In this paper, we investigate the dynamics of Hele-Shaw flow in a multiply connected domain. We consider multiple fluid domains enclosed by a moving outer interface in a radial Hele-Shaw cell, with several inner interfaces separating these fluid regions. To compute the long-time evolution of interface morphologies, we develop a spectral-accurate boundary integral method and a nonstiff time updating scheme, together with a time adaptive scheme to speed up the computation. Our numerical results reveal that interface instabilities are strongly influenced by the initial configuration of fluid domains and physical parameters such as fluid viscosities. Notably, at early times, the fingering instability observed on the outer interface-triggered by the presence of inner interfaces-differs fundamentally from the classical perturbation-initiated growth in single-interface scenarios. Depending on their configuration, the inner interfaces can either promote or suppress the development of fingering on the outer boundary, offering a potential strategy for morphological control in practical applications. Motivated by the self-similar theory and the shape-control concept introduced in Li et al. [Phys. Rev. Lett. 102, 174501 (2009)], where self-similarity is only realized at large interface sizes under time-dependent flux, we demonstrate that one can preselect a self-similar limiting morphology and promote its formation at significantly smaller scales. This is achieved through a carefully designed multi-interface setup that promotes the desired symmetry while suppressing other unfavorable instabilities.
Glutamate dehydrogenases (GDH; EC 1.4.1.2 and EC 1.4.1.4) play a pivotal role in fungal nitrogen metabolism by catalyzing the reversible conversion of 2-ketoglutarate to L-glutamate. In fungi, NAD- as well as NADP-dependent GDHs function at the interface of ammonia assimilation and glutamate catabolism, contributing to growth, differentiation, and morphogenesis. The evolution of fungi to adapt and occupy various ecological niches is closely aligned to the diversity of regulations of the functions of GDHs, their localisation and biochemical characteristics. This review explores the biochemical, molecular, and structural studies on fungal GDHs, emphasizing their catalytic diversity, coenzyme specificity, and regulatory mechanisms, including phosphorylation, thiol modulation, and allosteric control. Structural elucidations of NADP-GDHs from Aspergillus niger, Aspergillus terreus, and Candida albicans provide new insights into cofactor binding, substrate recognition, and inhibitor interactions. Molecular analyses reveal distinct evolutionary trajectories for NAD- and NADP-GDHs across fungal taxa, with GDH-mediated transitions linked to morphogenetic processes such as the yeast-to-hypha (Y-H) switch, highlighting GDHs as promising antifungal drug targets. The comprehensive survey of fungal GDHs presented here emphasises their biochemical versatility, evolutionary significance, and translational potential in agriculture, biosensor development and in industry. The review also highlights gaps in our understanding of fungal GDHs and potential areas for further research.
An isometric path is a shortest path between two vertices. An isometric path partition (IPP) of a graph G is a set I of vertex-disjoint isometric paths in G that partition the vertices of G. The isometric path partition number of G, denoted by ipp(G), is the minimum cardinality of an IPP of G. An induced path partition (IndPP) of a graph G is a set I of vertex-disjoint induced paths in G that partition the vertices of G. The induced path partition number of G, denoted by indpp(G), is the minimum cardinality of an IndPP of G. In this article, we study both these parameters and observe that every graph G satisfies indpp(G) <= ipp(G)<= |V(G)| - v(G), where v(G) is matching number of G. We further prove that a connected graph G is extremal with respect to this upper bound, i.e. satisfies ipp(G) = |V(G)| -v(G), (resp. indpp(G) = |V(G)| -v(G)), if and only if either (i) all blocks of G are odd complete graphs, or (ii) all blocks of G except one are odd complete graphs, and the unique block B of G that is not an odd complete graph is even and satisfies ipp(B) = |V(B)| -v(B) (resp. indpp(B) = |V(B)| -v(B)). As corollaries of this result, we obtain a full structural characterization of all connected odd graphs that are extremal with respect to our upper bound, as well as of all extremal block graphs. (c) 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Wigner's Friend-type paradoxes challenge the assumption that events are absolute—that when we measure a system, we obtain a single result, which is not relative to anything or anyone else. These paradoxes highlight the tension between quantum theory and our intuitions about reality being observer independent. Building on a recent result that developed these paradoxes into a no-go theorem, namely, the Local Friendliness theorem, we introduce the Causal Time-Symmetric Friendliness Paradox, a time-ordered analog of it. In this framework, we replace the usual locality assumption with Axiological Time Symmetry and show that, when combined with the assumptions of Absoluteness of Observed Events (AOE), No Retrocausality, and Screening via Pseudo Events, we obtain a Causal Time-Symmetric Friendliness inequality. We then show that quantum mechanics violates this inequality and is therefore incompatible with at least one of these assumptions. To probe which assumption might be incompatible, we then examine whether AOE in its entirety is essential for this no-go result. We propose a weaker, operational form of AOE that still leads to inequalities that quantum mechanics violates. This result shows that even under relaxed assumptions, quantum theory resists reconciliation with classical notions of absolute events, reinforcing the foundational significance of Wigner's Friend-type paradoxes in timelike scenarios.
The Version Age of Information (VAoI) quantifies information freshness by measuring the number of versions the receiver lags behind. This paper studies VAoI minimization in an M-user uplink non-orthogonal multiple access (NOMA) system where users maintain single-packet buffers and transmissions are constrained by average power and information-quality constraints, modeled by a general distortion function. A fundamental trade-off arises: transmitting more bits per update improves information quality but increases power consumption, reducing transmission opportunities and increasing VAoI, while transmitting fewer bits has the opposite effect. We formulate a weighted-sum VAoI minimization problem as a convex optimization problem. However, users' power allocations are coupled through multiple-access capacity constraints per channel state, leading to exponential complexity. To address this, we develop a VAoI-agnostic stationary randomized policy that jointly optimizes scheduling, bit allocation, and power control without tracking instantaneous VAoI, and achieves a provable 2-approximation to the globally optimal average VAoI. Leveraging Lagrangian dual decomposition, we derive closed-form expressions for the scheduling probabilities and power allocations, and efficiently determine the optimal successive interference cancellation decoding order, avoiding exhaustive search Numerical results show that NOMA significantly outperforms time-division multiple access (TDMA): at high power budgets, NOMA achieves near-zero VAoI, whereas TDMA saturates at a non-zero value, consistent with the analysis. The proposed general distortion framework accommodates diverse bit-priority structures by assigning unequal importance to different bits within an update.
