Spherical harmonics to quantify cranial asymmetry in deformational plagiocephaly

Cranial deformation and deformational plagiocephaly (DP) in particular affect an important percentage of infants. The assessment and diagnosis of the deformation are commonly carried by manual measurements that provide low interuser accuracy. Another approach is the use of three-dimensional (3D) models. Nevertheless, in most cases, deformation measurements are carried out manually on the 3D model. It is necessary to develop methodologies for the detection of DP that are automatic, accurate and take profit on the high quantity of information of the 3D models. Spherical harmonics are proposed as a new methodology to identify DP from head 3D models. The ideal fitted ellipsoid for each head is computed and the orthogonal distances between head and ellipsoid are obtained. Finally, the distances are modelled using spherical harmonics. Spherical harmonic coefficients of degree 2 and order − 2 are identified as the correct ones to represent the asymmetry characteristic of DP. The obtained coefficient is compared to other anthropometric deformation indexes, such as Asymmetry Index, Oblique Cranial Length Ratio, Posterior Asymmetry Index and Anterior Asymmetry Index. The coefficient of degree 2 and order − 2 with a maximum degree of 4 is found to provide better results than the commonly computed anthropometric indexes in the detection of DP.

Study on Power Grid Partition and Attack Strategies Based on Complex Networks

Based on the community discovery method in complex network theory, a power grid partition method considering generator nodes and network weightings is proposed. Firstly, the weighted network model of a power system is established, an improved Fast-Newman hierarchical algorithm and a weighted modular Q function index are introduced, and the partitioning algorithm process is practically improved combined with the characteristics of the actual power grid. Then, the partition results of several IEEE test systems with the improved algorithm and with the Fast-Newman algorithm are compared to demonstrate its effectiveness and correctness. Subsequently, on the basis of subnet partition, two kinds of network attack strategies are proposed. One is attacking the maximum degree node of each subnet, and the other is attacking the maximum betweenness node of each subnet. Meanwhile, considering the two traditional intentional attack strategies, that is, attacking the maximum degree nodes or attacking the maximum betweenness nodes of the whole network, the cascading fault survivability of different types of networks under four attack strategies is simulated and analyzed. It was found that the proposed two attack strategies based on subnet partition are better than the two traditional intentional attack strategies.

Integrative parameter of platelet aggregation in intensive care of COVID-19 patients

Objective. To conduct a comparative analysis of changes in platelet aggregation parameters in COVID-19 patients which are related to anticoagulant therapy and to determine the effectiveness of the integrative parameter of platelet aggregation.Materials and methods. 34 patients with confirmed COVID-19 (group 1) were included into the study. To compare the obtained results, healthy females were included into group 2 (n = 30). The following parameters of aggregation were determined: degree, time, rate and area of aggregation (until its maximum degree).Results. The area of aggregation is the best among all the parameters of platelet aggregation to diagnose COVID-19 in patients according to the Hosmer-Lemeshow test: with an ADP inducer — 0.3 μg/ml (Chi-square = 9.481, p = 0.303); ADP — 1.25 μg/ml (Chi square = 12.577, p = 0.127); ADP — 2.5 μg/ml (Chi-square = 6.226, p = 0.622); adrenaline — 2.5 μM (Chi-square = 7.367, p = 0.498); adrenaline — 5 μM (Chi-square = 6.824, p = 0.556).Conclusion. The area of aggregation is an informative integrative parameter that allows to quantify the degree of aggregation in the treatment of hypercoagulation syndrome in COVID-19 patients.

PREFERENTIAL ATTACHMENT WITH FITNESS DEPENDENT CHOICE

Исследуется асимптотическое поведение максимальной степени вершины в графе предпочтительного присоединения с выбором вершины, основанном как на ее степени, так и на дополнительном параметре (пригодности). Модели предпочтительного присоединения широко используются для моделирования сложных сетей (таких как нейронные сети и т.д.). Они строятся следующим образом. Мы начинаем с двух вершин и ребра между ними. Затем на каждом шаге мы рассматриваем выборку из уже существующих вершин, выбранных с вероятностями, пропорциональными их степеням плюс некоторый параметр β>- 1. Затем мы добавляем новую вершину и соединяем ее ребром с вершиной из выборки, на которой достигается максимум произведения ее степени на ее пригодность. Мы доказали, что в зависимости от параметров модели возможны три типа поведения максимальной степени вершины - сублинейное, линейное и порядка /ln , где n - число вершин в графе. We study the asymptotic behavior of the maximum degree in the preferential attachment tree model with a choice based on both the degree and fitness of a vertex. The preferential attachment models are natural models for complex networks (like neural networks, etc.) and constructed in the following recursive way. To each vertex is assigned a parameter that is called a fitness of a vertex. We start from two vertices and an edge between them. On each step, we consider a sample with repetition of d vertices, chosen with probabilities proportional to their degrees plus some parameter β>-1. Then we add a new vertex and draw an edge from it to the vertex from the sample with the highest product of fitness and degree. We prove that the maximum degree, dependent on parameters of the model, could exhibit three types of asymptotic behavior: sublinear, linear, and of /ln order, where n is the number of edges in the graph.

Fair allocation of conflicting items

We study fair allocation of indivisible items, where the items are furnished with a set of conflicts, and agents are not permitted to receive conflicting items. This kind of constraint captures, for example, participating in events that overlap in time, or taking on roles in the presence of conflicting interests. We demonstrate, both theoretically and experimentally, that fairness characterizations such as EF1, MMS and MNW still are applicable and useful under item conflicts. Among other existence, non-existence and computability results, we show that a $$1/\Delta $$ 1 / Δ -approximate MMS allocation for n agents may be found in polynomial time when $$n>\Delta >2$$ n > Δ > 2 , for any conflict graph with maximum degree $$\Delta$$ Δ , and that, if $$n > \Delta $$ n > Δ , a 1/3-approximate MMS allocation always exists.

Distributed computation and reconfiguration in actively dynamic networks

We study here systems of distributed entities that can actively modify their communication network. This gives rise to distributed algorithms that apart from communication can also exploit network reconfiguration to carry out a given task. Also, the distributed task itself may now require a global reconfiguration from a given initial network $$G_s$$ G s to a target network $$G_f$$ G f from a desirable family of networks. To formally capture costs associated with creating and maintaining connections, we define three edge-complexity measures: the total edge activations, the maximum activated edges per round, and the maximum activated degree of a node. We give (poly)log(n) time algorithms for the task of transforming any $$G_s$$ G s into a $$G_f$$ G f of diameter (poly)log(n), while minimizing the edge-complexity. Our main lower bound shows that $$\varOmega (n)$$ Ω ( n ) total edge activations and $$\varOmega (n/\log n)$$ Ω ( n / log n ) activations per round must be paid by any algorithm (even centralized) that achieves an optimum of $$\varTheta (\log n)$$ Θ ( log n ) rounds. We give three distributed algorithms for our general task. The first runs in $$O(\log n)$$ O ( log n ) time, with at most 2n active edges per round, a total of $$O(n\log n)$$ O ( n log n ) edge activations, a maximum degree $$n-1$$ n - 1 , and a target network of diameter 2. The second achieves bounded degree by paying an additional logarithmic factor in time and in total edge activations. It gives a target network of diameter $$O(\log n)$$ O ( log n ) and uses O(n) active edges per round. Our third algorithm shows that if we slightly increase the maximum degree to polylog(n) then we can achieve $$o(\log ^2 n)$$ o ( log 2 n ) running time.

A spanning bandwidth theorem in random graphs

The bandwidth theorem of Böttcher, Schacht and Taraz states that any n-vertex graph G with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)n$ contains all n-vertex k-colourable graphs H with bounded maximum degree and bandwidth o(n). Recently, a subset of the authors proved a random graph analogue of this statement: for $p\gg \big(\tfrac{\log n}{n}\big)^{1/\Delta}$ a.a.s. each spanning subgraph G of G(n,p) with minimum degree $\big(\tfrac{k-1}{k}+o(1)\big)pn$ contains all n-vertex k-colourable graphs H with maximum degree $\Delta$ , bandwidth o(n), and at least $C p^{-2}$ vertices not contained in any triangle. This restriction on vertices in triangles is necessary, but limiting. In this paper, we consider how it can be avoided. A special case of our main result is that, under the same conditions, if additionally all vertex neighbourhoods in G contain many copies of $K_\Delta$ then we can drop the restriction on H that $Cp^{-2}$ vertices should not be in triangles.