Mix design optimisation for concrete with alternative binders and aggregates incorporating environmental, mechanical and durability performance

Long-range frustration in minimal vertex cover problem on random graphs

Recent branch-based MaxIS solvers improve solution quality through recursive search and targeted branching [Hespe D, Lamm S, Schorr C. Targeted branching for the maximum independent set problem. 2021], but their runtime can grow rapidly on large IoT conflict graphs. This paper proposes KernelGreedyMaxIS, a deterministic polynomial-time framework for scalable independent-set computation. The method combines lightweight degree-based kernelization with minimum-degree greedy inference, separating locally justified reductions from heuristic selection. This design improves reproducibility, avoids random seeds and training data, and provides predictable runtime behavior. Theoretical analysis proves reduction correctness, feasibility, deterministic termination, and O ( n 2 logn ) worst-case complexity. Experiments show competitive solution quality with fast runtime on benchmark and real-world graphs.

Partial temporal vertex cover with bounded activity intervals

ABSTRACT The disposal of coal waste heap has induced critical environmental issue worldwide. To mitigate the spontaneous combustion of coal waste heaps and address the environmental concerns associated with fly ash accumulation, permeability tests were conducted on two types of circulating fluidized bed desulfurization ash (fly ash A1 and A2) and one low-calcium ash (fly ash B) from power plants in Wuhai, as well as a mixture of these ashes (fly ash C). By analyzing air seepage through fly ash under various pressures, compaction levels, and thicknesses, this study establishes methods to predict seepage velocity and determine the minimum cover thickness required to inhibit coal gangue oxidation. The results reveal that the air seepage velocity of all fly ash samples shows a linear relationship with pressure difference, with the slope decreasing exponentially as compaction work increases and inversely correlating with thickness. The capability of obstructing airflow of fly ash mainly depends on the content of particles with diameter less than 0.075 mm. The air barrier performance follows the order: A1 < C < A2 < B, with finer particles (<0.075 mm) requiring thinner cover layers to meet flame-retardant standards. A functional relationship was developed based on Darcy’s law between air seepage velocity, pressure difference, thickness, and compaction work, and a predictive formula was proposed, offering a theoretical basis for analyzing the air barrier performance of fly ash under varying conditions.

We present a polynomial-time algorithm for minimum vertex cover achieving an approximation ratio strictly less than 2 for any finite undirected graph with at least one edge. The algorithm reduces the problem to a minimum weighted vertex cover on a degree-1 auxiliary graph using weights 1 / d v , solves it optimally via Cauchy–Schwarz-balanced selection, and projects the solution back to a valid cover. Correctness and the strict sub-2 ratio are rigorously proved. Runtime is O ( | V | + | E | ) , confirming practical scalability.

Probabilistic neural networks are good at solving complex optimization tasks, but require stochastic, energy-efficient probabilistic bit (p-bit) neurons and reliable artificial synapses. Here we show stochastic ferroelectric tunnel junctions (s-FTJs) and reliable-FTJs (r-FTJs) by tuning the oxygen vacancy concentration in Hf0.5Zr0.5O2 ferroelectric film, which are utilized to set up p-bit neurons and synapses, respectively. The s-FTJ-based p-bit outputs 0 or 1 with a tunable probability, and it can operate as a true random number generator at a probability of 0.5. The write power per p-bit is ~76 nW, significantly lower than other reported p-bit implementations. A hardware prototype of a four-neuron Boltzmann machine is experimentally constructed for probabilistic computing, which successfully solves the maximum independent set problem. Simulations show that a 655-neuron Boltzmann machine can accurately predict the secondary structure of a 64-nucleotide RNA. This work provides a high-performance probabilistic computing solution with low energy consumption and excellent process compatibility.

Sustainable agriculture requires maintaining soil health, yet conventional management (CM) practices may not protect soils from stresses such as compaction. This study compared microbial resilience to compaction in two soils collected from sugarcane farms under improved management (IM: minimum tillage, cover cropping and stubble retention) and CM (conventional tillage, no cover crop and stubble retention) practices. Samples were placed in 96-well deep-well plates and compacted using a bespoke device to achieve bulk densities of 0.9 (control), 1.1 (low), and 1.2 g cm⁻³ (moderate). Microbial resistance was assessed 14 days after compaction, and resilience 14 days after stress relief. Under low and moderate compaction, IM soils showed 49.5 % and 45.7 % higher CO₂ emission resistance indices (i.e., the ability of soil to maintain microbial respiration under compaction stress) than CM, indicating greater stability. Microbial biomass carbon and nitrogen were 56.2 % and 47.9 % higher in IM soils under low compaction, compared to CM. Soil microbial metabolic quotient ( q CO₂) was similar across compaction levels within each system, but was 19.5 %–36.3 % lower in IM soils than CM at equivalent compaction, indicating lower microbial stress under IM. Fourteen days after stress relief, q CO₂ in moderately compacted CM soil increased by 41.1 % and 25.0 % compared to control and low compaction. In contrast, IM soil under moderate compaction had 40.6 % lower q CO₂ than CM. The CM showed no effects of compaction on hot water extractable organic carbon content, while compaction of IM showed a 13 % decline compared to its control. Hot water extractable total nitrogen did not vary with compaction within the management systems but was 12 %–15 % higher in IM than CM under the same compaction during the resistance phase. Total mineral nitrogen was unaffected by compaction treatments under each system but was 11 %–13 % higher in IM than CM during resistance phase. These findings highlight the potential of improved management practices to sustain soil health and resilience under compaction stress. • A novel test used to assess microbial functional resilience to compaction stress. • Improved management had higher respiration resistance than conventional management. • Improved management reduced microbial metabolic quotient under compaction stress. • Improved management enhanced microbial functional stability and nutrient retention.

Wireless sensor networks (WSNs) are the backbone of IoT-enabled smart manufacturing, environmental monitoring, and industrial automation. However, their broadcast nature makes communication links vulnerable to eavesdropping, routing manipulation, and denial-of-service attacks. Strategically placing monitor nodes to check each link is an effective approach to protect against attacks, but energy, connectivity, and capacity constraints should be considered while picking monitor nodes. In this paper, we tackle the Minimum-Weighted Connected Capacitated Vertex Cover (MWCCVC) problem, which minimizes monitoring costs, ensures backbone connectivity, and adheres to per-node capacity constraints. Unlike prior works that consider weighted vertex cover, connectivity constraints, or capacitated variants separately, the proposed MWCCVC model jointly integrates all three dimensions within a single vertex cover-based monitoring framework. We first provide a Branch-and-Bound (B&B) solver with linear programming relaxation bounds and constraint-based pruning strategies that produces optimum solutions. Three constructive greedy heuristics (GD, GR, GW) and two hybrid genetic algorithms (HGA, HGA-v2) that combine parameterized greedy decoders with evolutionary search are proposed; all methods guarantee full edge coverage, induced-subgraph connectivity, and max-flow-validated capacity feasibility. Tests on 130 small, 160 medium, and 19 large benchmark instances show that HGA matches B&B optima on every small instance, beats the time-limited B&B by 6.6% on medium instances, where the percentage is computed based on the relative difference in average total weight with respect to B&B, and stays the best on large graphs with up to 1000 nodes. The HGA-v2 tries to balance the quality and speed, with only a 3.1% difference at faster execution.

Machine learning interatomic potentials (MLIPs) balance high accuracy and lower costs compared to density functional theory calculations, but their performance often depends on the size and diversity of training datasets. Large datasets improve model accuracy and generalization but are computationally expensive to produce and train on, while smaller datasets risk discarding rare but important atomic environments and compromising MLIP accuracy/reliability. Here, we develop an information-theoretical framework to quantify the efficiency of dataset compression methods and propose an algorithm that maximizes this efficiency. By framing atomistic dataset compression as an instance of the minimum set cover (MSC) problem over atom-centered environments, our method identifies the smallest subset of structures that contains as much information as possible from the original dataset while pruning redundant information. The approach is extensively demonstrated on the GAP-20 and TM23 datasets and validated on 64 varied datasets from the ColabFit repository. Across all cases, MSC consistently retains outliers, preserves dataset diversity, and reproduces the long-tail distributions of forces even at high compression rates, outperforming other subsampling methods. Furthermore, MLIPs trained on MSC-compressed datasets exhibit reduced error for out-of-distribution data even in low-data regimes. We explain these results using an outlier analysis and show that such quantitative conclusions could not be achieved with conventional dimensionality reduction methods. The algorithm is implemented in the open-source QUESTS package and can be used for several tasks in atomistic modeling, from data subsampling, outlier detection, and training improved MLIPs at a lower cost.

A cover by left ideals of an associative (not necessarily commutative or unital) ring R is a collection of proper left ideals whose set-theoretic union equals R. If such a cover exists, then η l ( R ) is the cardinality of a minimal cover, and R is η l -elementary if η l ( R ) < η l ( R / I ) for every nonzero two-sided ideal I of R. We classify all η l -elementary rings, and determine their covering numbers. Covers by right or two-sided ideals are also studied. This completely characterizes rings admitting finite covers by ideals. Our results generalize to finite covers of modules by submodules, and we determine all possible covering numbers.

We introduce a simple structural property of bipartite graphs—edge-stability—which states that removing an edge whose endpoints lie in a minimum vertex cover does not change the vertex cover number. This property admits an elementary proof and serves as a bridge between several classical theorems in matching theory. We show that edge-stability follows directly from Kőnig’s Theorem and, conversely, can be used to rederive it. Moreover, we employ edge-stability to obtain short proofs of Berge’s characterization of maximum independent sets and Hall’s Marriage Theorem. Thus within the framework of Reichmeider’s equivalence of Mengerian theorems, edge-stability, Kőnig’s, Berge’s, and Hall’s theorems are all equivalent. The approach highlights new conceptual and pedagogical connections between these cornerstone results in matching theory.

A set $S \subseteq V(G)$ is a vertex cover of an undirected graph $G$ if for every edge $uv$ in $G$, we must have $u \in S$ or $v \in S$. A vertex cover $S \subseteq V(G)$ is a certified vertex cover (covering) of $G$ if for every $v \in S$, it holds that $|N_G(v) \cap (V(G) \setminus S)|=0$ or $|N_G(v) \cap (V(G) \setminus S)| \geq 2$. The smallest cardinality of a certified vertex covering of $G$, denoted $\beta_{cer}(G)$, is called the certified vertex covering number of $G$. In this paper, we show that given two positive integers $a$ and $b$ such that $2 \leq a \leq b$, there exists a connected graph $G$ such that $\gamma_{cer}(G)=a$ and $\beta_{cer}(G)=b$, where $\gamma_{cer}(G)$ is the certified domination number of $G$. We also characterize the certified vertex covers of the corona, edge corona, and lexicographic product. From these characterizations, we determine a bound or the exact value of the certified vertex covering number of each of these graphs. Received: January 21, 2026Accepted: March 23, 2026

A binary tree (more precisely, an unrooted binary tree) is a tree in which all internal vertices (i.e., non-leaves) are exactly of degree 3. We give an upper bound and a lower bound for the number of maximal independent sets in binary trees together with a characterization of the extremal binary trees. The binary trees with second largest number of maximal independent sets are also characterized.

Abstract Maximal Independent Set (MIS) is one of the fundamental and most well-studied problems in distributed graph algorithms. Even after four decades of intensive research, the best known (randomized) MIS algorithms have $$O(\log {n})$$ round complexity on general graphs [Luby, STOC 1986] (where n is the number of nodes), while the best known lower bound is $$\Omega (\sqrt{\log {n}/\log \log {n}})$$ [Kuhn, Moscibroda, Wattenhofer, JACM 2016]. Breaking past the $$O(\log {n})$$ round complexity upper bound or showing stronger lower bounds have been longstanding open problems. Energy is a premium resource in various settings such as battery-powered wireless networks and sensor networks. The bulk of the energy is used by nodes when they are awake , i.e., when they are sending, receiving, and even just listening for messages. On the other hand, when a node is sleeping , it does not perform any communication and thus spends very little energy. Several recent works have addressed the problem of designing energy-efficient distributed algorithms for various fundamental problems. These algorithms operate by minimizing the number of rounds in which any node is awake , also called the (worst-case) awake complexity . An intriguing open question is whether one can design a distributed MIS algorithm that has significantly smaller awake complexity compared to existing algorithms. In particular, the question of obtaining a distributed MIS algorithm with $$o(\log n)$$ awake complexity was left open in [Chatterjee, Gmyr, Pandurangan, PODC 2020]. Our main contribution is to show that MIS can be computed in awake complexity that is exponentially better compared to the best known round complexity of $$O(\log n)$$ and also bypassing its fundamental $$\Omega (\sqrt{\log {n}/\log \log {n}})$$ round complexity lower bound exponentially. Specifically, we show that MIS can be computed by a randomized distributed (Monte Carlo) algorithm in $$O(\log \log {n} )$$ awake complexity with high probability (i.e., with probability at least $$1 - n^{-1}$$ ). This algorithm has a round complexity of $$O((\log ^7 n) \log \log n)$$ . We also show that we can improve the round complexity at the cost of a slight increase in awake complexity, by presenting a randomized distributed (Monte Carlo) algorithm for MIS that, with high probability, computes an MIS in $$O((\log \log {n})\log ^*n)$$ awake complexity and $$O((\log ^3 n) (\log \log n) \log ^*n)$$ round complexity. Our algorithms work in the $$\mathcal{CONGEST}$$ model where messages of size $$O(\log n)$$ bits can be sent per edge per round.

Many real-world applications call for incorporating fairness constraints into the k-center clustering problem, where the dataset is partitioned into m demographic groups, each with a specified upper bound on the number of centers to ensure fairness. Focusing on big data scenarios, this paper addresses the problem in a streaming setting, where data points arrive sequentially in a continuous stream. Leveraging a structure called the λ-independent center set, we propose a one-pass streaming algorithm that first computes a reserved set of points during the streaming process. In the post-streaming process, we then select centers from the reserved point set by analyzing three possible cases and transforming the most complex one into a specially constrained vertex-cover problem on an auxiliary graph. Our algorithm achieves an approximation ratio of 5 + ? and memory complexity O(k log ?), where ? is the aspect ratio and ? &gt; 0 is any small constant. Furthermore, we extend our approach to semi-structured data streams, where data points arrive in groups. In this setting, we present a (3 + ?)-approximation algorithm for m = 2, which can be readily adapted to solve the offline fair k-center problem, achieving an approximation ratio of 3 that matches the current state of the art. Lastly, we conduct extensive experiments to evaluate the performance of our approaches, demonstrating that they outperform existing baselines in both clustering cost and runtime efficiency.

Moisture loss due to evaporation decreases soil cohesion or causes cracks in archaeological sites under excavation or exhibition when the soil is covered with tarpaulins or buildings. Desiccation-induced degradation is difficult to fix; however, effective methods for mitigating evaporation have not been established. This work aims to demonstrate the potential application of sand protection covers to archaeological sites. Coarse sand covers with small water retention mitigate upward porewater transfer as they have small hydraulic conductivity in dry conditions. Evaporation experiments were performed on soil layers with sand covers of four different thicknesses, and the results were simulated with hydro-thermal coupled FE analysis. The experimental results demonstrated that all the 5 mm-thick or thicker sand layers significantly reduced evaporation rate and moderated desiccation cracks, compared to the bare soil case. The numerical simulations calibrated with the experimental data were extended to explore the effects of sand cover thickness. The results showed that the sand cover mitigated the evaporation, and the period of the 1st evaporation stage was extended with increasing sand layer thickness. The required minimum sand cover thickness, defined as the cover thickness that most efficiently reduces cumulative evaporation, was found to have a relationship with the period length of the continuous drying process. That is, the seasonal average rainfall interval of the archaeological site. The proposed protection method is useful to mitigate evaporation-induced damage in soil heritage and has prospective applications for long-term soil moisture retention.

While variational quantum algorithms (VQAs) have demonstrated considerable success in unconstrained optimization, their application to constrained combinatorial problems face a trade-off. Penalty-based methods, despite their circuit simplicity, suffer from a fundamental limitation: inefficient sampling in vast infeasible regions. This often results in suboptimal solutions that violate constraints and impede convergence to high-quality results. In contrast, ansatz-based approaches enforce solution feasibility by design but require complex, problem-specific circuits that are challenging to implement on current noisy intermediate-scale quantum devices. To overcome these limitations, we introduce an alternative VQA whose core innovation lies in a strategically designed loss function. This function offers a dual advantage. First, it is provably guaranteed that its global minimum corresponds uniquely to the optimal feasible solution, as this is achieved by ensuring universally higher loss values for all infeasible solutions. Second, it furnishes distinct computational pathways for feasible versus infeasible regions, thus creating clear and non competing guidance for the optimizer. As a result of these combined features, the algorithm's overall performance is significantly enhanced. Regarding hardware overhead, our design requires adding only an efficient validation oracle module to the penalty-based circuit, resulting in a circuit complexity significantly lower than that of ansatz-based approaches with their custom mixers. To validate the practical efficiency of our method, we empirically demonstrate its effectiveness by solving minimum vertex cover and maximum independent set problems on random graphs of varying small-scale sizes.

Maximal independent sets in graphs with a given matching number

Maximizing the number of maximal independent sets in graphs with a given matching number