In graph theory and network design, the minimum cut is a fundamental measure of system connectivity and communication capacity. While prior research has largely focused on computing the minimum cut for a fixed source–sink pair, practical scenarios such as data center communication often demand a different objective: identifying the source node whose minimum cut to a designated sink is maximized. This task, which we term the Global Maximum Minimum Cut with Fixed Sink (GMMC-FS) problem, captures the goal of locating a high-capacity source relative to a shared sink node that aggregates multiple servers. The problem is of significant engineering importance, yet it is computationally challenging as it involves a nested max–min optimization. In this paper, we present a recursive reduction (RR) algorithm for solving the GMMC-FS problem. The key idea is to iteratively select pivot nodes, compute their minimum cuts with respect to the sink, and prune dominated candidates whose cut values cannot exceed that of the pivot. By recursively applying this elimination process, RR dramatically reduces the number of max-flow computations required while preserving exact correctness. Compared with classical contraction-based and Gomory–Hu tree approaches that rely on global cut enumeration, the proposed RR framework offers a more direct and scalable mechanism for identifying the source that maximizes the minimum cut to a fixed sink. Its novelty lies in exploiting the structural properties of the sink side of suboptimal cuts, which leads to both theoretical efficiency and empirical robustness across large-scale networks. We provide a rigorous theoretical analysis establishing both correctness and complexity bounds, and we validate the approach through extensive experiments. Results demonstrate that RR consistently achieves optimal solutions while significantly outperforming baseline methods in runtime, particularly on large and dense networks.

A significant challenge in thermal device designs across diverse industries is optimizing heat dissipation rates to enhance system performance. Among different geometric configurations, a partially heated–cooled annular system containing magneto-nanofluids presents unique complexities due to the curvature ratio and strategic positioning of thermal sources–sinks, which substantially influences flow dynamics and thermal transfer mechanisms. The present investigation examines the buoyancy-driven heat transfer in an annular cavity containing a hybrid nanofluid under the influence of an inclined magnetic field and thermal source–sink pairs. Five different thermal source–sink arrangements and a wide range of magnetic field orientations are considered. The governing equations are solved using a finite difference approach that combines the Alternating Direction Implicit (ADI) method with relaxation techniques to capture the flow and thermal characteristics. An artificial neural network (ANN) is trained using simulation data to estimate the average Nusselt number for a range of physical conditions. Among different source–sink arrangements, the Case-1 arrangement is found to produce a stronger flow circulation and thermal dissipation rates. Also, an oblique magnetic field offers greater control compared with vertical or horizontal magnetic orientations. The network, structured with multiple hidden layers and optimized using a conjugate gradient algorithm, produces predictions that closely match the numerical results. Our analysis reveals that Case-1 demonstrates superior thermal performance, with approximately 19% greater heat dissipation compared with other chosen heating configurations. In addition, the Case-1 heating configuration combined with blade-shaped nanoparticles yields more than 27% superior thermal performance among the considered configurations. The outcomes suggest that at stronger magnetic fields (Ha=50), the orientation angle becomes critically important, with perpendicular magnetic fields (γ=90∘) significantly outperforming other orientations.

For a trajectory generated by dynamical systems, Hénon has presented a method called the Hénon trick or Hénon method. In this method, a surface of a section (Poincaré surface) is defined, and the Poincaré map (i.e., the trajectory points distributed on it) is collected when the trajectory crosses the Poincaré surface. Whenever the Hénon trick is used to calculate the Poincaré map, the autonomous chaotic system's trajectory deviates from the original path, causing a deformation in its attractor. In this paper, the Hénon trick is discussed to calculate the Poincaré map for the attractor Lorenz system, after which a 1-parameter pulsed dipole (source-sink pairs) model is defined on an unbounded domain, and a Python data science code is built to plot the results. The paper provided a reformed Hénon trick to calculate the Poincaré map for a 1-parameter pulsed dipole model by defining a cross-section (Poincaré surface), then I calculate the Poincaré map of the intersection points between this cross-section and the streamlines generated by that pulsed dipole model. The Poincaré map is important to investigate the uniformity of the distribution of streamlines generated by the pulsed dipole system.

Comment on: “Fluid flow and heat transfer characteristics of natural convection in square cavities due to discrete source-sink pairs” [International Journal of Heat and Mass Transfer 51 (2008) 5949–5957]

A three-stage evaluation model for biomass co-firing combined with carbon capture and storage (in oil wells) retrofit in coal-fired power plants based on multi-criteria decision-making: An example from Hebei Province, China

Reducing carbon dioxide (CO2) emissions urgently requires the large-scale deployment of carbon-capture technologies. These technologies must separate CO2 from various sources and deliver it to different sinks1,2. The quest for optimal solutions for specific source–sink pairs is a complex, multi-objective challenge involving multiple stakeholders and depends on social, economic and regional contexts. Currently, research follows a sequential approach: chemists focus on materials design3 and engineers on optimizing processes4,5, which are then operated at a scale that impacts the economy and the environment. Assessing these impacts, such as the greenhouse gas emissions over the plant’s lifetime, is typically one of the final steps6. Here we introduce the PrISMa (Process-Informed design of tailor-made Sorbent Materials) platform, which integrates materials, process design, techno-economics and life-cycle assessment. We compare more than 60 case studies capturing CO2 from various sources in 5 global regions using different technologies. The platform simultaneously informs various stakeholders about the cost-effectiveness of technologies, process configurations and locations, reveals the molecular characteristics of the top-performing sorbents, and provides insights on environmental impacts, co-benefits and trade-offs. By uniting stakeholders at an early research stage, PrISMa accelerates carbon-capture technology development during this critical period as we aim for a net-zero world.

A network flow approach to a common generalization of Clar and Fries numbers

Abstract Let $T=(V,E)$ be a tree in which each edge is assigned a cost; let $\mathcal{P}$ be a set of source–sink pairs of vertices in V in which each source–sink pair produces a profit. Given a lower bound K for the profit, the K-prize-collecting multicut problem in trees with submodular penalties is to determine a partial multicut $M\subseteq E$ such that the total profit of the disconnected pairs after removing M from T is at least K, and the total cost of edges in M plus the penalty of the set of still-connected pairs is minimized, where the penalty is determined by a nondecreasing submodular function. Based on the primal-dual scheme, we present a combinatorial polynomial-time algorithm by carefully increasing the penalty. In the theoretical analysis, we prove that the approximation factor of the proposed algorithm is $(\frac{8}{3}+\frac{4}{3}\kappa+\varepsilon)$ , where $\kappa$ is the total curvature of the submodular function and $\varepsilon$ is any fixed positive number. Experiments reveal that the objective value of the solutions generated by the proposed algorithm is less than 130% compared with that of the optimal value in most cases.

Carbon dioxide (CO2) emissions from industry significantly contribute to increasing CO2 in the atmosphere as the main cause of the Green House Gas (GHG) effect and climate change. CO2 emissions cause the need for evaluation in finding emission reduction systems. The CCUS (Carbon Capture Utilization and Storage) system is one of the most studied emission reduction systems. This study aims to obtain an intuitive and quantitative CCUS network design framework using GAMS (General Algebraic Modeling System) software with a mathematical approach. Several sources of CO2 emissions and potential absorbers are scattered in several regions in Indonesia. A mathematical approach was developed to optimize the amount of CO2 stored and utilized by varying the minimum time difference (dt min) between source and sink from 0, 3, 5, 8, to 10 years. The economic potential of the source-sink pair decreases with the change in dt with an average of 6.50 x 106 USD. Based on the potential economic value, the CCUS system with industrial CO2 emission sources has a positive value that can be applied in Indonesia.

Levelized-cost optimal design of long-distance CO2 transportation facilities

Context-free language reachability (CFL-reachability) is a fundamental framework for program analysis. A large variety of static analyses can be formulated as CFL-reachability problems, which determines whether specific source-sink pairs in an edge-labeled graph are connected by a reachable path, i.e., a path whose edge labels form a string accepted by the given CFL. Computing CFL-reachability is expensive. The fastest algorithm exhibits a slightly subcubic time complexity with respect to the input graph size. Improving the scalability of CFL-reachability is of practical interest, but reducing the time complexity is inherently difficult. In this paper, we focus on improving the scalability of CFL-reachability from a more practical perspective---reducing the input graph size. Our idea arises from the existence of trivial edges, i.e., edges that do not affect any reachable path in CFL-reachability. We observe that two nodes joined by trivial edges can be folded---by merging the two nodes with all the edges joining them removed---without affecting the CFL-reachability result. By studying the characteristic of the recursive state machines (RSMs), an alternative form of CFLs, we propose an approach to identify foldable node pairs without the need to verify the underlying reachable paths (which is equivalent to solving the CFL-reachability problem). In particular, given a CFL-reachability problem instance with an input graph G and an RSM, based on the correspondence between paths in G and state transitions in RSM, we propose a graph folding principle, which can determine whether two adjacent nodes are foldable by examining only their incoming and outgoing edges. On top of the graph folding principle, we propose an efficient graph folding algorithm GF. The time complexity of GF is linear with respect to the number of nodes in the input graph. Our evaluations on two clients (alias analysis and value-flow analysis) show that GF significantly accelerates RSM/CFL-reachability by reducing the input graph size. On average, for value-flow analysis, GF reduces 60.96% of nodes and 42.67% of edges of the input graphs, obtaining a speedup of 4.65× and a memory usage reduction of 57.35%. For alias analysis, GF reduces 38.93% of nodes and 35.61% of edges of the input graphs, obtaining a speedup of 3.21× and a memory usage reduction of 65.19%.

Given a graph [Formula: see text], a set of [Formula: see text] source-sink pairs [Formula: see text] [Formula: see text] and a profit bound [Formula: see text], every edge [Formula: see text] has a cost [Formula: see text], and every source-sink pair [Formula: see text] has a profit [Formula: see text] and a penalty [Formula: see text]. The [Formula: see text]-prize-collecting multicut problem ([Formula: see text]-PCMP) is to find a multicut [Formula: see text] such that the objective cost, which consists of the total cost of the edges in [Formula: see text] and the total penalty of the pairs still connected after removing [Formula: see text], is minimized and the total profit of the disconnected pairs by removing [Formula: see text] is at least [Formula: see text]. In this paper, we firstly consider the [Formula: see text]-PCMP in paths, and prove that it is [Formula: see text]-hard even when [Formula: see text] for any [Formula: see text]. Then, we present a fully polynomial time approximation scheme (FPTAS) whose running time is [Formula: see text] for the [Formula: see text]-PCMP in paths. Based on this algorithm, we present an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in spider graphs, and an FPTAS whose running time is [Formula: see text] for the [Formula: see text]-PCMP in rings, respectively, where [Formula: see text] is the number of leaves of spider graph.

The current numerical investigation deals with natural convection in a nanofluid-saturated porous cylindrical annulus subjected to partial heating and cooling of side walls by adopting Brinkman-extended Darcy Model to govern the fluid flow in porous media. By choosing five different locations and four lengths of thermal source–sink pairs, the impact of discrete heating–cooling on fluid flow, thermal transport rates and thermal mixing in a porous annular enclosure has been addressed. From the vast range of numerical simulations, the results provide information on the proper size and location of source–sink combinations to dissipate maximum thermal transport along with better thermal mixing in the enclosure. The importance of porosity, nanoparticle concentration, Darcy and Rayleigh numbers on overall thermal dissipation rate has also been discussed. The results showed that identifying an optimum source–sink location along with an appropriate choice of other control parameters can lead to higher thermal transport enhancement and thermal mixing.

Non-Darcy nanoliquid buoyant flow and entropy generation analysis in an inclined porous annulus: Effect of source-sink arrangement

Abstract Introduction The relation between slow oscillations (SOs, <1Hz) during non-rapid eye movement (NREM) sleep and systems-level memory consolidation is one of the most robust findings in cognitive neuroscience. However, NREM is a brain state seemingly unfavorable to systems consolidation because a hallmark characteristic of this state is a breakdown in connectivity and reduction in synaptic plasticity with increasing depth of sleep. Our study addresses this apparent paradox and how SOs orchestrate neural communication. Methods We employed generalized partial directed coherence to estimate directional causal information flow between EEG channels across the electrode manifold during SO and non-SO periods. We examined the magnitude of causal information flow over the phase of SOs and found two peaks of flow preceding and following the trough of the SO. We categorized source-sink pairs of flows into three groups based on distance between source and sink of information flow. All the peak flows in each group were averaged and we tested relation between averaged magnitude of the flow and overnight episodic memory improvement using correlation test. Results The results reveal that NREM generally (non-SO periods) and during the SO trough show dampened neural communication. Causal communication during non-rapid eye movement sleep peaks during specific phases of the SO ( before and after SO trough), but only across long distances. Correlation test results showed that episodic memory improvement was predicted by peaks of information flow with longest distances between sinks and sources, and not by any other phase of the SO or non-SO period. Conclusion This work introduces a non-invasive approach to examine information processing during sleep, a behavioral stage whose function, until now, has been understood only at a delay. The findings represent a conceptual leap in understanding how slow oscillations unlock memory consolidation in a broken down network which is by promoting long range effective communication. This research will promote further investigations of understanding how brain oscillations alone and in nested rhythms promote network communication, as well as to investigate how these properties vary and predict patterns of deficits in clinical populations and aging humans. Support (If Any)

Numerical Investigations on Melting of Phase Change Material (PCM) with Different Arrangements of Heat Source-sink Pairs Under Microgravity

Transient thermogravitational convection for magneto hybrid nanofluid in a deep cavity with multiple isothermal source-sink pairs

Semi-decentralized energy routing algorithm for minimum-loss transmission in community energy internet

Paths Through the Yeast Regulatory Network in Different Physiological States

This work focused on the computational fluid dynamics (CFD) modeling of H2/N2 separation in a membrane permeator module containing a supported dense Pd-based membrane that was prepared using electroless pore-plating (ELP-PP). An easy-to-implement model was developed based on a source–sink pair formulation of the species transport and continuity equations. The model also included the Darcy–Forcheimer formulation for modeling the porous stainless steel (PSS) membrane support and Sieverts’ law for computing the H2 permeation flow through the dense palladium film. Two different reactor configurations were studied, which involved varying the hydrogen flow permeation direction (in–out or out–in). A wide range of experimental data was simulated by considering the impact of the operating conditions on the H2 separation, such as the feed pressure and the H2 concentration in the inlet stream. Simulations of the membrane permeator device showed an excellent agreement between the predicted and experimental data (measured as permeate and retentate flows and H2 separation). Molar fraction profiles inside the permeator device for both configurations showed that concentration polarization near the membrane surface was not a limit for the hydrogen permeation but could be useful information for membrane reactor design, as it showed the optimal length of the reactor.