Algorithms and complexity for path covers of temporal DAGs

A path cover of a digraph is a collection of paths collectively containing its vertex set. A path cover with minimum cardinality for a directed acyclic graph can be found in polynomial time [Fulkerson, AMS’56; Cáceres et al., SODA’22]. Moreover, Dilworth’s celebrated theorem on chain coverings of partially ordered sets equivalently states that the minimum size of a path cover of a DAG is equal to the maximum size of a set of mutually unreachable vertices. In this paper, we examine how far these classic results can be extended to a dynamic setting. A temporal digraph has an arc set that changes over discrete time-steps; if the underlying digraph is acyclic, then it is a temporal DAG. A temporal path is a directed path in the underlying digraph, such that the time-steps of arcs are strictly increasing along the path. Two temporal paths are temporally disjoint if they do not occupy any vertex at the same time. A temporal path cover is a collection C of temporal paths that covers all vertices, and C is temporally disjoint if all its temporal paths are pairwise temporally disjoint. We study the computational complexities of the problems of finding a minimum-size temporal (disjoint) path cover (denoted as Temporal Path Cover and Temporally Disjoint Path Cover). On the negative side, we show that both Temporal Path Cover and Temporally Disjoint Path Cover are NP-hard even when the underlying DAG is planar, bipartite, subcubic, and there are only two arc-disjoint time-steps. Moreover, Temporally Disjoint Path Cover remains NP-hard even on temporal oriented trees. We also observe that natural temporal analogues of Dilworth’s theorem on these classes of temporal DAGs do not hold. In contrast, we show that Temporal Path Cover is polynomial-time solvable on temporal oriented trees by a reduction to Clique Cover for (static undirected) weakly chordal graphs (a subclass of perfect graphs for which Clique Cover admits an efficient algorithm). This highlights an interesting algorithmic difference between the two problems. Although it is NP-hard on temporal oriented trees, Temporally Disjoint Path Cover becomes polynomial-time solvable on temporal oriented lines and temporal rooted directed trees. Motivated by the hardness result on trees, we show that, in contrast, Temporal Path Cover admits an XP time algorithm with respect to parameter tmax + tw, where tmax is the maximum time-step and tw is the treewidth of the underlying static undirected graph; moreover, Temporally Disjoint Path Cover admits an FPT algorithm with respect to the same parameterization

Non-interpenetrated metal-organic frameworks based on copper(II) paddlewheel and oligoparaxylene-isophthalate linkers: synthesis, structure and gas adsorption

Two metal–organic framework materials, MFM-130 and MFM-131 (MFM = Manchester Framework Material), have been synthesized using two oligoparaxylene (OPX) tetracarboxylate linkers containing four and five aromatic rings, respectively. Both fof-type non-interpenetrated networks contain Kagomé lattice layers comprising [Cu2(COO)4] paddlewheel units and isophthalates, which are pillared by the OPX linkers. Desolvated MFM-130, MFM-130a, shows permanent porosity (BET surface area of 2173 m2/g, pore volume of 1.0 cm3/g), high H2 storage capacity at 77 K (5.3 wt% at 20 bar and 2.2 wt% at 1 bar), and a higher CH4 adsorption uptake (163 cm3(STP)/cm3 (35 bar and 298 K)) compared with its structural analogue, NOTT-103. MFM-130a also shows impressive selective adsorption of C2H2, C2H4, and C2H6 over CH4 at room temperature, indicating its potential for separation of C2 hydrocarbons from CH4. The single-crystal structure of MFM-131 confirms that the methyl substituents of the paraxylene units block the windows in the Kagomé lattice layer of the framework, effectively inhibiting network interpenetration in MFM-131. This situation is to be contrasted with that of the doubly interpenetrated oligophenylene analogue, NOTT-104. Calculation of the mechanical properties of these two MOFs confirms and explains the instability of MFM-131 upon desolvation in contrast to the behavior of MFM-130. The incorporation of paraxylene units, therefore, provides an efficient method for preventing network interpenetration as well as accessing new functional materials with modified and selective sorption properties for gas substrates

Pharmacokinetic-pharmacodynamic correlation of imipenem in pediatric burn patients using a bioanalytical liquid chromatographic method

A bioanalytical method was developed and applied to quantify the free imipenem concentrations for pharmacokinetics and PK/PD correlation studies of the dose adjustments required to maintain antimicrobial effectiveness in pediatric burn patients. A reverse-phase Supelcosil LC18 column (250 x 4.6 mm 5 micra), binary mobile phase consisting of 0.01 M, pH 7.0 phosphate buffer and acetonitrile (99:1, v/v), flow rate of 0.8 mL/min, was applied. The method showed good absolute recovery (above 90%), good linearity (0.25-100.0 µg/mL, r2=0.999), good sensitivity (LLOQ: 0.25 µg/mL; LLOD: 0.12 µg/mL) and acceptable stability. Inter/intraday precision values were 7.3/5.9%, and mean accuracy was 92.9%. A bioanalytical method was applied to quantify free drug concentrations in children with burns. Six pediatric burn patients (median 7.0 years old, 27.5 kg), normal renal function, and 33% total burn surface area were prospectively investigated; inhalation injuries were present in 4/6 (67%) of the patients. Plasma monitoring and PK assessments were performed using a serial blood sample collection for each set, totaling 10 sets. The PK/PD target attained (40%T>MIC) for each minimum inhibitory concentration (MIC: 0.5, 1.0, 2.0, 4.0 mg/L) occurred at a percentage higher than 80% of the sets investigated and 100% after dose adjustment. In conclusion, the purification of plasma samples using an ultrafiltration technique followed by quantification of imipenem plasma measurements using the LC method is quite simple, useful, and requires small volumes for blood sampling. In addition, a small amount of plasma (0.25 mL) is needed to guarantee drug effectiveness in pediatric burn patients. There is also a low risk of neurotoxicity, which is important because pharmacokinetics are unpredictable in these critical patients with severe hospital infection. Finally, the PK/PD target was attained for imipenem in the control of sepsis in pediatric patients with burns.</p

Contribution to the understanding of tribological properties of graphite intercalation compounds with metal chloride

Intrinsic tribological properties of lamellar compounds are usually attributed to the presence of van der Waals gaps in their structure through which interlayer interactions are weak. The controlled variation of the distances and interactions between graphene layers by intercalation of electrophilic species in graphite is used in order to explore more deeply the friction reduction properties of low-dimensional compounds. Three graphite intercalation compounds with antimony pentachloride, iron trichloride and aluminium trichloride are studied. Their tribological properties are correlated to their structural parameters, and the interlayer interactions are deduced from ab initio bands structure calculations

Differences in Nevirapine Biotransformation as a Factor for its Sex-Dependent Dimorphic Profile of Adverse Drug Reactions

OBJECTIVES: Nevirapine is widely used for the treatment of HIV-1 infection; however, its chronic use has been associated with severe liver and skin toxicity. Women are at increased risk for these toxic events, but the reasons for the sex-related differences are unclear. Disparities in the biotransformation of nevirapine and the generation of toxic metabolites between men and women might be the underlying cause. The present work aimed to explore sex differences in nevirapine biotransformation as a potential factor in nevirapine-induced toxicity. METHODS: All included subjects were adults who had been receiving 400 mg of nevirapine once daily for at least 1 month. Blood samples were collected and the levels of nevirapine and its phase I metabolites were quantified by HPLC. Anthropometric and clinical data, and nevirapine metabolite profiles, were assessed for sex-related differences. RESULTS: A total of 52 patients were included (63% were men). Body weight was lower in women (P = 0.028) and female sex was associated with higher alkaline phosphatase (P = 0.036) and lactate dehydrogenase (P = 0.037) levels. The plasma concentrations of nevirapine (P = 0.030) and the metabolite 3-hydroxy-nevirapine (P = 0.035), as well as the proportions of the metabolites 12-hydroxy-nevirapine (P = 0.037) and 3-hydroxy-nevirapine (P = 0.001), were higher in women, when adjusted for body weight. CONCLUSIONS: There was a sex-dependent variation in nevirapine biotransformation, particularly in the generation of the 12-hydroxy-nevirapine and 3-hydroxy-nevirapine metabolites. These data are consistent with the sex-dependent formation of toxic reactive metabolites, which may contribute to the sex-dependent dimorphic profile of nevirapine toxicity

A reference high-pressure CH₄ adsorption isotherm for zeolite Y: results of an interlaboratory study

This paper reports the results of an international interlaboratory study led by the National Institute of Standards and Technology (NIST) on the measurement of high-pressure surface excess methane adsorption isotherms on NIST Reference Material RM 8850 (Zeolite Y), at 25 °C up to 7.5 MPa. Twenty laboratories participated in the study and contributed over one-hundred adsorption isotherms of methane on Zeolite Y. From these data, an empirical reference equation was determined, along with a 95% uncertainty interval (Uk=2). By requiring participants to replicate a high-pressure reference isotherm for carbon dioxide adsorption on NIST Reference Material RM 8852 (ZSM-5), this interlaboratory study also demonstrated the usefulness of reference isotherms in evaluating the performance of high-pressure adsorption experiments

Développement et enjeux de l’action du « 25 » à Marcinelle

Le quartier du « 25 » est situé dans la banlieue de Charleroi, au coeur d’une région en voie de restructuration économique. Ce quartier est, depuis plusieurs années l’objet de plans de rénovation qui tiennent peu compte des habitants, en majorité immigrés, et de l’environnement, témoin d’un riche passé industriel et social.L’association du « 25 », constituée en 1978, se veut le porte-parole de ces intérêts sociaux et culturels. Elle cherche à permettre aux habitants de prendre leur place dans le quartier, d’y réaliser progressivement ce qu’ils veulent, si nécessaire avec l’aide de personnes extérieures en évitant au maximum que ces intervenants ne supplantent la demande des intéressés.Le « petit coin du 25 », maison de quartier en voie d’aménagement, apparaît actuellement comme la cheville ouvrière du projet de l’association : partir des demandes individuelles, souvent très concrètes et ponctuelles, des habitants (problèmes de plomberie, d’électricité de leur habitation mais aussi soucis quant à la scolarité et aux loisirs des enfants), en essayant d’insérer ces demandes dans un projet collectif.Neighbourhood "25" is located in the suburbs of Charleroi in the heart of a region that is in the throes of severe economic difficulty. This neighbourhood has been threatened now for several years by vast urban renewal projects which take little account of the interests of the residents who are mostly immigrant workers and even less of the rich social and industrial history of the area.The "25" committee, founded in 1978, defends the social and cultural objectives of the residents. It seeks to make the voice of the people more powerful and effective. Technical resource people from the outside are occasionaly called in but every effort is made to ensure that they de not deviate the committee from its fundamental objectives.A Neighbourhood Association Center is a key factor in the success of the committee. The individual needs of various residents (which range from plumbing and electricity repairs to educational and recreational facilities) are dealt with in a manner that seeks to reinforce a positive collective identity.El barrio "del 25" está situado en la periferia de Charleroi, en una región en plena reestructuración económica. Este barrio es, desde hace algunos años, el objecto de planes de renovación que toman poco en cuenta los habitantes, en su mayoría inmigrantes, y el medio ambiente, testigo de un rico pasado industrial y social.La asociación "del 25", creada en 1978, quiere ser el portavoz de estos intereses sociales y culturales. Ella busca el permitir a los habitantes de ocupar el lugar que merecen en el barrio, de realizar en él lo que quieren, con la ayuda de personas exteriores en casos de necesidad, pero evitando al máximo que estos intervinientes suplanten la demanda de los interesados."El ricóncito del 25", es una casa del barrio envías de habilitación, es la base obrera del proyecto de la asociación: a partir de pedidos individuales, muchas veces concretos y puntuales, de los habitantes (problemas de plomería, de electricidad, y también de las escuelas y los esparcimientos de los niños), ensayar de insertarlas en un proyecto colectivo

LEAP: a Manual for Learning Evaluation and Planning in Community Development

This manual is designed to assist in the planning and evaluation of practice in a participatory manner. This is a detailed exploration of the LEAP model. Shorter introductory explanations are available in ' LEAP - step by step' and in the online learning tool. These may be particularly useful for those coming to LEAP for the first time