Viscoelastic Networks: Forming Cells and Tissues

Spatiotemporal changes in viscoelasticity are a key component of the morphogenesis of living systems. Experimental and theoretical findings suggest that cellular- and tissue-scale viscoelasticity can be understood as a collective property emerging from macromolecular and cellular interactions, respectively. Linking the changes in the structural or material properties of cells and tissues, such as material phase transitions, to the microscopic interactions of their constituents, is still a challenge both at the experimental and theoretical level. In this review, we summarize work on the viscoelastic nature of cytoskeletal, extracellular and cellular networks. We then conceptualize viscoelasticity as a network theory problem and discuss its applications in several biological contexts. We propose that the statistical mechanics of networks can be used in the future as a powerful framework to uncover quantitatively the biomechanical basis of viscoelasticity across scales.

Density of sets with missing differences and applications

For a given set M of positive integers, a well-known problem of Motzkin asks to determine the maximal asymptotic density of M-sets, denoted by μ(M), where an M-set is a set of non-negative integers in which no two elements differ by an element in M. In 1973, Cantor and Gordon find μ(M) for |M| ≤ 2. Partial results are known in the case |M| ≥ 3 including some results in the case when M is an infinite set. Motivated by some 3 and 4-element families already discussed by Liu and Zhu in 2004, we study μ(M) for two families namely, M = {a, b,a + b, n(a + b)} and M = {a, b, b − a, n(b − a)}. For both of these families, we find some exact values and some bounds on μ(M). This number theory problem is also related to various types of coloring problems of the distance graphs generated by M. So, as an application, we also study these coloring parameters associated with these families.

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a k-clique covering vertex set for Maximum Clique Problems.

The Maximum clique problem (MCP) is graph theory problem that demand complete subgraf with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm, in this paper we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarenteed finnding maximum clique.

Alternative Branching Strategies in the Branch and Bound Algorithm by Using a K-Clique Covering Vertex Set for Maximum Clique Problems

The maximum clique problem (MCP) is graph theory problem that demand complete subgraph with maximum cardinality (maximum clique) in arbitrary graph. Solving MCP usually use Branch and Bound (BnB) algorithm. In this paper, we will show how n + 1 color classes (where n is the difference between upper and lower bound) selected to form k-clique covering vertex set which later used for branching strategy can guarantee finding maximum clique.

Divisions by Two in Collatz Sequences: A Data Science Approach

The Collatz conjecture is an unsolved number theory problem. We approach the question by examining the divisions by two that are performed within Collatz sequences. Aside from classical mathematical methods, we use techniques of data science. Based on the analysis of 10,000 sequences we show that the number of divisions by two lies within clear boundaries. Building on the results, we develop and prove an equation to calculate the maximum possible number of divisions by two for any given a Collatz sequence. Whenever this maximum is reached, a sequence leads to the result one, as conjectured by Lothar Collatz. Furthermore, we show how many divisions by two are required for a cycle of a specific length. The findings are valuable for further investigations and could form the basis for a comprehensive proof of the conjecture.

TINGKAT KESESUAIAN SOAL TEORI UJI KOMPETENSI KEAHLIAN TEKNIK GAMBAR BANGUNAN DENGAN STANDAR KOMPETENSI NASIONAL BIDANG GAMBAR BANGUNAN

ABSTRACT Phenomena that show the competence of building drawings that are needed in the world of work but have not been studied in schools are the basis of research. It is necessary to measure the level of compatability between the materials being studied with the competencies required by the world of work. The purpose of this study was to determine the suitability level of the content of the skills competency test (UKK) based on the National Competency Standars in the Building Drawing Field. The research method used is comparative descriptive. The subject of this research is the matter of the theory of UKK Building Drawing Engineering. Data were analyzed by comparing the level of competency suitability implemented in the UKK theory problem with the National Competency Standards in Building Drawing Field. The results of the study showed that in the implementation of the UKK Building Drawing Tecnique in theory there were 37 competencies tested. Total competencies at the level of young photographers for vocational graduates are 55 competencies. There are 18 competencies that have not been tested on UKK, so there needs to be an adjustment so that the UKK content goes hand in hand with the work competencies required for building drawing skills. Keywords: expertise competency test, building drawing ABSTRAK Fenomena menunjukkan adanya kompetensi gambar bangunan yang diperlukan di dunia kerja tetapi belum dipelajari di Sekolah menjadi dasar dalam pengkajian. Perlu adanya pengukuran tingkat kesesuaian antara materi yang dipelajari dengan kompetensi yang disyaratkan dunia kerja. Tujuan dari pengkajian ini adalah mengetahui tingkat kesesuaian antara konten soal Uji Kompetensi Keahlian (UKK) mengacu pada Standar Kompetensi Nasional Bidang Gambar Bangunan. Metode pengkajian yang digunakan adalah deskriptif komparatif. Subjek pada pengkajian ini adalah soal teori UKK Teknik Gambar Bangunan. Data dianalisis dengan membandingkan antara tingkat kesesuaian kompetensi yang dilaksanakan dalam soal teori UKK dengan Standar Kompetensi Nasional Bidang Gambar Bangunan. Hasil pengkajian menunjukkan dalam pelaksanaan UKK Teknik Gambar Bangunan secara teori terdapat 37 kompetensi yang diujikan. Total kompetensi pada level juru gambar muda untuk lulus SMK adalah 55 kompetensi. Terdapat 18 kompetensi yang belum diujikan pada UKK, sehingga perlu adanya penyesuaian agar konten UKK beriringan dengan kompetensi kerja yang disyaratkan pada keahlian gambar bangunan.Kata Kunci: Uji Kompetensi Keahlian, gambar bangunan