method to evaluate static application security testing (SAST) tools through longitudinal measurements and perform the largest academic study of CodeQL -- the most prevalent static analysis tool from GitHub -- on OSS codebases. We apply our apparatus on 114 versions of CodeQL over time on 3993 CVEs from 1622 repositories to measure key properties of the tool, culminating in more than 20 billion lines of code analyzed. First, we measure its effectiveness, i.e., its ability to detect vulnerabilities before they are fixed. Then, we determine whether these detections were actionable through two measures of the distance between findings and vulnerability location either over the entire codebase or within the vulnerable file. Finally, we study the stability of CodeQL by examining how vulnerability detections hold across versions and the evolution of CodeQL on the accuracy-precision trade-off. We find that CodeQL identifies a total of 171 CVEs, and that for 83 of them, a CodeQL version prior to the fix could detect it. Such detections are in general actionable if findings are triaged across files, as for 50% of the 171 detections, more than 50% of findings in the vulnerable file are located in the vulnerable location. Finally, we show that CVE detections are not monotonic across versions as 21 CVEs were no longer detected following a version change and 17 that were never redetected. Our study shows that using SAST tools is a matter of best practice as they prevent numerous vulnerabilities from being introduced, but that developers should be aware of changes that may leave blind spots in detections upon updates of the tool.

The lettericity of a graph $G=(V,E)$ is defined as the smallest size of an alphabet $Σ$ such that there is a word $w_1 \dots w_{|V|} \in Σ^*$ and a decoder $\mathcal{D} \subseteq Σ^2$ with the property that $G$ is isomorphic to the letter graph $G(\mathcal{D}, w)$, that is, the graph with vertex set $\{1, \dots, n\}$ and edge set $\{ij \mid 1\leq i < j \leq n, w_iw_j \in \mathcal{D}\}$. Note that $G(\mathcal{D}, w)$ can be seen as a graph with inherent coloring $χ\colon V(G) \rightarrow Σ$. It is unknown whether the lettericity of a given graph can be computed in polynomial time. The problem to determine the lettericity of a given graph is called the lettericity problem. As a step towards answering the complexity of this problem, we investigate the following retrieval problems: given a graph $G$ together with two of the three solution-objects (word $w$, decoder $\mathcal{D}$, and coloring $χ$), the goal is to compute the third solution-object. We show that word retrieval and decoder retrieval are solvable in polynomial time, while coloring retrieval is equivalent to the graph isomorphism problem. Beyond this, we introduce symmetric lettericity which is a restricted version of lettericity where each decoder needs to be symmetrical ($ab\in \mathcal{D}$ if and only if $ba\in \mathcal{D}$). As we show, the symmetric lettericity of a graph always equals the neighborhood diversity of the graph, which in fact can be computed in linear time.

This paper proposes an approach to information-based logics using many-logic modal structures (MLMS). These structures can express accessibility relations between worlds with different underlying logics by anchoring them to a base lattice, which contains the semantics of each logic as a down-complete sublattice. MLMS are suitable for representing connections between information states (i.e., configurations of databases) and the evolution of information states over time. We will illustrate the application of MLMS by means of the six-valued logic of evidence and truth LET+K , related to the lattice L6, and some four-, three-, and two-valued logics related to down-complete sublattices of L6. These logics are capable of representing paracomplete, paraconsistent, and classical contexts with six-, four-, three-, and two-valued scenarios.