The breaking of translational symmetry in the inner crust of a neutron star leads to the depletion of the neutron superfluid reservoir similarly to cold atomic condensates in optical lattices and in supersolids. This effect is studied in the general framework of the self-consistent time-dependent Hartree-Fock-Bogoliubov (HFB) theory, treating the crust as a perfect crystal. The superfluid fraction is derived in the Bardeen-Cooper-Schrieffer approximation for superfluid velocities much smaller than Landau's critical velocity within the linear-response theory. The different assumptions made in previous studies are clarified. Fully three-dimensional band-structure calculations of superfluid neutrons in a body-centered cubic lattice are carried out. Although the formation of Cooper pairs is essential for the occurrence of superfluidity, the superfluid fraction is found to be insensitive to the pairing gap, as in uniform neutron matter. In the intermediate region of the inner crust at the average baryon number density 0.03 fm$^{-3}$, only 8\% of the free neutrons are found to participate to the superflow. Such very low superfluid fraction challenges the classical interpretation of pulsar frequency glitches and calls for more systematic calculations within the full HFB approach.

Let $X:=\{X(t)\}_{t\ge0}$ be a generalized fractional Brownian motion given by $$ \{X(t)\}_{t\ge0}\overset{d}{=}\left\{ \int_{\mathbb R} \left((t-u)_+^α-(-u)_+^α \right) |u|^{-γ/2} B(du) \right\}_{t\ge0}, $$ with parameters $γ\in (0, 1)$ and $α\in \left(-1/2+ γ/2, \, 1/2+γ/2\right)$. This process was introduced by Pang and Taqqu (2019) as the scaling limit of a class of power-law shot noise processes. The parameters $α$ and $γ$ govern the probabilistic and statistical properties of $X$. In particular, the parameter $γ$ breaks the stationarity of increments of $X$. In this paper, we establish Strassen's local law of the iterated logarithm for $X$ at a given point $t_0 \in (0, \infty)$. This result describes explicitly the roles played by the parameters $α, γ$, and the location $t_0$. Our theorem differs from the earlier Strassen's {global law of the iterated logarithm} for $X$ proved by Ichiba, Pang and Taqqu (2022).

Eukaryotic cells are characterized by a stiff nucleus whose effect in modeling the collective behavior of cell aggregates is usually underestimated. However, increasing experimental evidence links nuclear modifications with phenotypic transition, like the one between epithelial and mesenchymal states. In this work, we explore the effect of short-range repulsive forces in the non-equilibrium dynamics of the self-propelled Voronoi model. We show that the competition between steric repulsions (representing nuclear/cellular compressibility) and Vertex interactions (mimicking cell-cell adhesion/interaction and cytoskeleton organization) generate a variety of non-equilibrium phase transitions from Motility-Induced Phase Separation to mesenchymal-like phases up to disordered confluent configurations. Notably, we found that tuning the nucleus's effective size/compressibility provides an additional way to cross the boundary between the different possible phases in line with experimental observations.

The integration of immersive communication into a human-centric ecosystem has intensified the demand for sophisticated Human Digital Twins (HDTs) driven by multifaceted human data. However, the effective construction of HDTs faces significant challenges due to the heterogeneity of data collection devices, the high energy demands associated with processing intricate data, and concerns over the privacy of sensitive information. This work introduces a novel biologically-inspired (bio-inspired) HDT framework that leverages Brain-Computer Interface (BCI) sensor technology to capture brain signals as the data source for constructing HDT. By collecting and analyzing these signals, the framework not only minimizes device heterogeneity and enhances data collection efficiency, but also provides richer and more nuanced physiological and psychological data for constructing personalized HDTs. To this end, we further propose a bio-inspired neuromorphic computing learning model based on the Spiking Neural Network (SNN). This model utilizes discrete neural spikes to emulate the way of human brain processes information, thereby enhancing the system's ability to process data effectively while reducing energy consumption. Additionally, we integrate a Federated Learning (FL) strategy within the model to strengthen data privacy. We then conduct a case study to demonstrate the performance of our proposed twofold bio-inspired scheme. Finally, we present several challenges and promising directions for future research of HDTs driven by bio-inspired technologies.

Accurate modelling of magnetism is pivotal for elucidating the microscopic origins of magnetic phenomena in functional materials. However, for a specified class of materials, such as random dilute ferromagnets or alloys, the reliance on simplifying assumptions, such as single-ion anisotropy, limits the accuracy of existing spin models. In such systems, there is a significant probability of the formation of nearest-neighbor magnetic ion pairs or higher order clusters, whose presence breaks the local symmetry of otherwise isolated magnetic species. Here, we introduce the concept of pair-induced uniaxial anisotropy and demonstrate how nearby atoms influence each other's anisotropic behavior. This effect is investigated in the dilute magnetic semiconductor Ga$_{1-x}$Mn$_x$N, by means of density functional theory calculations. The inclusion of pair anisotropy in the atomistic spin simulations significantly improves the agreement between simulated and experimental magnetization curves, in contrast to models that consider only single-ion anisotropy.

In this work, we consider the problems of learning junta distributions, their quantum counterparts (quantum junta states) and $\mathsf{QAC}^0$ circuits, which we show to be close to juntas. (1) Junta distributions. A probability distribution $p:\{-1,1\}^n\to \mathbb [0,1]$ is a $k$-junta if it only depends on $k$ bits. We show that they can be learned with to error $\varepsilon$ in total variation distance from $O(2^k\log(n)/\varepsilon^2)$ samples, which quadratically improves the upper bound of Aliakbarpour et al. (COLT'16) and matches their lower bound in every parameter. (2) Junta states. We initiate the study of $n$-qubit states that are $k$-juntas, those that are the tensor product of a $k$-qubit state and an $(n-k)$-qubit maximally mixed state. We show that these states can be learned with error $\varepsilon$ in trace distance with $O(12^{k}\log(n)/\varepsilon^2)$ single copies. We also prove a lower bound of $Ω((4^k+\log (n))/\varepsilon^2)$ copies. Additionally, we show that, for constant $k$, $\tildeΘ(2^n/\varepsilon^2)$ copies are necessary and sufficient to test whether a state is $\varepsilon$-close or $7\varepsilon$-far from being a $k$-junta. (3) $\mathsf{QAC}^0$ circuits. Nadimpalli et al. (STOC'24) recently showed that the Pauli spectrum of $\mathsf{QAC}^0$ circuits (with a limited number of auxiliary qubits) is concentrated on low-degree. We remark that they implied something stronger, namely that the Choi states of those circuits are close to be juntas. As a consequence, we show that $n$-qubit $\mathsf{QAC}^0$ circuits with size $s$, depth $d$ and $a$ auxiliary qubits can be learned from $2^{O(\log(s^22^a)^d)}\log (n)$ copies of the Choi state, improving the $n^{O(\log(s^22^a)^d)}$ by Nadimpalli et al.

In this article, we investigate the entanglement entropy for neutrino oscillations when neutrino propogate in matter, utilising Von Neumann entropy. We discuss two flavour neutrino oscillation in vaccum and matter. We demonstrate statistically that, depending on the length of oscillation for each energy, the entanglement entropy for the succeeding periods of the two-flavor neutrino oscillations in matter.

Quantum error correction is essential for achieving fault-tolerant quantum computation. However, most typical quantum error-correcting codes are designed for generic noise models, which may fail to accurately capture the intricate noise characteristics of real quantum devices, limiting their practical performance. This work introduces a learning-based framework for the constructing of quantum error-correcting codes, termed Variational Graphical Quantum Error Correction (VGQEC) codes, which adapts to specific noise profiles of different quantum devices, enabling the design of noise-tailored codes. Specifically, inspired by Quon, a graphical language for quantum information, VGQEC codes incorporate tunable parameters embedded within their Quon graphs, allowing dynamic reconfigurations of the graph structures through parameter adjustments. As the first application of this approach, we show that this flexibility in code designs facilitates seamless transitions between various code families, exemplified by the establishment of a bridge between the five-qubit repetition code and the [[5,1,3]] code, thereby combining their respective advantages. Additionally, a VGQEC code derived from the three-qubit repetition code is fine-tuned for the amplitude damping noise, showcasing the approach's ability for noise-specific code design. Moreover, we experimentally demonstrate the effectiveness of the three-qubit VGQEC code in the low-to-medium noise regime with a photonic system, highlighting its potential for real-world applications.

Using the fourth-order extended Thomas-Fermi method with Strutinsky-integral shell and pairing corrections, we calculate the inner crust of neutron stars with the BSk31 functional, whose pairing has two terms: i) a term that is fitted to the results of microscopic calculations on homogeneous nuclear matter (accounting for both medium polarization and self-energy effects) that are more realistic than those of our earlier functionals; ii) an empirical term that is dependent on the density gradient, which permits an excellent fit to nuclear masses. Both proton and neutron pairing are taken into account, the former in the BCS theory and the latter in the local density approximation. We found that the equilibrium value of the proton number $Z$ remains 40 over the entire density range considered, whether or not neutron pairing is included. The new equation of state and the composition are very similar to those of our previously preferred functional, BSk24. However, the predicted neutron pairing fields are quite different. In particular, clusters are found to be impermeable to the neutron superfluid. The implications for the neutron superfluid dynamics are briefly discussed. Since the new pairing is more realistic, the functional BSk31 is better suited for investigating neutron superfluidity in neutron-star crusts.

We determine the behavior of an out-of-equilibrium superfluid, composed of a $U(1)$ Goldstone mode coupled to hydrodynamic modes in a M\" uller-Israel-Stewart theory, in expanding backgrounds relevant to heavy ion collision experiments and cosmology. For suitable initial conditions, the evolution of the hydrodynamic variables leads to a change in the potential of the Goldstone mode, spontaneously breaking the symmetry. After some time, the condensate becomes small, leading the system evolution to be well described via hydrodynamic attractors for a timescale that we determine in Bjorken and Gubser flows. We define this new timescale as the \textit{attractor time} and show its dependence on initial conditions. In the case of the Gubser flow, we provide for the first time a complete description of the nonlinear evolution of the system, including a novel nonlinear regime of constant anisotropy not found in the Bjorken evolution. Finally, we consider the superfluid in the dynamical FLRW (Friedmann-Lemaitre-Roberston-Walker) background, where we observe a similar attractor behavior, dependent on the initial conditions, that at late times approaches a regime dominated by the condensate.

We study the neutral excitations in the bulk of the fractional quantum Hall (FQH) fluids generated by acting with the Girvin-MacDonald-Platzman (GMP) density operator on the uniform ground state. Creating these density modulations atop the ground state costs energy, since any density fluctuation in the FQH system has a gap stemming from underlying interparticle interactions. We calculate the GMP density-mode dispersion for many bosonic and fermionic FQH states on the Haldane sphere using the ground state static structure factor computed on the same geometry. Previously, this computation was carried out on the plane. Analogous to the GMP algebra of the lowest Landau level (LLL) projected density operators in the plane, we derive the algebra for the LLL-projected density operators on the sphere, which facilitates the computation of the density-mode dispersion. Contrary to previous results on the plane, we find that, in the long-wavelength limit, the GMP mode accurately describes the dynamics of the primary Jain states.

The high-temperature limit of the superconformal index, especially on higher sheets, often captures useful universal information about a theory. In 4d $\mathcal{N}=2$ superconformal field theories with fractional r-charges, there exists a special notion of high-temperature limit on higher sheets that captures data of three-dimensional topological quantum field theories arising from r-twisted circle reduction. These TQFTs are closely tied with the VOA of the 4d SCFT. We study such high-temperature limits. More specifically, we apply Di~Pietro-Komargodski type supersymmetric effective field theory techniques to r-twisted circle reductions of $(A_1,A_{2n})$ Argyres-Douglas theories, leveraging their Maruyoshi-Song Lagrangian with manifest $\mathcal{N}=1$ supersymmetry. The result on the second sheet is the Gang-Kim-Stubbs family of 3d $\mathcal{N}=2$ SUSY enhancing rank-$0$ theories with monopole superpotentials, whose boundary supports the Virasoro minimal model VOAs $M(2,2n+3)$. Upon topological twist, they give non-unitary TQFTs controlled by the $M(2,2n+3)$ modular tensor category (MTC). The high-temperature limit on other sheets yields their unitary or non-unitary Galois conjugates. This opens up the prospect of a broader four-supercharge perspective on the celebrated correspondence between 4d $\mathcal{N}=2$ SCFTs and 2d VOAs via interpolating 3d EFTs. Several byproducts follow, including a systematic approach to 3d SUSY enhancement from 4d SUSY enhancement, and a 3d QFT handle on Galois orbits of various MTCs associated with 4d $\mathcal{N}=2$ SCFTs.

Biot's consolidation model is a classical model for the evolution of deformable porous media saturated by a fluid and has various interdisciplinary applications. While numerical solution methods to solve poroelasticity by typical schemes such as finite differences, finite volumes or finite elements have been intensely studied, lattice Boltzmann methods for poroelasticity have not been developed yet. In this work, we propose a novel semi-implicit coupling of lattice Boltzmann methods to solve Biot's consolidation model in two dimensions. To this end, we use a single-relaxation-time lattice Boltzmann method for reaction-diffusion equations to solve the Darcy flow and combine it with a recent pseudo-time multi-relaxation-time lattice Boltzmann scheme for quasi-static linear elasticity. We employ a multi-grid method for the latter scheme to achieve quasi-optimal computational cost. For the coupling between the equations, we develop a centered update scheme, that incorporates both explicit and semi-implicit contributions. The numerical results demonstrate that naive (explicit or semi-implicit) coupling schemes lead to instabilities when the poroelastic system is strongly coupled. However, the newly developed centered coupling scheme is stable and accurate in all considered cases, even for the Biot--Willis coefficient being one. Furthermore, the numerical results for Terzaghi's consolidation problem and a two-dimensional extension thereof highlight that the scheme is even able to capture discontinuous solutions arising from instantaneous loading.

We study a system of interacting particles in the presence of the relativistic kinetic energy, external confining potentials, singular repulsive forces as well as a random perturbation through an additive white noise. In comparison with the classical Langevin equations that are known to be exponentially attractive toward the unique statistically steady states, we find that the relativistic systems satisfy algebraic mixing rates of any order. This relies on the construction of Lyapunov functions adapting to previous literature developed for irregular potentials. We then explore the Newtonian limit as the speed of light tends to infinity and establish the validity of the approximation of the solutions by the Langevin equations on any finite time window.

We propose a novel method to probe light-quark dipole moments by examining the azimuthal asymmetries between a collinear pair of hadrons in semi-inclusive deep inelastic lepton scattering off an unpolarized proton target at the Electron-Ion Collider. These asymmetries provide a means to observe transversely polarized quarks, which arise exclusively from the interference between the dipole and the Standard Model interactions, thereby depending linearly on the dipole couplings. We demonstrate that this novel approach can enhance current constraints on light-quark dipole operators by an order of magnitude, free from contamination of other new physics effects. Furthermore, it allows for a simultaneous determination of both the real and imaginary parts of the dipole couplings, offering a new avenue for investigating potential $CP$-violating effects at high energies.

We prove the scalar curvature rigidity for $L^\infty$ metrics on $\mathbb S^n\backslashΣ$, where $\mathbb S^n$ is the $n$-dimensional sphere with $n\geq 3$ and $Σ$ is a closed subset of $\mathbb S^n$ of codimension at least $\frac{n}{2}+1$ that satisfies the wrapping property. The notion of wrapping property was introduced by the second author for studying related scalar curvature rigidity problems on spheres. For example, any closed subset of $\mathbb S^n$ contained in a hemisphere and any finite subset of $\mathbb S^n$ satisfy the wrapping property. The same techniques also apply to prove an analogous scalar rigidity result for $L^\infty$ metrics on tori that are smooth away from certain subsets of codimension at least $\frac{n}{2}+1$. As a corollary, we obtain a positive mass theorem for complete asymptotically flat spin manifolds with arbitrary ends for $L^\infty$ metrics.

In this paper we show that a countable structure admitting a finite monomorphic decomposition has finite big Ramsey degrees if and only if so does every monomorphic part in its minimal monomorphic decomposition. The necessary prerequisite for this result is the characterization of monomorphic structures with finite big Ramsey degrees: a countable monomorphic structure has finite big Ramsey degrees if and only if it is chainable by a chain with finite big Ramsey degrees. Interestingly, both characterizations require deep structural properties of chains. Fraïssé's Conjecture (actually, its positive resolution due to Laver) is instrumental in the characterization of monomorphic structures with finite big Ramsey degrees, while the analysis of big Ramsey combinatorics of structures admitting a finite monomorphic decomposition requires a product Ramsey theorem for big Ramsey degrees. We find this last result particularly intriguing because big Ramsey degrees misbehave notoriously when it comes to general product statements. In the addendum, we combine a recent result by Oudrar and Pouzet with our analysis of finite big Ramsey degrees for structures admitting finite monomorphic decomposition to characterize the existence of finite Big Ramsey degrees for all countable relational structures whose language has a linear order and age has polynomial growth.

In van der Waals heterostructures (vdWHs), the manipulation of interlayer stacking/coupling allows for the construction of customizable quantum systems exhibiting exotic physics. An illustrative example is the diverse range of states of matter achieved through varying the proximity coupling between two-dimensional (2D) quantum spin liquid (QSL) and superconductors within the TaS2 family. This study presents a demonstration of the intertwined physics of spontaneous rotational symmetry breaking, hidden magnetism, and Ising superconductivity in the three-fold rotationally symmetric, non-magnetic natural vdWHs 6R-TaS2. A distinctive phase emerges in 6R-TaS2 below a characteristic temperature (T*) of approximately 30 K, which is characterized by a remarkable set of features, including a giant extrinsic anomalous Hall effect (AHE), Kondo screening, magnetic field-tunable thermal hysteresis, and nematic magneto-resistance. At lower temperatures, a coexistence of nematicity and Kondo screening with Ising superconductivity is observed, providing compelling evidence of hidden magnetism within a superconductor. This research not only sheds light on unexpected emergent physics resulting from the coupling of itinerant electrons and localized/correlated electrons in natural vdWHs but also emphasizes the potential for tailoring exotic quantum states through the manipulation of interlayer interactions.

The increasing adoption of connectivity and electronic components in vehicles makes these systems valuable targets for attackers. While automotive vendors prioritize safety, there remains a critical need for comprehensive assessment and analysis of cyber risks. In this context, this paper proposes a Social Media Automotive Threat Intelligence (SOCMATI) framework, specifically designed for the emerging field of automotive cybersecurity. The framework leverages advanced intelligence techniques and machine learning models to extract valuable insights from social media. Four use cases illustrate the framework's potential by demonstrating how it can significantly enhance threat assessment procedures within the automotive industry.

In this work we study the existence of closed magnetic geodesics on three-dimensional Heisenberg nilmanifolds for every left-invariant Lorentz force. Our first objective is to establish the existence of closed contractible magnetic geodesics on $H_3$. Once the invariant magnetic field is induced to a compact quotient $M=Λ\backslash H_3$, we study magnetic geodesics on $M$. Firstly, we determine conditions on a lattice $Λ\subset H_3$ to ensure that a given magnetic geodesic projects to a closed curve on $M$. In particular, we prove that for {\it any} energy level below the Mañé critical value there always exists a contractible closed magnetic geodesic on the compact manifold $M$. On the other hand, we show that closed magnetic geodesics do not necessarily exist in every homotopy class. Finally, we present examples of compact quotients $Γ_k\backslash H_3$ that admit infinitely many closed magnetic trajectories, as well as examples for which no closed non-contractible magnetic trajectories exist for a given left-invariant Lorentz force.

We consider a residuals-based distributionally robust optimization (DRO) model, where the underlying uncertainty depends on both covariate information and our decisions. We adopt both parametric and nonparametric regression models to learn the latent decision dependency and construct a nominal distribution (thereby ambiguity sets) around the learned model using empirical residuals from the regressions. We formulate the ambiguity set via the Wasserstein distance, where the nominal distribution is both decision- and covariate-dependent. We provide conditions under which desired statistical properties such as asymptotic optimality, rate of convergence, and finite sample guarantees are satisfied. To solve the resulting DRO model, we develop a specialized Bender's decomposition algorithm with nonlinear cuts and prove its finite convergence. Through numerical experiments, we illustrate the effectiveness of our approach and the benefits of integrating decision dependency into a residuals-based DRO framework.

Waldhausen categories were introduced to extend algebraic $K$-theory beyond Quillen's exact categories. In this article, we modify Waldhausen's axioms so that it matches better with the theory of extriangulated categories, introducing a weak Waldhausen category and defining its Grothendieck group. Examples of weak Waldhausen categories include any extriangulated category, hence any exact or triangulated category, and any Waldhausen category. A key feature of this structure is that it allows for "one-sided" extriangulated localization theory, and thus enables us to extract right exact sequences of Grothendieck groups that we cannot obtain from the theory currently available. To demonstrate the utility of our Weak Waldhausen Localization Theorem, we give three applications. First, we give a new proof of the Extriangulated Localization Theorem proven by Enomoto--Saito, which is a generalization at the level of $K_0$ of Quillen's classical Localization Theorem for exact categories. Second, we give a new proof that the index with respect to an $n$-cluster tilting subcategory $\mathscr{X}$ of a triangulated category $\mathscr{C}$ induces an isomorphism between $K_0^{\mathsf{sp}}(\mathscr{X})$ and the Grothendieck group of an extriangulated substructure of $\mathscr{C}$. Last, we produce a weak Waldhausen $K_0$-generalization of a localization construction due to Sarazola that involves cotorsion pairs but allows for non-Serre localizations. We show that the right exact sequences of Grothendieck groups obtained from our Sarazola construction and the Extriangulated Localization Theorem agree under a common setup.

We present a generative approach to price options and extract risk-neutral densities from the market. Specifically, we model the underlying log-returns on the time-to-maturity continuum as a generative model from standard normal. Neural nets are used to represent the term structures of the location, the scale, and the higher-order moments. We impose stringent conditions on the learning process to ensure no arbitrage. This model allows for the efficient generation of samples to price options across strikes and maturities. We have validated the effectiveness of this approach by benchmarking it against a comprehensive set of baseline models. Experiments show that the extracted risk-neutral densities accommodate a diverse range of shapes. Its accuracy significantly outperforms the extensive set of baseline models--including three parametric models and nine stochastic process models--in terms of accuracy and stability. The success of this approach is attributed to its capacity to offer flexible term structures for risk-neutral skewness and kurtosis.

We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras.

In this series, we introduce and investigate the concept of connectoids, which captures the connectivity structure of various discrete objects such as undirected graphs, directed graphs, bidirected graphs, hypergraphs and finitary matroids. In the first paper, we developed a universal end space theory based on connectoids that unifies the existing end spaces of undirected and directed graphs. In this paper, we establish normal trees of connectoids as a natural generalisation of normal trees of undirected graphs, which are one of the most important tools in infinite graph theory. More precisely, we show that the existence of normal trees of connectoids can be characterised in the same way as for normal trees of undirected graphs: We extend Jung's famous characterisation via dispersed sets to connectoids, and prove that normal spanning trees exist if they exist in some neighbourhood of each end. Furthermore, we show that a connectoid has a normal spanning tree if and only if its groundset can be well-ordered in a certain way, called countable separation number.

Free electrons interacting coherently with optical fields provide a powerful platform for quantum simulation and quantum control. For kiloelectron-volt electron energies, even optical photon emission and absorption produce appreciable quantum recoils, endowing the electron with a discrete and controllable energy ladder. Starting from relativistic quantum electrodynamics, we derive an exact recoil-resolved interaction Hamiltonian in a traveling wave picture. The resulting recoil ladder forms a high-dimensional qudit with programmable couplings and sufficient controllability for universal quantum computation. We demonstrate applications to quantum simulation, including one-dimensional analogue black-hole models including Hawking radiation physics, and to quantum information processing, where multiple logical qubits and high-fidelity gates can be realized with a single electron. In parallel, the same recoil-enabled dynamics enable the controlled creation of complex hybrid electron--photon states, in which engineered ladder transitions imprint nonclassical correlations and structure onto the emitted light. Together, these results establish recoiled free electrons as a versatile platform bridging quantum optics, Hamiltonian engineering, and quantum simulation.

In the theory of voting, the Plurality rule for preferences that come in the form of linear orders selects the alternatives most frequently appearing in the first position of those orders, while the Anti-Plurality rule selects the alternatives least often occurring in the final position. We explore extensions of these rules to preferences that are partial orders, offering axiomatic characterisations for them.

Next-generation mobile networks are expected to facilitate fast AI model downloading to end users. By caching models on edge servers, mobile networks can deliver models to end users with low latency, resulting in a paradigm of edge model caching. In this paper, we develop a novel model placement framework, called parameter-sharing model caching (TrimCaching). TrimCaching exploits the key observation that a wide range of AI models, such as convolutional neural networks or large language models, can share a significant proportion of parameter blocks containing reusable knowledge, thereby improving storage efficiency. To this end, we formulate a parameter-sharing model placement problem to maximize the cache hit ratio in multi-edge wireless networks by balancing the fundamental tradeoff between storage efficiency and service latency. We show that the formulated problem is a submodular maximization problem with submodular constraints, for which no polynomial-time approximation algorithm exists. To tackle this challenge, we study an important special case, where a small fixed number of parameter blocks are shared across models, which often holds in practice. In such a case, a polynomial-time algorithm with a $\left(1-ε\right)/2$-approximation guarantee is developed. Subsequently, we address the original problem for the general case by developing a greedy algorithm. Simulation results demonstrate that the proposed TrimCaching framework significantly improves the cache hit ratio compared with state-of-the-art content caching without exploiting shared parameters in AI models.

To measure the tree-likeness of a directed acyclic graph (DAG), a new width parameter that considers the directions of the arcs was recently introduced: scanwidth. We present the first algorithm that efficiently computes the exact scanwidth of general DAGs. For DAGs with one root and scanwidth $k$ it runs in $O(k \cdot n^k \cdot m)$ time. The algorithm also functions as an FPT algorithm with complexity $O(2^{4 \ell - 1} \cdot \ell \cdot n + n^2)$ for phylogenetic networks of level-$\ell$, a type of DAG used to depict evolutionary relationships among species. Our algorithm performs well in practice, being able to compute the scanwidth of synthetic networks up to 30 reticulations and 100 leaves within 500 seconds. Furthermore, we propose a heuristic that obtains an average practical approximation ratio of 1.5 on these networks. While we prove that the scanwidth is bounded from below by the treewidth of the underlying undirected graph, experiments suggest that for networks the parameters are close in practice.

This work investigates a privacy metric based on Chernoff information motivated by its importance in characterizing the optimal classifier's performance. Adversarial classification centers on minimizing the probability of error when deciding between two classes in the binary setting. Classical hypothesis testing treats false alarm and mis-detection probabilities separately, resulting in asymmetric optimal error exponents. Here, we instead characterize the relationship between $\varepsilon-$differential privacy (DP), the optimal error exponent of one error probability conditioned on the other, and the optimal average error exponent. Thus, we re-derive Chernoff DP in connection with $\varepsilon-$DP using the Radon-Nikodym derivative and establish its relationship with Kullback-Leibler (KL) DP to prove that Chernoff DP is sandwiched between the two. We then present numerical evaluations demonstrating that Chernoff information outperforms the KL divergence as a function of the privacy parameter, particularly in capturing the impact of adversarial attacks under Laplace mechanisms. Finally, we upper bound the adversary's advantage in membership inference attacks based on Chernoff DP and numerically compare its performance with existing bounds. We re-derive Chernoff DP in connection with $\varepsilon-$DP using the Radon-Nikodym derivative, and prove its relation with KL-DP. Subsequently, we present numerical evaluation results, which demonstrates that Chernoff information outperforms KL divergence as a function of the privacy parameter $\varepsilon$ and the impact of the adversary's attack in Laplace mechanisms. Lastly, we introduce a new upper bound on adversary's membership advantage in membership inference attacks using Chernoff DP and numerically compare its performance with existing alternatives based on $(\varepsilon,δ)-$DP in the literature.