Dimensional Complexity and Algorithmic Efficiency

This paper uses the concept of algorithmic efficiency to present a unified theory of intelligence. Intelligence is defined informally, formally, and computationally. We introduce the concept of dimensional complexity in algorithmic efficiency and deduce that an optimally efficient algorithm has zero time complexity, zero space complexity, and an infinite dimensional complexity. This algorithm is used to generate the number line.

Enhanced effect of dimension of receptor-ligand complex and depletion effect on receptor-mediated endocytosis of nanoparticles

We present an extended analytical model including the depletion effect and the dimension of ligand-receptor complex, aiming to elucidate their influences on endocytosis of spherocylindrical nanoparticles （NPs）. It is found that the dimension of ligand-receptor complex （δ） and the depletion effect interrelatedly govern the optimal conditions of NP endocytosis. The endocytosis phase diagram constructed in the space of NP radius and relative aspect ratio indicates that the endocytosis of NP is enhanced evidently by reducing the optimal radius and the threshold radius of endocytosed NP. Meanwhile, through thermodynamic and kinetic analysis of the diffusion of receptors, the dependence of diffusion length on depletion effect and the dimension of ligand-receptor complex can be identified in great detail. For small aspect ratio, diffusion length decreases with increasing concentration c of small bioparticles in cellular environment. Endocytosis speed corresponding to large radius R and high concentration c of small bioparticles strongly depends on the increasing （2r-δ）. These results may show some highlights into the conscious design of NPs for diagnostic agents and therapeutic drug delivery applications.

Synthesis and Crystal Structure of a Mixed Cu - Cd Bim etallic Com plex ｛〔 Cu Cd(pba)( H_2 O)_3〕·2 H_2 O｝ _n

A one dimensional bimetallic compound ｛〔CuCd(pba)(H 2O) 3〕·2H 2O｝ n in which pba was propylenebis (oxamic acid), was prepared. Crystal structure of the title compound was determined. It belongs to orthorhombic system, molecular formula CuCdC 7H 16 N 2O 11 , M r =480.17, space group Pnma(#62), a=12.953(2), b=21 626(6), c=5.253(3), V=1471(2) 3 and D x =2.17g/cm 3 for Z =4. The structure was solved by direct methods with final R =0.052 and R w =0.063 for 1055 observed reflections with I>3σ(I ). Two nitrogen atoms and two oxygen atoms from the oxamide and a water molecule coordinated to the Cu II ion forming a square pyramidal geometry. Four oxygen atoms from the oxamide and two water molecules coordinated to the Cd II ion forming an elongated octahedral geometry.

Mathematical theory of signal analysis vs. complex analysis method of harmonic analysis

We present recent work of harmonic and signal analysis based on the complex Hardy space approach.

Dimensions of receptor-ligand complex and the optimal radius of endocytosed virus-like particle

Recent experiments have pointed out that cellular uptake is strongly dependent on the physical dimensions of endocytosed nanoparticles and tile optimal radius of endocytosed virus-like particle coated by transferrin is around 50 nm. As the same time, the dimensions of receptor-ligand complex have strong effects on the size-dependent exclusion of proteins ill cell environments. Inspired by these experimental results, a continuum elastic model is constructed to resolve the relationship between the dinlensions of receptor-ligand complex and the optimal radius of endocytosed virus-like particle. These results demonstrate that the optimal radius of endocytosed virus-like particle depends on the dimensions of reeeptor-ligand complex and the dimension of receptor-ligand complex reduces the depletion zone.

Optimal aspect ratio of endocytosed spherocylindrical nanoparticle

Recent simulations have demonstrated that bioparticle size and shape modulate the process of endocytosis, and studies have provided more quantitative information that the endocytosis efficiency of spherocylindrical bioparticles is decided by its aspect ratio. At the same time, the dimensions of the receptor-ligand complex have strong effects on the size-dependent exclusion of proteins within the cellular environment. However, these earlier theoretical works including simulations did not consider the effects of ligand-receptor complex dimension on the endocytosis process. Thus, it is necessary to resolve the effects of ligand-receptor complex dimension and determine the optimal aspect ratio of spherocylindrical bioparticles in the process of endocytosis. Accordingly, we proposed a continuum elastic model, of which the results indicate that the aspect ratio depends on the ligand-receptor complex dimension and the radius of the spherocylindrical bioparticle. This model provides a phase diagram of the aspect ratio of endocytosed spherocylindrical bioparticles, the larger aspect ratio of which appears in the phase diagram with increasing ligand density, and highlights the bioparticle design.

Synthesis and Structure of a Novel Copper(II) Dinuclear Complex with 4,4′-Dipyridyl as the Bridge

With N,N′ bis(benzimidazol 2 yl methyl)amine as the ligand, a novel Cu(II) dinuclear complex was synthesized as a mimetic compound of superoxide dismutase (SOD). The complex was characterized with element analysis, UV and IR spectra. The crystal structure was determined by using X ray diffraction analysis. The crystal structure shows that Cu(II) and its coordinated atoms construct distorted octahedron configuration with oxygen atoms of (ClO - 4) s in the axial directions. The coordinated cations are linked by (ClO - 4) s to form nonplanar sheets. All sheets are linked together into three dimensional network by the intermolecular hydrogen bonds. The result of the activity assay indicates that the complex does have certain biological activity.