Maximizing Happiness in Graphs of Bounded Clique-Width

Clique-width is one of the most important parameters that describes structural complexity of a graph. Probably, only treewidth is more studied graph width parameter. In this paper we study how clique-width influences the complexity of the Maximum Happy Vertices (MHV) and Maximum Happy Edges (MHE) problems. We answer a question of Choudhari and Reddy '18 about parameterization by the distance to threshold graphs by showing that MHE is NP-complete on threshold graphs. Hence, it is not even in XP when parameterized by clique-width, since threshold graphs have clique-width at most two. As a complement for this result we provide a $n^{\mathcal{O}(\ell \cdot \operatorname{cw})}$ algorithm for MHE, where $\ell$ is the number of colors and $\operatorname{cw}$ is the clique-width of the input graph. We also construct an FPT algorithm for MHV with running time $\mathcal{O}^*((\ell+1)^{\mathcal{O}(\operatorname{cw})})$, where $\ell$ is the number of colors in the input. Additionally, we show $\mathcal{O}(\ell n^2)$ algorithm for MHV on interval graphs.Comment: Accepted to LATIN 202

Тестирование гидрогеля p-HEMA в качестве имплантационного материала для замещения костно-хрящевых дефектов у животных

Objective: to evaluate the features of reparative chondrogenesis and osteogenesis in animal experiments with the implantation of porous poly(2-hydroxyethyl methacrylate) (pHEMA) hydrogel into osteochondral defects. Materials and methods. Cylindrical pHEMA implants (5 mm in diameter) were synthesized by radical polymerization. The implants were subjected to light microscopy and mechanical tests to characterize the structure and viscoelastic properties of the material. In experimental group #1, four pHEMA specimens were implanted into formed defects in the distal femoral epiphysis of rabbits. In experimental group #2, allogeneic chondrocytes were applied to the surface of four specimens before implantation. In the control series, four defects were not replaced with implants. Tissue regeneration was investigated by morphological and morphometric methods 30 days after operation. Results. The pHEMA implants were heterogeneous specimens with irregularly shaped pores – up to 30 × 10 μm at the surface and 300 × 120 μm inside. With >10% static compressive stress, the Young’s modulus was 54.7 kPa. For dynamic stress, increased frequency of compression-relaxation cycles from 0.01 Hz to 20.0 Hz led to increased storage modulus from 20 kPa to 38 kPa on average, and increased loss modulus from 2 kPa to 10 kPa. Indicators of semi-quantitative assessment of local inflammatory response to pHEMA implantation had the following values in points: pHEMA, 4.7 ± 0.3; pHEMA with allogeneic chondrocytes, 6.0 ± 1.0; control, 4.3 ± 0.3. The ratio of connective, bone, and cartilage tissues proper in the regenerates had the following respective values: pHEMA, 79%, 20%, 1%; pHEMA with chondrocytes, 82%, 16%, 2%; control, 9%, 74%, 17%. Conclusion. In a short-term experiment, pHEMA implants did not trigger a pronounced inflammatory response in the surrounding tissues and can be classified as biocompatible materials. However, the tested implants had low conductivity with respect to bone and cartilage cells, which can be improved by stabilizing the pore size and increasing the rigidity when synthesizing the material.Цель исследования. В экспериментах на животных оценить особенности репаративного хондрогенеза и остеогенеза при имплантации пористого поли-2-гидроксиэтилметакрилатного (p-HEMA) гидрогеля в костно-хрящевые дефекты. Материалы и методы. Имплантаты p-HEMA цилиндрической формы (5 мм в диаметре) были синтезированы методом радикальной полимеризации. Световая микроскопия и механические испытания имплантатов были применены для характеристики структуры и вязкоупругих свойств материала. В опытной серии № 1 четыре образца p-HEMA были имплантированы в сформированные дефекты дистальных эпиметафизов бедренных костей кроликов. В опытной серии № 2 перед имплантацией на поверхность четырех образцов были нанесены аллогенные хондроциты. В контрольной серии четыре дефекта не замещали имплантатами. Регенерация тканей была исследована морфологическим и морфометрическим методами через 30 дней после операции. Результаты. Имплантаты p-HEMA представляли собой неоднородные по структуре образцы с порами неправильной формы до 30 × 10 мкм у поверхности и до 300 × 120 мкм внутри. При статических компрессионных деформациях образцов более 10% модуль Юнга был равен 54,7 кПа. При динамических деформациях увеличение частоты циклов «сжатие–расслабление» от 0,01 до 20,0 Гц приводило к возрастанию модуля накопления в среднем с 20 до 38 кПа, а модуля потерь – с 2 до 10 кПа. Показатели полуколичественной оценки местной воспалительной реакции на имплантацию р-HEMA имели следующие значения в баллах: p-HEMA – 4,7 ± 0,3; p-HEMA с аллогенными хондроцитами – 6,0 ± 1,0; контроль – 4,3 ± 0,3. Соотношения собственно соединительной, костной и хрящевой тканей в составе регенератов имели следующие соответствующие значения: p-HEMA – 79, 20, 1%; p-HEMA с хондроцитами – 82, 16, 2%; контроль – 9, 74, 17%. Заключение. В краткосрочном эксперименте имплантаты p-HEMA не вызывали выраженной воспалительной реакции в прилежащих тканях и могут быть отнесены к биосовместимым материалам. Вместе с тем тестируемые имплантаты имели низкую кондуктивность для клеток костной и хрящевой тканей, которая может быть повышена за счет стабилизации размера пор и увеличения жесткости при синтезе материала

Post-traumatic pelvic deformity with old injuries of rectum and urogenital tract: 18-year follow-up

The authors described a case of management the severe combined pelvis trauma in female patient with 18 years follow-up. At the age of seven, the patient was injured: the open vertical unstable pelvis injury with severe damage of urogenital tract and rectum. Numerous operations on the pelvic organs without surgical treatment of pelvic ring fractures were accompanied by complications. At the age of 21 (14 years later) the patient was subjected to the surgery according to the techniques designed in the Chaklin Ural Scientific Research Institute of Traumatology and Orthopaedics: percutaneous osteotomy of posterior and anterior pelvis, external pelvis fixation using circular device with a further gradual (within 1.5 months) correction of the deformity with apparatus and subsequent internal fixation with screws. There were achieved partially elimination of shortening of the right lower limb, correction of the pelvic ring form, increasing the pelvic cavity volume, elimination of vaginal impingement, that allowed to correct urological problems with the possibility of further recovery of the vagina and hip replacement surgery. This case showed that the management of patients with complicated pelvis injuries required a multidisciplinary approach: emergency fixation of the unstable injuries and application of techniques to correct long-standing pelvis deformities to restore stability and shape of the pelvic ring, which created the more favorable conditions for reconstructive surgery of the pelvic organs