Diffusion Probabilistic Model (DDPM) for generating one-day-ahead arbitrage-free implied volatility surfaces. To capture the path-dependent nature of volatility dynamics, we condition our model on a set of market variables, including exponentially weighted moving averages (EWMAs) of historical vol-surfaces, returns and squared returns of the underlying asset, and scalar risk indicators associated with the underlying asset. A key challenge is that historical data often contains arbitrage opportunities in the earlier dataset for training, which conflicts with the goal of generating arbitrage-free surfaces. We address this by using a parameter-free weighting scheme based on the signal-to-noise ratio (SNR) to incorporate the arbitrage penalty into the loss function. The scheme dynamically adjusts the penalty strength across the diffusion process. Through numerical experiments using market data, we demonstrate the superior performance of our proposed model in volatility forecasting compared to existing approaches.

Gérard and Grellier proposed, under the name of the cubic Szegő equation, a remarkable classical field theory on a circle with a quartic Hamiltonian. The Lax integrability structure that emerges from their definition is so constraining that it allows for writing down an explicit general solution for prescribed initial data, and at the same time, the dynamics is highly nontrivial and involves turbulent energy transfer to arbitrarily short wavelengths. The quantum version of the same Hamiltonian is even more striking: not only the Hamiltonian itself, but also its associated conserved hierarchies display purely integer spectra, indicating a structure beyond ordinary quantum integrability. Here, we initiate a systematic study of this quantum system by presenting a mixture of analytic results and empirical observations on the structure of its eigenvalues and eigenvectors, conservation laws, ladder operators, etc.

It is well-known by now that the BFGS method is an effective method for minimizing nonsmooth functions. However, despite its popularity, theoretical convergence results are almost non-existent. One of the difficulties when analyzing the nonsmooth case is the fact that the secant equation forces certain eigenvalues of the quasi-Newton matrix to vanish, which is a behavior that has not yet been fully analyzed. In this article, we show what kind of behavior of the eigenvalues would be sufficient to be able to prove the convergence for piecewise differentiable functions. More precisely, we derive assumptions on the behavior from numerical experiments and then prove criticality of the limit under these assumptions. Furthermore, we show how quasi-Newton methods are able to explore the piecewise structure. While we do not prove that the observed behavior of the eigenvalues actually occurs, we believe that these results still give insight, and a certain intuition, for the convergence for nonsmooth functions.

We study a single-sided black hole with an end-of-the-world (EoW) brane behind the horizon in the double-scaled SYK (DSSYK). The new Hamiltonian is a deformation of the original DSSYK Hamiltonian with an extra exponential wormhole length operator, which leads to a new chord diagram rule. The boundary algebra is defined as generated by the new Hamiltonian and boundary matter. There is an alternative but equivalent definition with a $q$-coherent state due to a nontrivial isomorphism of the vN algebra of DSSYK. This isomorphism induces a unitary equivalence, which yields a surprising result that the boundary algebra of a single-sided black hole in DSSYK has a non-trivial commutant and is a type II$_1$ vN factor. It follows that the full bulk reconstruction from the boundary is impossible, and there is a ``no man's island" behind the horizon in the semiclassical JT limit. Inspired by the EoW brane, we construct a family of matter-brane states with an arbitrary number of matter chords and behaving like an EoW brane. They exactly solve the full spectrum of DSSYK. We take different ways to understand the nontrivial commutant. We show that the commutant is complex on chord number basis and thus non-geometric. In the semiclassical JT limit, the commutant becomes the canonical purification of the boundary algebra and claims the no man's island. In the context of Hawking radiation after Page time, the unitary equivalence is interpreted as encoding the canonical purification into the old Hawking radiation, and the no man's island has the same essence as the island. Including the exponential wormhole length operator independently, the boundary algebra is extended to all bounded operators and reconstructs the no man's island. This can be regarded as a different choice for the definition of boundary algebra. This type I$_\infty$ algebra is closely related to the EoW brane in Kourkoulou-Maldacena.

Collective motion in active matter is usually modelled through instantaneous local alignment, where each agent updates its heading from the current configuration of its neighbours. Many biological and engineered agents, however, possess internal regulatory variables that evolve more slowly than alignment itself and can store information about past alignment states. We introduce a minimal two-timescale model in which each agent carries a fast perceptual register and a slow regulatory variable. The fast register encodes the instantaneous tendency to align with neighbouring headings, while the slow variable integrates recent alignment and feeds back into subsequent alignment decisions. The internal dynamics are formulated using a GKSL-derived Bloch representation, used only as a positivity-preserving effective description of bounded two-state variables; no microscopic quantum dynamics is assumed. The model reduces to Vicsek-type alignment in the fast-relaxation, weak-feedback limit, but shows distinct behaviour when slow feedback is active. Simulations reveal slow-fast relaxation, feedback-induced hysteresis, finite memory-dependent loop area, and non-monotonic coordination between collective order and regulatory tone. These results show how effective non-Markovian collective motion can emerge from local internal feedback.

We study parallel sampling from high-dimensional strongly log-concave distributions. Langevin-based samplers converge rapidly in continuous time, but their discretizations are typically sequential and often require polynomially many steps in the dimension $d$, the target accuracy $\varepsilon^{-1}$, or both. Picard-based parallel sampling methods reduce this sequential depth to polylogarithmic scale by solving for many time-discretization points in parallel; however, existing guarantees often require a polynomial number of processors, leading to substantial memory and gradient-evaluation costs in high dimensions. We show that higher-order Langevin structure can reduce this parallel resource burden while preserving polylogarithmic sequential depth. Our method combines arbitrary-order Langevin dynamics with blockwise Lagrange polynomial interpolation. This sharper discretization reduces the number of parallel points required to achieve a target accuracy. Our results cover both higher-order smooth potentials and ridge-separable potentials, including models such as Bayesian logistic regression and two-layer neural networks, and improve upon the space complexity of the current literature on parallel log-concave sampling.

The Borel-Weil-Bott theorem can be used to decompose the cohomology of twisted sheaves of holomorphic forms on the complex Grassmannian into irreducible representations of the general linear group. By analyzing this decomposition, we provide two effective formulae for computing the associated Hodge numbers, and give examples in special cases. One of these involves a novel integer-valued hook-product statistic on bounded partitions, and the other is based on semistandard tableaux. We reformulate Snow's observation that the positivity of the Hodge numbers is equivalent to the existence of a partition satisfying certain properties, and improve known bounds on when this occurs. This involves a combinatorial proof of the Nakano vanishing theorem for the Grassmannian utilizing a map from core partitions to plane partitions. Finally, we extend our computation of the Hodge numbers of twisted holomorphic forms on the Grassmannian to a q-analogue.

An analysis of baryogenesis and stochastic gravitational wave production is presented for an extension of the standard model where the dark sector consists of dark matter particles charged under a $U(1)_x$ gauge symmetry, while a subset of dark fields also carry lepton number but no $U(1)_x$ charge. We demonstrate that with CP violation induced by Yukawa couplings, equal and opposite lepton asymmetries are generated in the visible and hidden sectors. Subsequent evolution preserves lepton number separately in each sector, and sphaleron interactions partially convert the lepton asymmetry into baryon asymmetry near the temperature of the first-order phase transition. Further, we discuss stochastic gravitational wave background production for the first-order phase transition using a gauge-independent bubble nucleation dynamics which yields spectra also valid in the supercooled low-temperature regime with {$T_p/m_{A_x} \ll 1$} where $T_p$ is the percolation temperature and $m_{A_x}$ is the dark photon mass. A parameter-space scan identifies regions that simultaneously account for cogenesis of baryon asymmetry and dark matter and predict stochastic gravitational wave signals within reach of current (NANOGrav, EPTA, PPTA) and future detectors at higher frequencies, providing a unified framework for cogenesis and associated gravitational wave production.

Enterprise chatbots show promise in supporting knowledge workers in information synthesis tasks by retrieving context from large, heterogeneous databases before generating answers. However, when the retrieved context misaligns with user intentions, the chatbot often produces "irrelevantly right" responses that provide little value. In this work, we introduce VizCopilot, a prototype that incorporates visualization techniques to actively involve end-users in context alignment. By combining topic modeling with document visualization, VizCopilot enables human oversight and modification of retrieved context while keeping cognitive overhead manageable. We used VizCopilot as a design probe in a Research-through-Design study to evaluate the role of visualization in context alignment and to surface future design opportunities. Our findings show that visualization not only helps users detect and correct misaligned context but also encourages them to adapt their prompting strategies, enabling the system to retrieve more relevant context from the outset. At the same time, the study reveals limitations in verification support regarding close-reading and trust in AI summaries. We outline future directions for visualization-enhanced chatbots, focusing on personalization, proactivity, and sustainable human-AI collaboration.

We analyze the classification problem for finitely generated orderable groups from the viewpoint of descriptive set theory. We analyze the standard Borel space of finitely generated left-orderable groups, and the subspace of finitely generated bi-orderable groups using spaces of relative cones. We use this setup to show that the isomorphism relation on finitely generated bi-orderable groups is weakly universal.

While diffusion models are attracting increasing attention for the design of novel materials, their ability to generate low-energy structures in unexplored chemical spaces has not been systematically assessed. Here, we evaluate the performance of two diffusion models, MatterGen and DiffCSP, against three databases: a ternary oxide set (constructed by a genetic algorithm), a ternary nitride set (constructed by template informatics), and the GNoME database (constructed by a combination of both). We find that diffusion models generally perform stably in well-sampled chemical spaces (oxides and nitrides), but are less effective in uncommon ones (GNoME), which contains many compositions involving rare-earth elements and unconventional stoichiometry. Finally, we assess their size-extrapolation capability and observe a significant drop in performance when the number of atoms exceeds the trained range. This is attributed to the limitations imposed by periodic boundary conditions, which we refer to as the curse of periodicity. This study paves the way for future developments in materials design by highlighting both the strength and the limitations of diffusion models.

Josephson junctions coupled through magnetic textures provide a controllable platform for odd-frequency superconductivity and Majorana physics. Within a tight-binding Green function framework, induced pair correlations and spectral properties are analyzed under various magnetic and geometric conditions. When the junction is in the topologically trivial regime, even-frequency singlet pairing is dominant, whereas the topological phase is characterized by the coexistence of Majorana bound states and robust odd-frequency equal-spin triplet pairing at the interface edges. The odd-frequency polarized triplets reveal a divergent $1/ω$ behavior when the Majorana states are decoupled, which is intrinsically connected to their self-conjugation property. The zero-frequency divergence evolves into shifted resonances and linear low-frequency behavior once hybridization occurs. A nonmagnetic interruption in the texture separates the topological superconductor into two topological segments and generates additional inner Majorana modes. When the nonmagnetic barrier is comparable to the inner Majorana states localization length, they hybridize and modify their associated odd-frequency triplet pairing, while the outer edge modes preserve their self-conjugated nature. Tuning the superconducting phase difference further controls the onset of the topological regime and the stability of localized Majorana states. The results highlight the central role of odd-frequency triplet correlations as a probe of topological superconductivity in magnetically engineered Josephson junctions.

We give a natural problem over input quantum oracles $U$ which cannot be solved with exponentially many black-box queries to $U$ and $U^\dagger$, but which can be solved with constant many queries to $U$ and $U^*$, or $U$ and $U^{\mathrm{T}}$. We also demonstrate a quantum commitment scheme that is secure against adversaries that query only $U$ and $U^\dagger$, but is insecure if the adversary can query $U^*$. These results show that conjugate and transpose queries do give more power to quantum algorithms, lending credence to the idea put forth by Zhandry that cryptographic primitives should prove security against these forms of queries. Our key lemma is that any circuit using $q$ forward and inverse queries to a state preparation unitary for a state $σ$ can be simulated to $\varepsilon$ error with $n = \mathcal{O}(q^2/\varepsilon)$ copies of $σ$. Consequently, for decision tasks, algorithms using (forward and inverse) state preparation queries only ever perform quadratically better than sample access. We also identify a motif, which we call the "acorn trick", where generically strengthening a quantum resource can be possible if the output is allowed to be random, bypassing no-go theorems for deterministic algorithms. We demonstrate this idea for several settings, including controlization and purification.

Synchronous Generators (SGs) currently provide important levels of Short-Circuit Current (SCC), a critical ancillary service that ensures line protections trip during short-circuit faults. Given the ongoing replacement of SGs by power-electronics-based generation, which has a hard limit on current injection, it has become relevant to optimize the procurement of SCC services provided by remaining SGs. Pricing this service is, however, challenging due to the integrality constraints in Unit Commitment (UC). Existing methods, e.g., dispatchable pricing and restricted pricing, attempt to address this issue but exhibit limitations in handling non-convexities, resulting in SCC prices that either fail to cover the operating costs of units or lack interpretability. To overcome these pitfalls, we adopt a primal-dual formulation of the SCC-constrained dispatch that preserves the binary UC for effectively computing shadow prices of SCC services. Using a modified IEEE 30-bus system, the proposed method is compared with the previously developed pricing schemes. It is demonstrated that, under the proposed pricing method, revenue-adequate and explicit service prices can be assigned without the need for uplift payments, an advantage that cannot be achieved by other pricing approaches.

Motivated by the first LHCb searches for the rare $\bar{B}_{s,d}^{0} \to J/ψμ^{+}μ^{-}$ decays, we perform a detailed study of these processes within the QCD factorization formalism. Since the transverse size of the $J/ψ$ meson is small in the heavy quark mass limit, this formalism is generally expected to hold for these decays. We include both the leading- and next-to-leading-order QCD corrections to the hard-scattering kernels, which are convoluted with the light-cone distribution amplitudes (LCDAs) of the initial- and final-state hadrons. It is numerically found that, depending on the model parameters for the leading-twist $B$-meson LCDA, the maximum branching ratios of $\bar{B}_{s}^{0}\to J/ψμ^{+}μ^{-}$ and $\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-}$, integrated over the dimuon invariant mass squared $q^2$ from $1\,\mathrm{GeV}^2$ to $(m_{B_{s,d}}-m_{J/ψ})^2$, can reach up to $2.21\times10^{-9}$ and $7.69\times10^{-11}$ at the leading order in $α_s$, respectively. After incorporating the non-factorizable one-loop vertex corrections, these branching ratios are further reduced by about one order of magnitude, with $\mathcal{B}(\bar{B}_{s}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=2.88\times10^{-10}$ and $\mathcal{B}(\bar{B}_{d}^{0} \to J/ψμ^{+}μ^{-})|_{q^2 \geq 1\,\mathrm{GeV}^2}=1.07\times10^{-11}$. In addition, we have presented the dimuon invariant mass distributions of the individual and total helicity amplitudes squared, as well as the differential and integrated longitudinal polarization fractions of the $J/ψ$ meson, which could be probed by the future LHCb and Belle II experiments with more accumulated data.

The faint 21 cm signal emitted by neutral hydrogen in cosmic filaments is expected to be detectable. However, due to its weakness, stacking techniques are required. We assessed two stacking methods--pair stacking and filament stacking--using the EAGLE and IllustrisTNG simulations. Pair stacking leverages the fact that cosmic filaments connect massive structures (i.e., knots) in the cosmic web, while filament stacking directly aggregates filaments identified from galaxy distributions. Our analysis indicates that, although pair stacking is convenient, it faces contamination from massive structures; after removing this contamination, the filament signal is significantly reduced. In contrast, HI detection via filament stacking appears more promising. The column density in filament stacking reaches $\sim 10^{16}$--$10^{17}~\mathrm{cm}^{-2}$ even when all haloes are masked, whereas pair stacking does not reach this level even without masking, and is further suppressed by several orders of magnitude once masking is applied. The effectiveness of filament stacking can be further improved with higher galaxy number density and better spatial resolution in radio intensity mapping observations. With the advent of upcoming optical and radio data, the detection of HI in cosmic filaments remains promising.

Spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that have excellent performance thanks to the degrees of freedom they offer. An SC code is designed by partitioning a base matrix into components, the number of which implies the code memory, then coupling and lifting them. In the same system, various error-correction coding schemes are typically needed. For example, in wireless communication standards, several channel conditions and data rates should be supported. In storage and computing systems, stronger codes should be adopted as the device ages. Adaptive code design enables switching from one code to another when needed, ensuring reliability while reducing hardware cost. In this paper, we introduce a class of reconfigurable SC codes named rate-memory-compatible SC (RMC-SC) codes, which we design probabilistically. In particular, rate compatibility in RMC-SC codes is achieved via increasing the SC code memory, which also makes the codes memory-compatible and improves performance. We express the expected number of short cycles in the SC code protograph as a function of the fixed probability distribution characterizing the already-designed SC code as well as the unknown distribution characterizing the additional components. We use the gradient-descent algorithm to find a locally-optimal distribution, in terms of cycle count, for the new components. The method can be recursively used to design any number of SC codes needed, and we show how to extend it to other cases. Next, we perform the finite-length optimization using a Markov chain Monte Carlo (MC$^2$) approach that we update to design the proposed RMC-SC codes. Experimental results demonstrate significant reductions in cycle counts and remarkable performance gains achieved by RMC-SC codes compared with a literature-based straightforward scheme.

We initiate and study the theory of ``real decomposable maps" between real operator systems. Formally, this is new even in the complex case, which hitherto has restricted itself to the case where the systems are complex C*-algebras. We investigate how our definition interacts with the existing theory (which it generalizes) and with the complexification. In particular, a surprising term appears in the `Jordan decomposition' of real decomposable maps. This term constitutes a new class of completely bounded maps, a class that also showed up in disguised form in our recent study of real noncommutative (nc) convexity, and whose theory is likely to have applications in that subject. We also check the real case of many important known results related to decomposability, for example results about the weak expectation property or injectivity of von Neumann algebras.

Adaptive Cruise Control has seen significant advancements, with Collaborative Adaptive Cruise Control leveraging Vehicle-to-Vehicle communication to enhance coordination and stability. However, the reliance on stable communication channels limits its reliability. Research on reducing information dependencies in Adaptive Cruise Control systems has remained limited, despite its critical role in mitigating collision risks during sudden braking scenarios. This study proposes a novel fallback longitudinal controller that relies solely on LiDAR-based distance measurements and the velocity of a follower vehicle. The controller is designed to be time-independent, ensuring operation in the presence of sensor delays or synchronization issues. Simulation results demonstrate that the proposed controller enables vehicle-following from standstill and prevents collisions during emergency braking, even under minimal onboard information.

We investigate the conditions under which a rotating traversable wormhole can be supported by a Casimir source in the presence of an external electric field. Extending previous studies of static Casimir wormholes and neutral rotating configurations, we construct an electrically charged rotating Casimir wormhole solution and determine the thermal stress-energy tensor required to consistently satisfy the Einstein field equations. A particularly simple configuration arises when the rotation is constant and coincides with that measured by a zero-angular-momentum observer (ZAMO). In this case, the rotating wormhole preserves the same redshift and shape functions as the well-known static charged Casimir case, provided that the angular velocity and thermal components satisfy specific constraints imposed by the field equations. We also examine a configuration in which the angular velocity depends on the radial coordinate and decreases exponentially away from the throat. This damping mechanism removes the unrealistic persistence of frame dragging at large distances, while still allowing a consistent solution supported by Casimir, electromagnetic and thermal contributions.

The electrical response of a material when illuminated with light is a key to many optoelectronic device applications. This so-called photoresponse typically has a non-uniform spatial distribution through the active device area, and the ability to spatially resolve the photoresponse enables an in-depth understanding of the underlying physical mechanisms. Scanning photocurrent microscopy (SPCM) is a method that allows the spatial mapping of the photoresponse by raster scanning a focused laser beam over the sample. SPCM is becoming more popular due to its simplicity and power in unraveling fundamental optoelectronic processes. In this review, first, we provide the fundamentals of SPCM to lay the basics for the subsequent discussions. Then, we focus on the literature that employs SPCM to identify the photoresponse of one- and two-dimensional materials. We discuss SPCM measurement results of common materials in detail and introduce a systematic approach to interpreting the SPCM measurements. We have given particular emphasis on the photothermal mechanisms that are excited by the focused laser beam and critically reviewed studies in the literature from the perspective of laser-induced heating of the electronic and the lattice degrees of freedom. Finally, we discuss the shortcomings of SPCM in determining the mechanisms leading to the photoresponse.

Beta-decay rates of extreme neutron-rich nuclei remain largely unknown experimentally, while they are critical inputs for $r$-process nucleosynthesis. We present first ab initio calculations of total beta-decay half-lives, with a focus on $N=50$ nuclei. Starting from nuclear forces and currents based on chiral effective field theory, we use the in-medium similarity renormalization group to consistently derive valence-space Hamiltonians and weak operators, from which we calculate the nuclear states involved and the Gamow-Teller transition strengths, without phenomenological adjustments. In addition, we explore effects of first-forbidden contributions. Our results show that the inclusion of two-body currents increases the total half-lives, which then show good agreement with the existing experimental data, thereby validating the predictive capability of our approach.

Functional Principal Components Analysis (FPCA) provides a parsimonious, semi-parametric model for multivariate, sparsely-observed functional data. Frequentist FPCA approaches estimate principal components (PCs) from the data, then condition on these estimates in subsequent analyses. As an alternative, we propose a fully-Bayesian inferential framework for multivariate, sparse functional data (MSFAST) which explicitly models the PCs and incorporates their uncertainty. MSFAST builds upon the FAST approach to FPCA for univariate, densely-observed functional data. Like FAST, MSFAST represents PCs using orthonormal splines and samples the orthonormal spline coefficients using parameter expansion. MSFAST extends FAST to multivariate, sparsely-observed data by (1) standardizing each functional covariate to mitigate poor posterior conditioning due to disparate scales; (2) using a better-suited orthogonal spline basis; (3) updating parameterizations for computational stability; (4) introducing routines that leverage multiple cores and threads to accelerate compute; (5) using a Procrustes-based posterior PC alignment procedure; and (6) providing efficient prediction routines. We evaluate MSFAST alongside existing implementations using simulations. MSFAST produces uniquely valid inferences and accurate estimates, particularly in smaller signal-to-noise regimes. MSFAST is motivated by and applied to a study of child growth, with an accompanying vignette illustrating the implementation step-by-step.

Building on the newly available solution of the Balitsky-Kovchegov (BK) equation with the full impact-parameter dependence, we extend the study of parton evolution from proton to nuclear targets. Since a key part of the scientific programme for future experimental facilities such as the EIC is to study gluon dynamics and shed new light on the phenomenon of parton saturation, we present predictions for key processes, such as deep-inelastic scattering or the diffractive production of vector mesons, on a variety of nuclear targets. Besides the standard BK equation, we employ its linearised version to identify a promising channel to search for gluon saturation in the nuclear collisions. Furthermore, we implement a tetrahedral model of oxygen to search for deviations from the standard, isotropic, Woods-Saxon approach. In addition to the future colliders, the presented results are also of interest for the current studies of nuclear vector meson production at the LHC.

In this paper, we undertake a systematic study of the parabolic-type sub-vertex operator algebras (subVOAs) \(V_P\) of rank-two lattice VOAs \(V_L\), originally introduced by the first-named author. We first classify all possible types of such subVOAs by analyzing the corresponding submonoids \(P \subseteq L\). For each type of \(V_P\), we then classify its irreducible modules. Certain Zhu algebras \(A(V_P)\) provide new examples of rings with nil ideals that are not nilpotent. Finally, we show that the simple quotient \(V_H\) of any parabolic-type subVOA \(V_P\) is a \(C_1\)-cofinite irrational VOA satisfying the strongly unital property recently introduced by Damiolini--Gibney--Krashen.

Objective: To enable reliable smartphone-based hearing assessments by developing methods to estimate device calibration offsets using categorical loudness scaling (CLS). Design: Calibration offsets were simulated from a Gaussian distribution. Two prediction models - a Bayesian regression model and a nearest neighbor model - were trained on CLS-derived parameters and data from the Oldenburg Hearing Health Repository (OHHR). CLS was chosen because it provides level-independent measures (e.g., dynamic range) that remain robust despite calibration errors. Study Sample: The dataset comprised CLS results from N = 847 participants with a mean age of 70.0 years (SD = 8.7), including 556 male and 291 female listeners with diverse hearing profiles. Results: The Bayesian regression model achieved correlations of up to 0.81 between estimated and true calibration offsets, enabling accurate individual-level correction. Compared to threshold-based approaches, calibration uncertainty was reduced by factors between 0.41 and 0.79, demonstrating greater robustness in uncontrolled environments. Conclusions: CLS-based models can effectively compensate for missing calibration in mobile hearing assessments. This approach provides a practical alternative to threshold-based methods, supporting the use of smartphone-based tests outside laboratory settings and expanding access to reliable hearing healthcare in everyday and resource-limited contexts.

Carlitz proved a few generalizations of Mehler's formula. Later, Srivastava et al. gave a new proof for some extensions of Carlitz's formula. Here, a direct proof of the further generalization is given.

Synthetic network data generators (SynNetGens) are increasingly used to share realistic traffic traces without exposing sensitive raw data. While substantial effort has gone into improving fidelity, privacy is either assumed to be a built-in property of synthesis or addressed through differential privacy at the packet or flow level. This paper uncovers a fundamental privacy vulnerability: SynNetGens preserve cross-flow behavioral correlations that expose source-level membership, allowing an attacker to determine whether traffic of specific user, or service was included in the training data. This leakage arises from a mismatch in abstraction: existing SynNetGens operate and are protected at the packet or flow level, while sensitive information is encoded in correlations across flows from the same source. To demonstrate that this vulnerability is exploitable in practice, we develop TraceBleed, the first source-level membership inference attack against black-box SynNetGens. Our evaluation spans five datasets and six SynNetGens, revealing that: (i) every generator leaks source-level information on at least some datasets; (ii) flow- or packet-level differential privacy fails to protect source privacy unless fidelity is degraded to unusable levels; and (iii) releasing 10X more synthetic data amplifies leakage by 130% on average. To support ongoing research in this area, we will maintain a public privacy-fidelity leaderboard so practitioners can choose generators that fit their needs and researchers can benchmark new designs faithfully.

In this work, we show how knowledge of the query distribution, combined with access-pattern leakage, is sufficient to break multi-dimensional encrypted range queries, with provable guarantees. Prior attacks either recover only data topology without concrete coordinates for plaintexts (and as a result require post-hoc transformations), or assume adversarial control over database content; a strong and unrealistic threat model. Given knowledge of the query distribution, we revisit frequency matching, one of the earliest cryptanalytic ideas in this area, and push it to its limits in the multi-dimensional regime through LAMa ($\underline{L}$eakage-$\underline{A}$buse via $\underline{Ma}$tching). LAMa is a three-component framework that reconstructs plaintext coordinates in arbitrary dimensions without post-hoc transformations or data injection/poisoning. We complement LAMa with the first rigorous guarantees for multi-dimensional frequency-matching cryptanalysis, covering its query complexity, optimal parameterization, and worst-case reconstruction quality. Experiments on real-world data show that LAMa consistently outperforms the state of the art.

In this paper, we introduce a new concept in graph coloring, namely the \textit{packing total coloring}, which extends the idea of packing coloring to both the vertices and the edges of a given graph. More precisely, for a graph $G$, a packing total coloring is a mapping $c: V(G) \cup E(G) \rightarrow \{1, 2, \ldots\}$ with the property that for any integer $i$, any two distinct elements $A, B \in V(G) \cup E(G)$ with $c(A) = c(B) = i$ must be at distance at least $i+1$ from each other. Note that the distance between $A$ and $B$ means: a) the usual shortest-path distance between $A$ and $B$ if $A, B \in V(G)$; b) the $\min \{d(a,d), d(a,c),d(b,c), d(b,d)\}+1$ if $\{A, B\} =\{ab, cd\} \subseteq E(G)$; c) the $ \min \{d(a,X), d(b,X)\}+1$ if $\{A, B\}=\{ab, X\}$, where $ab \in E(G)$ and $X \in V(G)$. The smallest integer $k$ such that $G$ admits a packing total coloring using $k$ colors is called the \textit{packing total chromatic number}, denoted by $χ_ρ^{''}(G)$. In addition to introducing this new concept, we provide lower and upper bounds for the packing total chromatic numbers of graphs. Furthermore, we consider packing total chromatic numbers of graphs from the perspective of their maximum degrees and characterize all graphs $G$ with $χ_ρ^{''}(G) \in \{1, 2, 3, 4, 5\}$.