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One fundamental question in database theory is the following: Given a Boolean conjunctive queryQ, what is the best complexity for computing the answer to Q in terms of the input database sizeN? When restricted to the class of combinatorial algorithms, it is known that the best known complexity for any queryQis captured by thesubmodular widthofQ. However, beyond combinatorial algorithms, certain queries are known to admit faster algorithms that often involve a clever combination of fast matrix multiplication and data partitioning. Nevertheless, there is no systematic way to derive and analyze the complexity of such algorithms for arbitrary queriesQ. In this work, we introduce a general framework that captures the best complexity for answering any Boolean conjunctive queryQusing matrix multiplication. Our framework unifies both combinatorial and non-combinatorial techniques under the umbrella of information theory. It generalizes the notion of submodular width to a new stronger notion called the ω-submodular widththat naturally incorporates the power of fast matrix multiplication. We describe a matching algorithm that computes the answer to any queryQin time corresponding to the ω-submodularwidth ofQ. We show that our framework recovers the best known complexities for Boolean queries that have been studied in the literature, to the best of our knowledge, and also discovers new algorithms for some classes of queries that improve upon the best known complexities. 

This study investigates the structural and functional enhancement of corn zein–chitosan composites via mild alkaline treatment to develop biodegradable protein-polysaccharide materials for diverse applications. Films with varying zein-to-chitosan ratios were fabricated and characterized using Fourier-transform infrared spectroscopy (FTIR), thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and scanning electron microscopy (SEM). Both untreated and sodium hydroxide (NaOH)-treated films were evaluated to assess changes in physicochemical properties. FTIR analysis revealed that NaOH treatment promoted deprotonation of chitosan’s amine groups, partial removal of ionic residues, and increased deacetylation, collectively enhancing hydrogen bonding and resulting in a denser molecular network. Simultaneously, partial unfolding of zein’s α-helical structures improved conformational flexibility and strengthened interactions with chitosan. These molecular-level changes led to improved thermal stability, reduced degradation, and the development of porous microstructures. Controlled NaOH treatment thus provides an effective strategy to tailor the physicochemical properties of zein–chitosan composite films, supporting their potential in sustainable food packaging, wound healing, and drug delivery applications. 

Given a self-join-free conjunctive queryQand a set of tuplesS, asynthetic witness Dis a database instance such that the result ofQonDisS. In this work, we are interested in two problems. First, the existence problem ESW decides whether any synthetic witnessDexists. Second, given that a synthetic witness exists, the minimization problem SSW computes a synthetic witness of minimal size. The SSW problem is related to thesmallest witness problemrecently studied by Hu and Sintos [22]; however, the objective and the results are inherently different. More specifically, we show that SSW is poly-time solvable for a wider range of queries. Interestingly, in some cases, SSW is related to optimization problems in other domains, such as therole miningproblem in data mining and theedge concentrationproblem in graph drawing. Solutions to ESW and SSW are of practical interest, e.g., fortest database generationfor applications accessing a database and fordata compressionby encoding a datasetSas a pair of a queryQand databaseD. We prove that ESW is in P, presenting a simple algorithm that, given anyS, decides whether a synthetic witness exists in polynomial time in the size ofS. Next, we focus on the SSW problem. We show an algorithm that computes a minimal synthetic witness in polynomial time with respect to the size ofSfor any queryQthat has thehead-dominationproperty. IfQdoes not have such a property, then SSW is generally hard. More specifically, we show that for the class ofpath queries(of any constant length), SSW cannot be solved in polynomial time unless P = NP. We then extend this hardness result to the class ofBerge-acyclicqueries that do not have the head-domination property, obtaining a full dichotomy of SSW for Berge-acyclic queries. Finally, we investigate the hardness of SSW beyond Berge-acyclic queries by showing that SSW cannot be solved in polynomial time for some cyclic queries unless P = NP. 

Biocompatible polymers have emerged as essential materials in medical 3D printing, enabling the fabrication of scaffolds, tissue constructs, drug delivery systems, and biosensors for applications in and on the human body. This review aims to provide a comprehensive overview of the current state of 3D-printable biocompatible polymers and their composites, with an emphasis on their processing methods, properties, and biomedical uses. The scope of this work includes both natural and synthetic biocompatible polymers, polymer–nanocomposite systems, and bioinks that do not require photo initiators. The relevant literature was critically examined to classify materials by type, evaluate their compatibility with major 3D printing techniques such as stereolithography, selective laser sintering, and fused deposition modeling, and assess their performance in various medical applications. Key findings highlight that reinforced polymer composites, tailored surface chemistries, and hybrid printing strategies significantly expand the range of functional, customizable, and affordable biomedical devices. This review concludes by discussing present-day applications and emerging trends, underscoring that 3D-printable biocompatible polymers are rapidly transitioning from research to clinical practice, offering transformative potential for patient-specific healthcare solutions. 

ABSTRACT We investigate the dynamics of dust concentration in actively accreting, substructured, non-ideal magnetohydrodynamic wind-launching discs using two-dimensional and three-dimensional (3D) simulations incorporating pressureless dust fluids of various grain sizes and their aerodynamic feedback on gas dynamics. Our results reveal that mm/cm-sized grains are preferentially concentrated within the inner 5–10 au of the disc, where the dust-to-gas surface density ratio (local metallicity Z) significantly exceeds the canonical 0.01, reaching values up to 0.25. This enhancement arises from the interplay of dust settling and complex gas flows in the meridional plane, including mid-plane accretion streams at early times, mid-plane expansion driven by magnetically braked surface accretion at later times, and vigorous meridional circulation in spontaneously formed gas rings. The resulting size-dependent dust distribution has a strong spatial variation, with large grains preferentially accumulating in dense rings, particularly in the inner disc, while being depleted in low-density gas gaps. In 3D, these rings and gaps are unstable to Rossby wave instability, generating arc-shaped vortices that stand out more prominently than their gas counterparts in the inner disc because of preferential dust concentration at small radii. The substantial local enhancement of the dust relative to the gas could promote planetesimal formation via streaming instability, potentially aided by the ‘azimuthal drift’ streaming instability that operates efficiently in accreting discs and a lower Toomre Q expected in younger discs. Our findings suggest that actively accreting young discs may provide favourable conditions for early planetesimal formation, which warrants further investigation. 

Natural proteins present a sustainable and biocompatible alternative to conventional fossil fuel-derived plastics, with versatile applications in fields ranging from medicine to food packaging. Extending our previous research on silk–corn zein composites, this study utilizes soy protein—another plant protein extensively employed within biomedical applications—in conjunction with silk fibroin proteins extracted from a variety of domestic (Mori and Thai) and wild (Muga, Tussah, and Eri) silkworm species. By combining these proteins in varying ratios (0%, 10%, 25%, 50%, 75%, 90%, and 100%), silk–soy films were successfully fabricated with high miscibility. The structural and thermal stability of these films was confirmed through various characterization techniques, including Fourier transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), and scanning electron microscopy (SEM). Structural refinements were then achieved through post-water annealing treatments. After annealing, it was observed that when soy protein was introduced into both types of silk, the silks exhibited a greater amount of intermolecular and intramolecular β-sheet content. This phenomenon can be attributed to soy’s intrinsic ability to self-assemble into β-sheets through electrostatic and hydrophobic interactions, which also improved the overall thermal stability and morphology of the composite films. The unique self-assembling properties of soy and its ability to promote β-sheet formation facilitate the customization of the silk source and the soy-to-silk ratio. This adaptability establishes protein-based thin films as a versatile and sustainable option for diverse applications in fields such as medicine, tissue engineering, food packaging, and beyond. 

ABSTRACT Recent high angular resolution ALMA observations have revealed rich information about protoplanetary discs, including ubiquitous substructures and three-dimensional gas kinematics at different emission layers. One interpretation of these observations is embedded planets. Previous 3D planet–disc interaction studies are either based on viscous simulations or non-ideal magnetohydrodynamics (MHD) simulations with simple prescribed magnetic diffusivities. This study investigates the dynamics of gap formation in 3D non-ideal MHD discs using non-ideal MHD coefficients from the look-up table that is self-consistently calculated based on the thermochemical code. We find a concentration of the poloidal magnetic flux in the planet-opened gap (in agreement with previous work) and enhanced field-matter coupling due to gas depletion, which together enable efficient magnetic braking of the gap material, driving a fast accretion layer significantly displaced from the disc mid-plane. The fast accretion helps deplete the gap further and is expected to negatively impact the planet growth. It also affects the corotation torque by shrinking the region of horseshoe orbits on the trailing side of the planet. Together with the magnetically driven disc wind, the fast accretion layer generates a large, persistent meridional vortex in the gap, which breaks the mirror symmetry of gas kinematics between the top and bottom disc surfaces. Finally, by studying the kinematics at the emission surfaces, we discuss the implications of planets in realistic non-ideal MHD discs on kinematics observations.