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In this paper, we consider the problem of numerical investigation of the counting statistics for a class of one-dimensional systems. Importance sampling, the cornerstone technique usually implemented for such problems, critically hinges on selecting an appropriate biased distribution. While an exponential tilt in the observable stands as the conventional choice for various problems, its efficiency in the context of counting statistics may be significantly hindered by the genuine discreteness of the observable. To address this challenge, we propose an alternative strategy, which we call importance sampling with the local tilt. We demonstrate the efficiency of the proposed approach through the analysis of three prototypical examples: a set of independent Gaussian random variables, Dyson gas, and symmetric simple exclusion process with a steplike initial condition. [ABSTRACT FROM AUTHOR]

Understanding the nonadiabatic dynamics of complex systems is a challenging task in computational photochemistry. Herein, we present an efficient and user-friendly quantum mechanics/molecular mechanics (QM/MM) interface to run on-the-fly nonadiabatic dynamics. Currently, this interface consists of an independent set of codes designed for general-purpose use. Herein, we demonstrate the ability and feasibility of the QM/MM interface by integrating it with our long-term developed JADE package. Tailored to handle nonadiabatic processes in various complex systems, especially condensed phases and protein environments, we delve into the theories, implementations, and applications of on-the-fly QM/MM nonadiabatic dynamics. The QM/MM approach is established within the framework of the additive QM/MM scheme, employing electrostatic embedding, link-atom inclusion, and charge-redistribution schemes to treat the QM/MM boundary. Trajectory surface-hopping dynamics are facilitated using the fewest switches algorithm, encompassing classical and quantum treatments for nuclear and electronic motions, respectively. Finally, we report simulations of nonadiabatic dynamics for two typical systems: azomethane in water and the retinal chromophore PSB3 in a protein environment. Our results not only illustrate the power of the QM/MM program but also reveal the important roles of environmental factors in nonadiabatic processes. [ABSTRACT FROM AUTHOR]

Cartesian tensors are widely used in physics and chemistry, especially for the formulation of linear and nonlinear spectroscopies as well as for molecular response properties. In this work, we review the problem of irreducible Cartesian tensor (ICT) decomposition of a generic Cartesian tensor of rank n into its irreducible parts, each characterized by a specific symmetry. The matrix formulation of the ICT decomposition is structurally similar to the problem of rotational averaging using isotropic Cartesian tensors. Analogously to the latter, the ICT decomposition can be considered as a problem of selecting a set of permutations of n indices that provides a linearly independent set of mappings between Cartesian tensor subspaces. This selection can be performed using a simple computational approach based on the reduced row echelon form (rref) algorithm. This protocol has been implemented in a computer code used to re-derive the already known ICT decomposition for 2 ≤ n ≤ 4. Finally, for the first time, we performed the explicit ICT decomposition of a Cartesian tensor of rank n = 5. [ABSTRACT FROM AUTHOR]

Summary: Fault‐tolerance and self‐organization are critical properties in modern distributed systems. Self‐stabilization is a class of fault‐tolerant distributed algorithms which has the ability to recover from any kind and any finite number of transient faults and topology changes. In this article, we propose a self‐stabilizing distributed algorithm for the 1‐MIS problem under the unfair central daemon assuming the distance‐3 model. Here, in the distance‐3 model, each process can refer to the values of local variables of processes within three hops. Intuitively speaking, the 1‐MIS problem is a variant of the maximal independent set (MIS) problem with improved local optimizations. The time complexity (convergence time) of our algorithm is O(n)$$ O(n) $$ steps and the space complexity is O(logn)$$ O\left(\log n\right) $$ bits, where n$$ n $$ is the number of processes. Finally, we extend the notion of 1‐MIS to p$$ p $$‐MIS for each nonnegative integer p$$ p $$, and compare the set sizes of p$$ p $$‐MIS (p=0,1,2,...$$ p=0,1,2,\dots $$) and the maximum independent set. [ABSTRACT FROM AUTHOR]

Fix a positive integer n and consider the bipartite graph whose vertices are the 3-element subsets and the 2-element subsets of [ n ] = { 1 , 2 , ... , n } , and there is an edge between A and B if A ⊂ B. We prove that the domination number of this graph is n 2 − ⌊ (n + 1) 2 8 ⌋ , we characterize the dominating sets of minimum size, and we observe that the minimum size dominating set can be chosen as an independent set. This is an exact version of an asymptotic result by Balogh, Katona, Linz and Tuza (2021). For the corresponding bipartite graph between the (k + 1) -element subsets and the k -element subsets of [ n ] (k ⩾ 3), we provide a new construction for small independent dominating sets. This improves on a construction by Gerbner, Kezegh, Lemons, Palmer, Pálvölgyi and Patkós (2012), who studied these independent dominating sets under the name saturating flat antichains. [ABSTRACT FROM AUTHOR]

Let Γ = (V (Γ),E(Γ)) be a graph. A subset C of V (Γ) is called a perfect code of Γ, when C is an independent set and every vertex of V (Γ)∖C is adjacent to exactly one vertex in C. Let Γ = Cay(G, S) be a Cayley graph of a finite group G. A subset C of G is called a perfect code of G, when there exists a Cayley graph Γ of G such that C is a perfect code of Γ. Recently, groups whose set of all subgroup perfect codes forms a chain are classified. Also, groups with no proper nontrivial subgroup perfect code are characterized. In this paper, we generalize it and classify groups whose set of all non-perfect code subgroups forms a chain. [ABSTRACT FROM AUTHOR]

Let G = (V , E) be a nontrivial connected simple graph and d (a , b) be the distance between the vertices a and b in G. The metric dimension of a graph G , denoted by dim(G), refers to the smallest set of vertices required to uniquely identify every vertex in the graph G. A family of simple connected graphs say F s , where s ∈ ℕ has a constant metric dimension, if dim ( F s ) is finite and does not depend on the choice of s in F s . In this paper, we consider two infinite families of planar graphs, say Q s , where s ≥ 8 and Z s , where s ≥ 6 , and investigate their metric basis as well as the metric dimension. Additionally, we prove that the metric basis for these two graphs are independent. [ABSTRACT FROM AUTHOR]

Harary and Melter introduced the concept of resolving sets in graphs. Slater stated the term locating set and the minimum resolving set as reference sets. Chartrand mentioned the locating set as a resolving set and the minimum cardinality of a resolving set as metric dimension or simply dimension in later stage. Several types of resolving sets like connected resolving sets, independent resolving sets, acyclic resolving sets, etc. have been discussed in the past. In this work, weakly connected resolving set is introduced and we studied its bounds. [ABSTRACT FROM AUTHOR]

The fullerene derivative hexagonal system is obtained from fullerene Cn and hexagonal system sticked by a common edge. The Merrifield–Simmons index of a graph G is defined as the total number of the independent sets of G. In this paper, we give the lower and larger bound of Merrifield–Simmons index of the fullerene derivative hexagonal system. Furthermore, we give two formulas of the Merrifield–Simmons index of the fullerene derivative hexagonal system C20 ⊗ l(n) and C20 ⊗ (l(n1), l(n2)). [ABSTRACT FROM AUTHOR]

We study the approximability of the maximum size independent set (MIS) problem in bounded degree graphs. This is one of the most classic and widely studied NP-hard optimization problems. It is known for its inherent hardness of approximation. We focus on the well known minimum-degree greedy algorithm for this problem. This algorithm iteratively chooses a minimum degree vertex in the graph, adds it to the solution and removes its neighbors, until the remaining graph is empty. The approximation ratios of this algorithm have been widely studied, where it is augmented with an advice that tells the greedy algorithm which minimum degree vertex to choose if it is not unique. Our main contribution is a new mathematical theory for the design of such greedy algorithms for MIS with efficiently computable advice and for the analysis of their approximation ratios. Using this theory we obtain the ultimate approximation ratio of 5/4 for greedy algorithms on graphs with maximum degree 3, which completely solves an open problem from the paper by Halldórsson and Yoshihara (in: Staples, Eades, Katoh, Moffat (eds) Algorithms and computations—ISAAC '95, in 2026 LNCS, Springer, Berlin, Heidelberg, 1995). Our algorithm is the fastest currently known algorithm for MIS with this approximation ratio on such graphs. We also obtain a simple and short proof of the (Δ + 2) / 3 -approximation ratio of any greedy algorithms on graphs with maximum degree Δ , the result proved previously by Halldórsson and Radhakrishnan (Nord J Comput 1:475–492, 1994). We almost match this ratio by showing a lower bound of (Δ + 1) / 3 on the ratio of a greedy algorithm that can use an advice. We apply our new algorithm to the minimum vertex cover problem on graphs with maximum degree 3 to obtain a substantially faster 6/5-approximation algorithm than the one currently known. We complement our algorithmic, upper bound results with lower bound results, which show that the problem of designing good advice for greedy algorithms for MIS is computationally hard and even hard to approximate on various classes of graphs. These results significantly improve on the previously known hardness results. Moreover, these results suggest that obtaining the upper bound results on the design and analysis of the greedy advice is non-trivial. [ABSTRACT FROM AUTHOR]

Aimed to evaluate the diagnostic performance of preoperative MRI-based radiomic models for noninvasive prediction of lymphovascular space invasion (LVSI) in patients with cervical cancer (CC). A systematic search of the PubMed, Embase, Web of Science, and Cochrane databases was conducted up to December 21, 2023. The quality of the studies was assessed utilizing the Radiomics Quality Score (RQS) system and the Quality Assessment of Diagnostic Accuracy Studies (QUADAS-2) tool. Pooled estimates of sensitivity, specificity, diagnostic odds ratio (DOR), and area under the curve (AUC) of the summary receiver operating characteristic curve (SROC) were computed. The clinical utility was evaluated using the Fagan nomogram. Heterogeneity was investigated and subgroup analyses were conducted. Eleven studies were included, with nine studies reporting independent validation sets. In the training sets, the pooled sensitivity, specificity, DOR, and AUC of SROC were 0.81 (95% CI: 0.75–0.85), 0.78 (95% CI: 0.73–0.83), 15 (95% CI: 11–20), and 0.86 (95% CI: 0.79–0.92), respectively. For the validation sets, the overall sensitivity, specificity, DOR, and AUC of SROC were 0.79 (95% CI: 0.73–0.84), 0.73 (95% CI: 0.67–0.78), 10 (95% CI: 7–15), and 0.83 (95% CI: 0.71–0.91), respectively. The Fagan nomogram indicated good clinical utility. Subgroup analysis revealed that multi-sequence MRI-based models exhibited superior diagnostic performance compared to single-sequence MRI-based models in validation sets. This meta-analysis highlights the potential diagnostic efficacy of MRI-based radiomic models for predicting LVSI in CC. Nevertheless, large-sample, multicenter studies are still warranted, and improvements in the standardization of radiomics methodology are necessary. • Evaluate the diagnostic value of MR radiomics models for LVSI in cervical cancer. • The results suggest promising diagnostic performance of MR radiomics models. • This non-invasive tool can aid in preoperatively identifying LVSI in cervical cancer. [ABSTRACT FROM AUTHOR]

Inspired by Sheehan's conjecture that no 4-regular graph contains exactly one hamiltonian cycle, we prove results on hamiltonian cycles in regular graphs and nearly regular graphs. We fully disprove a conjecture of Haythorpe on the minimum number of hamiltonian cycles in regular hamiltonian graphs, thereby extending a result of Zamfirescu, as well as correct and complement Haythorpe's computational enumerative results from [Exp. Math. 27 (2018), no. 4, 426–430]. Thereafter, we use the Lovász Local Lemma to extend Thomassen's independent dominating set method. This extension allows us to find a second hamiltonian cycle that inherits linearly many edges from the first hamiltonian cycle. Regarding the limitations of this method, we answer a question of Haxell, Seamone, and Verstraete, and settle the first open case of a problem of Thomassen by showing that for k \in \{5, 6\} there exist infinitely many k-regular hamiltonian graphs having no independent dominating set with respect to a prescribed hamiltonian cycle. Motivated by an observation of Aldred and Thomassen, we prove that for every \kappa \in \{ 2, 3 \} and any positive integer k, there are infinitely many non-regular graphs of connectivity \kappa containing exactly one hamiltonian cycle and in which every vertex has degree 3 or 2k. [ABSTRACT FROM AUTHOR]

Background: Accurate differentiation between malignant and benign pulmonary nodules, especially those measuring 5–10 mm in diameter, continues to pose a significant diagnostic challenge. This study introduces a novel, precise approach by integrating circulating cell-free DNA (cfDNA) methylation patterns, protein profiling, and computed tomography (CT) imaging features to enhance the classification of pulmonary nodules. Methods: Blood samples were collected from 419 participants diagnosed with pulmonary nodules ranging from 5 to 30 mm in size, before any disease-altering procedures such as treatment or surgical intervention. High-throughput bisulfite sequencing was used to conduct DNA methylation profiling, while protein profiling was performed utilizing the Olink proximity extension assay. The dataset was divided into a training set and an independent test set. The training set included 162 matched cases of benign and malignant nodules, balanced for sex and age. In contrast, the test set consisted of 46 benign and 49 malignant nodules. By effectively integrating both molecular (DNA methylation and protein profiling) and CT imaging parameters, a sophisticated deep learning-based classifier was developed to accurately distinguish between benign and malignant pulmonary nodules. Results: Our results demonstrate that the integrated model is both accurate and robust in distinguishing between benign and malignant pulmonary nodules. It achieved an AUC score 0.925 (sensitivity = 83.7%, specificity = 82.6%) in classifying test set. The performance of the integrated model was significantly higher than that of individual methylation (AUC = 0.799, P = 0.004), protein (AUC = 0.846, P = 0.009), and imaging models (AUC = 0.866, P = 0.01). Importantly, the integrated model achieved a higher AUC of 0.951 (sensitivity = 83.9%, specificity = 89.7%) in 5–10 mm small nodules. These results collectively confirm the accuracy and robustness of our model in detecting malignant nodules from benign ones. Conclusions: Our study presents a promising noninvasive approach to distinguish the malignancy of pulmonary nodules using multiple molecular and imaging features, which has the potential to assist in clinical decision-making. Trial registration: This study was registered on ClinicalTrials.gov on 01/01/2020 (NCT05432128). https://classic.clinicaltrials.gov/ct2/show/NCT05432128. [ABSTRACT FROM AUTHOR]

In this paper, we consider the following two problems: (i) Deletion Blocker (α) where we are given an undirected graph G = (V , E) and two integers k , d ≥ 1 and ask whether there exists a subset of vertices S ⊆ V with | S | ≤ k such that α (G − S) ≤ α (G) − d , that is the independence number of G decreases by at least d after having removed the vertices from S ; (ii) Transversal (α) where we are given an undirected graph G = (V , E) and two integers k , d ≥ 1 and ask whether there exists a subset of vertices S ⊆ V with | S | ≤ k such that for every maximum independent set I we have | I ∩ S | ≥ d. We show that both problems are polynomial-time solvable in the class of co-comparability graphs by reducing them to the well-known Vertex Cut problem. Our results generalise a result of Chang et al. (2001) and a recent result of Hoang et al. (2023). [ABSTRACT FROM AUTHOR]

AbstractAA amyloidosis is a prototypic example of systemic amyloidosis: it results from the prolonged overproduction of SAA protein produced in response to chronic inflammation. AA amyloidosis primarily affects the kidneys, liver, spleen, gastrointestinal tract, leading to a variety of symptoms. First, this review examines AA amyloidosis in humans, focusing on pathogenesis, clinical presentation, and diagnosis and then in animals. In fact AA amyloidosis is the only systemic amyloidosis that has been largely documented in a remarkable number of vertebrate species: mammals, birds, and fishes, especially in individuals with comorbidities, chronic stress, or held in captivity. Secondly, here, we summarise independent sets of evidence obtained on different animal species, exploring the possible transmissibility of AA amyloidosis especially in crowded or confined populations. Finally, biochemical and structural data on native SAA and on AA amyloid fibrils from human, murine, and cat ex vivo samples are discussed. The available structural data depict a complex scenario, where SAA can misfold forming highly different amyloid assemblies. This review highlights the complexity of AA amyloidosis, emphasising the need for further research into its spread in the animal kingdom, its structural aspects, and pathogenetic mechanisms to evaluate its impact on human and animal health. [ABSTRACT FROM AUTHOR]

A set S ⊆ V of vertices in a graph G = (V , E) is called a dominating set if every vertex in V − S is adjacent to a vertex in S. Hamid defined a dominating set which intersects every maximum independent set in G to be an independent transversal dominating set. The minimum cardinality of an independent transversal dominating set is called the independent transversal domination number of G and is denoted by γ it (G). In this paper we prove that for trees T , γ it (T) is bounded above by ⌈ n 2 ⌉ and characterize the extremal trees. Further, we characterize the class of all trees whose independent transversal domination number does not alter owing to the deletion of an edge. [ABSTRACT FROM AUTHOR]

• The current study focused on the prediction of 5-methylcytosine (m5C) sites in RNA sequence • A novel method of feature generation has been proposed by incorporating statistical moments for features reduction. • The LSTM model revealed the maximum accuracy score in independent set test and k-fold cross validation as well. • A webserver, m5c-iDeep, is freely available online for the enhancement of research in m5C sites detection. 5-Methylcytosine (m5c) is a modified cytosine base which is formed as the result of addition of methyl group added at position 5 of carbon. This modification is one of the most common PTM that used to occur in almost all types of RNA. The conventional laboratory methods do not provide quick reliable identification of m5c sites. However, the sequence data readiness has made it feasible to develop computationally intelligent models that optimize the identification process for accuracy and robustness. The present research focused on the development of in-silico methods built using deep learning models. The encoded data was then fed into deep learning models, which included gated recurrent unit (GRU), long short-term memory (LSTM), and bi-directional LSTM (Bi-LSTM). After that, the models were subjected to a rigorous evaluation process that included both independent set testing and 10-fold cross validation. The results revealed that LSTM-based model, m5c-iDeep, outperformed revealing 99.9 % accuracy while comparing with existing m5c predictors. In order to facilitate researchers, m5c-iDeep was also deployed on a web-based server which is accessible at https://taseersuleman-m5c-ideep-m5c-ideep.streamlit.app/. [ABSTRACT FROM AUTHOR]

The tree‐independence number tree‐α, first defined and studied by Dallard, Milanič, and Štorgel, is a variant of treewidth tailored to solving the maximum independent set problem. Over a series of papers, Abrishami et al. developed the so‐called central bag method to study induced obstructions to bounded treewidth. Among others, they showed that, in a certain superclass C of (even hole, diamond, pyramid)‐free graphs, treewidth is bounded by a function of the clique number. In this paper, we relax the bounded clique number assumption, and show that C has bounded tree‐α. Via existing results, this yields a polynomial‐time algorithm for the Maximum Weight Independent Set problem in this class. Our result also corroborates, for this class of graphs, a conjecture of Dallard, Milanič, and Štorgel that in a hereditary graph class, tree‐α is bounded if and only if the treewidth is bounded by a function of the clique number. [ABSTRACT FROM AUTHOR]

Parameterized complexity, introduced to efficiently solve NP‐hard problems for small values of a fixed parameter, has been recently used as a tool to speed up algorithms for tractable problems. Following this line of research, we design algorithms parameterized by neighborhood diversity (nd$$ \mathsf{nd} $$) for several graph theoretic problems in P$$ P $$: Maximumb$$ b $$‐Matching, Triangle Counting and Listing, Girth, Global Minimum Vertex Cut, and Perfect Graphs Recognition. Such problems are known to admit algorithms parameterized by modular‐width (mw$$ \mathsf{mw} $$) and consequently—as nd$$ \mathsf{nd} $$ is a special case of mw$$ \mathsf{mw} $$—by nd$$ \mathsf{nd} $$. However, the proposed novel algorithms allow for improving the computational complexity from time O(f(mw)·n+m)$$ O\left(f\left(\mathsf{mw}\right)\cdotp n+m\right) $$—where n$$ n $$ and m$$ m $$ denote, respectively, the number of vertices and edges in the input graph—to time O(g(nd)+n+m)$$ O\left(g\left(\mathsf{nd}\right)+n+m\right) $$ which is only additive in the size of the input. Then we consider some classical NP‐hard problems (Maximum independent set, Maximum clique, and Minimum dominating set) and show that for several classes of hereditary graphs, they admit linear time algorithms for sufficiently small—nonnecessarily constant—values of the neighborhood diversity parameter. [ABSTRACT FROM AUTHOR]

Architects' practice is characterized by a narrative of progressive unease about lack of autonomy coupled with a recent steer from professional figureheads towards the benefits of connected ways of working with other occupations, such as contractors and developers, rather than boundary protection. We explore this through a study of UK architects working on residential facilities for later life, involving semi-structured interviews with architects and ethnographic fieldwork of two building projects followed over time. We show that architects experience key stakeholders in their intersection on two axes: as 'virtual-embodied' and 'individual(s)-collective(s)'. Facility end-users (residents, staff) are encountered more commonly in virtual (abstract) than in embodied (tangible, visible) form, and as collectives rather than as individuals (as 'virtual collectives'). In juxtaposition, they tend to encounter clients (facility owners, developers), building contractors, and planners in embodied rather than virtual form and as individuals rather than as collectives (as 'embodied individuals'). We explore the consequences for architects' 'practice modalities', broadly defined as how something happens, is done, or is experienced. We show that 'embodied individuals' foster a practice modality of 'dependency and contingency' where stakeholders tend to have more sway, whereas 'virtual communities' enable a practice modality of 'autonomy and personal artistry'. However, 'embodied individuals' and 'virtual collectives' are mutually informing rather than independent sets of relationships; that is, they bear on each other during the architect's work, sometimes in challenging, even conflicting, ways. An analysis of how architects navigate this helps to understand how a build evolves as it does from architects' perspectives. [ABSTRACT FROM AUTHOR]

Objective: Explore stakeholder perspectives of the benefits of continuously training general practitioners in the same rural or remote practice in distributed locations via the Remote Vocational Training Scheme (RVTS). Design, setting, participants: Online one‐hour semi‐structured interviews were conducted with 27 RVTS staff, participants and supervisors from all states and territories between 16 October and 24 November 2023. Data were deductively and inductively coded by stakeholder type and the range of benefits, and the findings were informed by insights from a project reference group and a stakeholder advisory group. Questions explored the benefits of the RVTS — a program which supports doctors already working in rural, remote and First Nations communities to train towards general practice or rural generalist fellowship while remaining in the same practice. Main outcomes measures: Perspectives on the nature and spread of benefits. Results: Broad benefits were perceived to flow to four system‐level stakeholders: communities, health services, participants and policy makers. Perceived participant and community benefits were doctors staying longer in distributed locations with tailored place‐based supports and training, doctors building relationships with patients, and doctors learning through longitudinal care. Health service benefits included reduced reliance on locums, improved continuity of accessible and appropriate services in areas otherwise facing major recruitment and retention issues, and the doctors having more time to contribute to improving service quality and upskilling local staff. Policy‐maker benefits were sustaining safe and high quality services for distributed populations with high needs. Conclusion: The RVTS model was perceived to offer diverse benefits for different system stakeholders which could improve quality of learning, service delivery and community care. It also aligned with key policy directions for a distributed and sustainable generalist workforce under the goals of the National Medical Workforce Strategy 2021–2031 and the directions set by the independent review of overseas health practitioner regulatory settings led by Robyn Kruk. However, models like the RVTS largely rely on distribution levers to recruit more doctors to the locations it supports. [ABSTRACT FROM AUTHOR]

Copyright of Transportation Science & Technolgy is the property of Transportation Science & Technology Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

We introduce a general method for obtaining fixed-parameter algorithms for problems about finding paths in undirected graphs, where the length of the path could be unbounded in the parameter. The first application of our method is as follows. We give a randomized algorithm, that given a colored \(n\) -vertex undirected graph, vertices \(s\) and \(t\) , and an integer \(k\) , finds an \((s,t)\) -path containing at least \(k\) different colors in time \(2^{k}n^{\mathcal{O}(1)}\). This is the first FPT algorithm for this problem, and it generalizes the algorithm of Björklund, Husfeldt, and Taslaman on finding a path through \(k\) specified vertices. It also implies the first \(2^{k}n^{\mathcal{O}(1)}\) time algorithm for finding an \((s,t)\) -path of length at least \(k\). Our method yields FPT algorithms for even more general problems. For example, we consider the problem where the input consists of an \(n\) -vertex undirected graph \(G\) , a matroid \(M\) whose elements correspond to the vertices of \(G\) and which is represented over a finite field of order \(q\) , a positive integer weight function on the vertices of \(G\) , two sets of vertices \(S,T\subseteq V(G)\) , and integers \(p,k,w\) , and the task is to find \(p\) vertex-disjoint paths from \(S\) to \(T\) so that the union of the vertices of these paths contains an independent set of \(M\) of cardinality \(k\) and weight \(w\) , while minimizing the sum of the lengths of the paths. We give a \(2^{p+\mathcal{O}(k^{2}\log(q+k))}n^{\mathcal{O}(1)}w\) time randomized algorithm for this problem. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer Engineering & Applications is the property of Beijing Journal of Computer Engineering & Applications Journal Co Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Non-invasive crop analysis through image-based methods holds great promise for applications in plant research, yet accurate and robust trait inference from images remains a critical challenge. Our study investigates the potential of AI model ensembling and hybridization approaches to infer sorghum crop traits from RGB images generated via unmanned aerial vehicle (UAV). In our study, we cultivated 21 sorghum cultivars in two independent seasons (2021 and 2022) with a gradient of fertilizer and water inputs. We collected 470 ground-truth N measurements and captured corresponding RGB images with a drone-mounted camera. We computed five RGB vegetation indices, employed several ML models such as MLR, MLP, and various CNN architectures (season 2021), and compared their prediction accuracy for N-inference on the independent test set (season 2022). We assessed strategies that leveraged both deep and handcrafted features, namely hybridized and ensembled AI architectures. Our approach considered two different datasets collected during the two seasons (2021 and 2022), with the training set from the first season only. This allowed for testing of the models' robustness, particularly their sensitivity to concept drifts, in the independent season (2022), which is fundamental for practical agriculture applications. Our findings underscore the superiority of hybrid and ensembled AI algorithms in these experiments. The MLP + CNN-VGG16 combination achieved the best accuracy (R2 = 0.733, MAE = 0.264 N% on an independent dataset). This study emphasized that carefully crafted AI-based models applied to RGB images can achieve robust trait prediction with accuracies comparable to the similar phenotyping tasks using more complex (multi- and hyper-spectral) sensors presented in the current literature. [ABSTRACT FROM AUTHOR]

This article develops statistical inference methods for a class of set‐identified models, where the errors are known functions of observations and the parameters satisfy either serial or/and cross‐sectional independence conditions. This class of models includes the independent component analysis (ICA), Structural Vector Autoregressive (SVAR), and multi‐variate mixed causal–non‐causal models. We use the Generalized Covariance (GCov) estimator to compute the residual‐based portmanteau statistic for testing the error independence hypothesis. Next, we build the confidence sets for the identified sets of parameters by inverting the test statistic. We also discuss the choice (design) of these statistics. The approach is illustrated by simulations examining the under‐identification condition in an ICA model and an application to financial return series. [ABSTRACT FROM AUTHOR]

Herein, a novel UV spectrophotometric method coupled with chemometric tools was developed for the simultaneous determination of three fluoroquinolone antibiotics: ciprofloxacin, lomefloxacin, and enrofloxacin. Such integration of UV spectroscopy and chemometric analysis proved to be a simple, rapid, and cost-effective approach for the quantification of these clinically important pharmaceutical compounds and aid in their quality control analysis. The method employed firefly algorithm for variable selection and partial least squares (PLS) regression for model calibration. The developed method was validated by independent test set in addition the accuracy, intra and inter-day precision as per ICH guidelines which showed a satisfactory performance with mean recovery ranged between 98.18 and 101.83 with %RSD < 2. Besides, the developed method displayed ultrasensitive levels with LODs (0.0803, 0.1125, 0.1309 µg/mL) and LOQs (0.2434, 0.3409, 0.3968 µg/mL) for ciprofloxacin, lomefloxacin, and enrofloxacin, respectively. The greenness and blueness of the developed method were also evaluated using the recently proposed Analytical GREEnness metric approach (AGREE) and Blue applicability grade index (BAGI) tools, which showed a high AGREE score of 0.79 and a BAGI score of 77.5. These results indicate that the developed method provides an environmentally friendly alternative to the traditionally used chromatographic techniques, while maintaining high analytical practicability. Finally, the application of the developed methodology was demonstrated on real pharmaceutical and tap water samples, and the results were in good agreement with those obtained by the reference HPLC method indicating the reliability and suitability of the proposed spectrophotometric method for routine analysis of fluoroquinolone antibiotics. [ABSTRACT FROM AUTHOR]

A combinatorial approach is given to compute bases for eigenspaces of zero-divisor graphs of finite Boolean rings. A commutative monoid $ \mathcal {S} $ S of graphs is shown to contain a cyclic submonoid $ \mathcal {U} $ U that determines values of the entries of basis elements, while the members of its complement $ \mathcal {S}\setminus \mathcal {U} $ S ∖ U encode the supports of these elements. Furthermore, every member of $ \mathcal {S}\setminus \mathcal {U} $ S ∖ U is associated with a Catalan-triangle number, which counts the number of basis elements whose supports are determined by the given member. This is established by using a combinatorial interpretation of Catalan-triangle numbers to produce linearly independent sets of eigenvectors. [ABSTRACT FROM AUTHOR]

An equitable coloring of a graph G is a proper vertex coloring of G such that the sizes of any two color classes differ by at most one. In the paper, we pose a conjecture that offers a gap-one bound for the smallest number of colors needed to equitably color every block graph. In other words, the difference between the upper and the lower bounds of our conjecture is at most one. Thus, in some sense, the situation is similar to that of chromatic index, where we have the classical theorem of Vizing and the Andersen–Goldberg–Seymour conjecture for multigraphs. The results obtained in the paper support our conjecture. More precisely, we verify it in the class of block graphs in which each vertex belongs to a maximum independent set. We also show that the conjecture is true for block graphs which contain a vertex that does not lie in an independent set of size larger than two. Finally, we verify the conjecture for some symmetric-like block graphs. In order to derive our results we obtain structural characterizations of block graphs from these classes. [ABSTRACT FROM AUTHOR]

Given a digraph and a subset of vertices representing initial positions, we study the existence problem of infinitely long walks, one starting from each initial position, that never meet. We show that the subsets for which this is possible constitute the independent sets of a matroid. We prove that the independence oracle is polynomial-time. We also provide a more efficient algorithm to compute the size of a basis. Then we focus on the orientation problem of the undirected edges of a mixed graph to either maximize or minimize the rank of a subset. Some NP-hardness results and inapproximability results are proved in the general case. Polynomial-time algorithms are described for subsets of size 1. We also report several connections with other matroid classes. For example, we show that the class of no-meet matroids strictly contains transversal matroids while it is strictly contained inside gammoids. Some extensions and related applications are also discussed. [ABSTRACT FROM AUTHOR]

Assume there exists a function h : E (G) → [ 0 , 1 ] such that g (x) ≤ ∑ e ∈ E (G) , x ∋ e h (e) ≤ f (x) for every vertex x of G. The spanning subgraph of G induced by the set of edges { e ∈ E (G) : h (e) > 0 } is called a fractional (g , f) -factor of G with indicator function h. Let M and N be two disjoint sets of independent edges of G satisfying | M | = m and | N | = n. We say that G possesses a fractional (g , f) -factor with the property E (m , n) if G contains a fractional (g , f) -factor with indicator function h such that h (e) = 1 for each e ∈ M and h (e) = 0 for each e ∈ N. In this article, we discuss stability number and minimum degree conditions for graphs to possess fractional (g , f) -factors with the property E (1 , n). Furthermore, we explain that the stability number and minimum degree conditions declared in the main result are sharp. [ABSTRACT FROM AUTHOR]

Increasing the binding affinity of an antibody to its target antigen is a crucial task in antibody therapeutics development. This paper presents a pretrainable geometric graph neural network, GearBind, and explores its potential in in silico affinity maturation. Leveraging multi-relational graph construction, multi-level geometric message passing and contrastive pretraining on mass-scale, unlabeled protein structural data, GearBind outperforms previous state-of-the-art approaches on SKEMPI and an independent test set. A powerful ensemble model based on GearBind is then derived and used to successfully enhance the binding of two antibodies with distinct formats and target antigens. ELISA EC50 values of the designed antibody mutants are decreased by up to 17 fold, and KD values by up to 6.1 fold. These promising results underscore the utility of geometric deep learning and effective pretraining in macromolecule interaction modeling tasks. Increasing the binding affinity of an antibody to its target antigen is key for antibody therapeutics. Here the authors report a pretrainable geometric graph neural network, GearBind, and explore its potential in in silico antibody affinity maturation. [ABSTRACT FROM AUTHOR]

The closure principle is a powerful approach to constructing efficient testing procedures controlling the familywise error rate in the strong sense. For small numbers of hypotheses and the setting of independent elementary p -values we consider closed tests where each intersection hypothesis is tested with a p -value combination test. Examples of such combination tests are the Fisher combination test, the Stouffer test, the Omnibus test, the truncated test, or the Wilson test. Some of these tests, such as the Fisher combination, the Stouffer, or the Omnibus test, are not consonant and rejection of the global null hypothesis does not always lead to rejection of at least one elementary null hypothesis. We develop a general principle to uniformly improve closed tests based on p -value combination tests by modifying the rejection regions such that the new procedure becomes consonant. For the Fisher combination test and the Stouffer test, we show by simulations that this improvement can lead to a substantial increase in power. [ABSTRACT FROM AUTHOR]

In this work, an efficient and generally applicable scheme for the automatic generation of the minimal set of independent model reactions to be used for the calculation of enthalpies of formation is presented. A post‐processing procedure targeting the selection of the most suitable model reactions by assigning them larger weights is suggested. The developed computational protocol exploiting high‐level ab initio calculations and accurate reference enthalpies of formation retrieved from the Active Thermochemical Tables reproduces with chemical accuracy well‐established enthalpies of formation of 15 relatively small (C10–C24) polycyclic aromatic hydrocarbons (PAHs). A promising alternative single‐reaction strategy encompassing all reference species is outlined. Both methods are then applied to predict ΔfHm0${\Delta }_{\mathrm{f}}H_{\mathrm{m}}^0$ for the set of 43 larger (C32) PAHs, and revealed significant deviation (Mean Unsigned Error, MUE = 23.2 kJ mol−1) compared to the earlier theoretical results obtained from B3LYP calculations with subsequent group‐based empirical corrections. In the absence of the experimental data, these evaluations of ΔfHm0${\Delta }_{\mathrm{f}}H_{\mathrm{m}}^0$ are expected to be more realistic as the approach employed in this work demonstrated better performance on the benchmarking set of 15 smaller PAHs with the MUE of 1.3–1.5 versus 6.2 kJ mol−1. [ABSTRACT FROM AUTHOR]

In the design optimization of fiber-reinforced composites, spatial material discontinuity is considered intractable within the manufacturing reality imposed by advanced technologies. This paper presents a topological optimization framework based on truss-like material to design composite structures with continuous fiber. Specifically, the fiber morphology at the scattered design points, which controls the orientation and volume fraction, is taken as design variables. Using the Shepard interpolant scheme, the fiber morphology at any given computational point is interpolated by scattered design variables within a certain circular influence domain. The employed interpolation inherently ensures the spatial continuity and range-restricted of the physical field in an element-independent manner. Since separating the design variable field and analysis mesh on two independent sets of points, this method is well suited for using a sparse design variable field. The computational savings are compelling due to the reduced number of design variables without significantly restricting the design freedom. Numerical instability such as checkerboard and mesh dependencies vanished as no intermediate densities are suppressed in optimization. The continuous fiber-reinforced composites (CFRCs) in the form of truss-like continua are ready to be manufactured with the aid of a simple post-processing. Several numerical examples are investigated to demonstrate the feasibility and effectiveness of the proposed formulation and numerical techniques. [ABSTRACT FROM AUTHOR]

The subcellular localization of messenger RNA (mRNA) not only helps us to understand the localization regulation of gene expression but also helps to understand the relationship between RNA localization pattern and human disease mechanism, which has profound biological and medical significance. Several predictors have been proposed for predicting the subcellular localization of mRNA. However, there is still considerable room for improvement in their predictive performance, especially regarding multi-label prediction. This study proposes a novel multi-label predictor, DRpred, for mRNA subcellular localization prediction. This predictor first utilizes Bayesian networks to capture the dependencies among labels. Subsequently, it combines these dependencies with features extracted from mRNA sequences using Word2vec, forming the input for the predictor. Finally, it employs a neural network combining BiLSTM and an attention mechanism to capture the internal relationships of the input features for mRNA subcellular localization. The experimental validation on an independent test set demonstrated that DRpred obtained a competitive predictive performance in multi-label prediction and outperformed state-of-the-art predictors in predicting single subcellular localizations, obtaining accuracies of 82.14%, 93.02%, 80.37%, 94.00%, 90.58%, 84.53%, 82.01%, 79.71%, and 85.67% for the chromatin, cytoplasm, cytosol, exosome, membrane, nucleolus, nucleoplasm, nucleus, and ribosome, respectively. It is anticipated to offer profound insights for biological and medical research. [ABSTRACT FROM AUTHOR]

In this paper we consider the nonlocal theory for porous thermoelastic materials based on Mindlin's strain gradient theory with nonlocal dual-phase-lag law. This makes the derived equations more physically realistic, as they overcome the infinite propagation velocity property of the Fourier law. This approach consists of adding the second strain gradient and the second volume fraction gradient field to the set of independent constituent variables. We then obtain a system of three second order time equations with higher gradient terms. Using semigroup theory, we show the well-posedness of the one-dimensional problem. By an approach based on the Gearhart–Herbst–Prüss–Huang theorem, we prove that the associated semigroup is exponentially stable but not differentiable. The lack of analyticity and the impossibility to localize the solutions in time are direct consequences. [ABSTRACT FROM AUTHOR]

The internal ribosome entry site (IRES) is a cis -regulatory element that can initiate translation in a cap-independent manner. It is often related to cellular processes and many diseases. Thus, identifying the IRES is important for understanding its mechanism and finding potential therapeutic strategies for relevant diseases since identifying IRES elements by experimental method is time-consuming and laborious. Many bioinformatics tools have been developed to predict IRES, but all these tools are based on structure similarity or machine learning algorithms. Here, we introduced a deep learning model named DeepIRES for precisely identifying IRES elements in messenger RNA (mRNA) sequences. DeepIRES is a hybrid model incorporating dilated 1D convolutional neural network blocks, bidirectional gated recurrent units, and self-attention module. Tenfold cross-validation results suggest that DeepIRES can capture deeper relationships between sequence features and prediction results than other baseline models. Further comparison on independent test sets illustrates that DeepIRES has superior and robust prediction capability than other existing methods. Moreover, DeepIRES achieves high accuracy in predicting experimental validated IRESs that are collected in recent studies. With the application of a deep learning interpretable analysis, we discover some potential consensus motifs that are related to IRES activities. In summary, DeepIRES is a reliable tool for IRES prediction and gives insights into the mechanism of IRES elements. [ABSTRACT FROM AUTHOR]

As the complexity of machine learning (ML) models increases and their application in different (and critical) domains grows, there is a strong demand for more interpretable and trustworthy ML. A direct, model‐agnostic, way to interpret such models is to train surrogate models—such as rule sets and decision trees—that sufficiently approximate the original ones while being simpler and easier‐to‐explain. Yet, rule sets can become very lengthy, with many if–else statements, and decision tree depth grows rapidly when accurately emulating complex ML models. In such cases, both approaches can fail to meet their core goal—providing users with model interpretability. To tackle this, we propose DeforestVis, a visual analytics tool that offers summarization of the behaviour of complex ML models by providing surrogate decision stumps (one‐level decision trees) generated with the Adaptive Boosting (AdaBoost) technique. DeforestVis helps users to explore the complexity versus fidelity trade‐off by incrementally generating more stumps, creating attribute‐based explanations with weighted stumps to justify decision making, and analysing the impact of rule overriding on training instance allocation between one or more stumps. An independent test set allows users to monitor the effectiveness of manual rule changes and form hypotheses based on case‐by‐case analyses. We show the applicability and usefulness of DeforestVis with two use cases and expert interviews with data analysts and model developers. [ABSTRACT FROM AUTHOR]

This paper is concerned with a rate-type theory of thermoviscoelasticity in which the second gradient of the displacement and the second temperature gradient are added to the classical set of independent constitutive variables. Viscoelasticity and related phenomena are of great importance in the study of biological materials. An adequate modeling of rubber-like materials and of biological soft tissues requires the use of the theory of viscoelasticity. Introduction of the concept of thermal displacement and the theory of multipolar continua allows us to show that Green-Naghdi thermomechanics can be used to derive a second gradient theory. The basic equations of the theory are established and the boundary conditions associated to nonsimple materials are investigated. The stress tensor and hyperstress tensor are shown to depend on the first and second temperature gradients. For rigid heat conductors we find that the temperature satisfies a fourth order equation. The boundary-initial-value problems are formulated. A uniqueness result in the dynamic theory of thermoviscoelastic materials is presented. We establish an existence result and prove the analyticity of the solutions. As a consequence, the exponential decay of the solutions and their impossibility of localization are obtained. [ABSTRACT FROM AUTHOR]

Interval scheduling is a basic algorithmic problem and a classical task in combinatorial optimization. We develop techniques for partitioning and grouping jobs based on their starting/ending times, enabling us to view an instance of interval scheduling on many jobs as a union of multiple interval scheduling instances, each containing only a few jobs. Instantiating these techniques in a dynamic setting produces several new results. For (1 + ε) -approximation of job scheduling of n jobs on a single machine, we develop a fully dynamic algorithm with O (log n ε) update and O (log n) query worst-case time. Our techniques are also applicable in a setting where jobs have weights. We design a fully dynamic deterministic algorithm whose worst-case update and query times are poly (log n , 1 ε) . This is the first algorithm that maintains a (1 + ε) -approximation of the maximum independent set of a collection of weighted intervals in poly (log n , 1 ε) time updates/queries. This is an exponential improvement in 1 / ε over the running time of an algorithm of Henzinger, Neumann, and Wiese [SoCG, 2020]. Our approach also removes all dependence on the values of the jobs' starting/ending times and weights. [ABSTRACT FROM AUTHOR]

To investigate the utilization of an end-to-end multimodal convolutional model in the rapid and accurate diagnosis of pancreatic diseases using abdominal CT images. In this study, a novel lightweight label-free end-to-end multimodal network (eeMulNet) model was proposed for the rapid and precise diagnosis of abnormal pancreas. The eeMulNet consists of two steps: pancreatic region localization and multimodal CT diagnosis integrating textual and image data. A research dataset comprising 715 CT scans with various types of pancreas diseases and 228 CT scans from a control group was collected. The training set and independent test set for the multimodal classification network were randomly divided in an 8:2 ratio (755 for training and 188 for testing). The eeMulNet model demonstrated outstanding performance on an independent test set of 188 CT scans (Normal: 45, Abnormal: 143), with an area under the curve (AUC) of 1.0, accuracy of 100%, and sensitivity of 100%. The average testing duration per patient was 41.04 seconds, while the classification network took only 0.04 seconds. The proposed eeMulNet model offers a promising approach for the diagnosis of pancreatic diseases. It can support the identification of suspicious cases during daily radiology work and enhance the accuracy of pancreatic disease diagnosis. The codes and models of eeMulNet are publicly available at Rudeguy1/eeMulNet (github.com). • A label-free end-to-end multimodal network (eeMulNet) model were proposed. • On an independent test set of CT, the area under the curve was 1.0. • The classification network only took 0.04 seconds duration per patient. [ABSTRACT FROM AUTHOR]

We consider the stochastic matching model on a non-bipartite compatibility graph and analyze the impact of adding an edge to the expected number of items in the system. One may see adding an edge as increasing the flexibility of the system, for example, asking a family registering for social housing to list fewer requirements in order to be compatible with more housing units. Therefore, it may be natural to think that adding edges to the compatibility graph will lead to a decrease in the expected number of items in the system and the waiting time to be assigned. In our previous work, we proved this is not always true for the First Come First Matched discipline and provided sufficient conditions for the existence of the performance paradox: despite a new edge in the compatibility graph, the expected total number of items can increase. These sufficient conditions are related to the heavy-traffic assumptions in queueing systems. The intuition behind this is that the performance paradox occurs when the added edge in the compatibility graph disrupts the draining of a bottleneck. In this paper, we generalize this performance paradox result to a family of so-called greedy matching policies and explore the type of compatibility graphs where such a paradox occurs. Intuitively, a greedy matching policy never leaves compatible items unassigned, so the state space of the system consists of finite words of item classes that belong to an independent set of the compatibility graph. Some examples of greedy matching policies are First Come First Match, Match the Longest, Match the Shortest, Random, Priority. We prove several results about the existence of performance paradoxes for greedy disciplines for some family of graphs. More precisely, we prove several results about the lifting of the paradox from one graph to another one. For a certain family of graphs, we prove that there exists a paradox for the whole family of greedy policies. Most of these results are based on strong aggregation of Markov chains and graph theoretical properties. [ABSTRACT FROM AUTHOR]

• Presenting a computational predictor is comparable with sequence- and structure-based methods. • Proposing a computation predictor for prediction of protein-peptide interaction. • Combining dual DL-based pipeline, along with a combination predictor to detect protein-peptide binding regions. • Employing discriminative features using DL-based modules to improve classification performance. • Being comparable with both sequence-based and structure-based methods. • Using image-level transformation on evolutionary, structure-based, sequence-based, and physicochemical features of proteins. Protein-peptide interaction prediction is an important topic for several applications including various biological processes, understanding drug discovery, protein function abnormal cellular behaviors, and treating diseases. Over the years, studies have shown that experimental methods have improved the identification of this bio-molecular interaction. However, predicting protein-peptide interactions using these methods is laborious, time-consuming, dependent on third-party tools, and costly. To address these previous drawbacks, this study introduces a computational framework called DP-Site. The proposed framework concentrates on using a compound of a dual pipeline along with a combination predictor. A deep convolutional neural network for feature extraction and classification is embedded in pipeline 1. In addition, pipeline 2 includes a deep long-short-term memory - based and a random forest classifier for feature extraction and classification. In this investigation, the evolutionary, structure-based, sequence-based, and physicochemical information of proteins is utilized for identifying protein-peptide interaction at the residue level. The proposed method is evaluated on both the ten-fold cross-validation and independent test sets. The robust and consistent results between cross-validation and independent test sets confirm the ability of the proposed method to predict peptide binding residues in proteins. Moreover, experimental findings demonstrate that DP-Site has significantly outperformed other state-of-the-art sequence-based and structure-based methods. The proposed method achieves a remarkable balance between a specificity of 0.799 and a sensitivity of 0.770, along with the best f-measure of 0.661 and the highest precision of 0.580 using an independent test set. The outcome of various experiments confirms the proficiency of the proposed method and outperforms state-of-the-art sequence-based and structure-based methods in terms of the mentioned criteria. DP-Site can be accessed at https://github.com/shafiee 95/shima.shafiee.DP-Site. [ABSTRACT FROM AUTHOR]

For a set 풜 of connected graphs, an 풜-factor is a spanning subgraph of a graph, whose connected components are isomorphic to graphs from the set 풜. An 풜-factor is also referred as a component factor. A graph G is called an (풜, m)-factor deleted graph if for every E′⊆E(G) with |E′| = m, G−E′ admits an 풜-factor. A graph G is called an (풜, l)-factor critical graph if for every V′⊆V (G) with |V′| = l, G−V′ admits an 풜-factor. Let m, l and k be three positive integers with k ≥ 2, and write ℱ = {P2, C3, P5, 풯 (3)} and ℋ = {K1,1, K1,2,... , K1,k, 풯 (2k + 1)}, where 풯 (3) and 풯 (2k + 1) are two special families of trees. Inspired by finding a sufficient condition to check for the existence of path-factors with some special restraints, we focus on the sufficient conditions based on a graphic parameter called degree sum: σκ(G) = min⁡X⊆V(G) {Σx∈XdG(x):X is an independent set of k vertices}. σκ(G) = min⁡X⊆V(G) {Σx∈XdG(x):X is an independent set of k vertices}. σ κ (G) = min ⁡ X ⊆ V (G) { Σ x ∈ X d G (x) : X is an independent set of k vertices }. In this article, we verify that: (i) an (l + 2)-connected graph G of order n is an (ℱ, l)-factor critical graph if σ3(G) ≥ 6n+9l/5 σ3(G)≥6n+9l5 σ 3 (G) ≥ 6 n + 9 l 5 ; (ii) a (2m + 1)-connected graph G of order n is an (ℱ, m)-factor deleted graph if σm+2(G) ≥ 6/5n σm+2(G)≥65n σ m + 2 (G) ≥ 6 5 n ; (iii) an (l + 2)-connected graph G of order n is an (ℋ, l)-factor critical graph if σ2k+1(G) ≥ 6n+(6k+3)l/2k+3 σ2k+1(G)≥6n+(6k+3)l2k+3 σ 2 k + 1 (G) ≥ 6 n + (6 k + 3) l 2 k + 3 ; (iv) a (2m + 1)-connected graph G of order n is an (ℋ, m)-factor deleted graph if σm+2(G) ≥ 6n/2k+3 σm+2(G)≥6n2k+3 σ m + 2 (G) ≥ 6 n 2 k + 3 . [ABSTRACT FROM AUTHOR]

We propose a task-specific method for calculating cascaded phase diffractive optical elements (DOEs) for focusing Q incident beams with different wavelengths to Q given points. Due to the utilization of a special optimization criterion, the proposed method makes it possible to calculate the elements of the cascaded DOE in a sequential way. In addition, the calculation of the diffractive microrelief of each DOE in the cascade is reduced to solving a set of independent and computationally simple "pointwise" optimization problems. Using the proposed method, cascades of two DOEs were designed to focus radiation of 11 different wavelengths to 11 different points. The presented numerical simulation results demonstrate good performance of the method. The chosen operating wavelengths correspond to a set of widely used vegetation indices enabling monitoring the vegetation status conditions and tracking the environmental stresses. This makes the obtained results promising for the application in remote sensing and smart agriculture. [ABSTRACT FROM AUTHOR]

PIWI‐interacting RNAs (piRNAs) are a typical class of small non‐coding RNAs, which are essential for gene regulation, genome stability and so on. Accumulating studies have revealed that piRNAs have significant potential as biomarkers and therapeutic targets for a variety of diseases. However current computational methods face the challenge in effectively capturing piRNA‐disease associations (PDAs) from limited data. In this study, we propose a novel method, MRDPDA, for predicting PDAs based on limited data from multiple sources. Specifically, MRDPDA integrates a deep factorization machine (deepFM) model with regularizations derived from multiple yet limited datasets, utilizing separate Laplacians instead of a simple average similarity network. Moreover, a unified objective function to combine embedding loss about similarities is proposed to ensure that the embedding is suitable for the prediction task. In addition, a balanced benchmark dataset based on piRPheno is constructed and a deep autoencoder is applied for creating reliable negative set from the unlabeled dataset. Compared with three latest methods, MRDPDA achieves the best performance on the pirpheno dataset in terms of the five‐fold cross validation test and independent test set, and case studies further demonstrate the effectiveness of MRDPDA. [ABSTRACT FROM AUTHOR]

In the context of the matching-with-contracts model, we generalize the cumulative offer process to allow for arbitrary subsets of doctors to make proposals in each round. We show that, under a condition on the hospitals' choice functions, the outcome of this generalized cumulative offer process is independent of the sets of doctors making proposals in each round. The flexibility of the resulting model allows it to be used to describe different dynamic processes and their final outcomes. [ABSTRACT FROM AUTHOR]