Inertia groups of (n−1)(n-1)-connected 2n2n-manifolds

In this paper, we compute the inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds where $n \geq 3$. As a consequence, we complete the diffeomorphism classification of such manifolds, finishing a program initiated by Wall sixty years ago, with the exception of the $126$-dimensional case of the Kervaire invariant one problem. In particular, we find that the inertia group always vanishes for $n \neq 4,8,9$ -- for $n \gg 0$, this was known by the work of several previous authors, including Wall, Stolz, and Burklund and Hahn with the first named author. When $n = 4,8,9$, we apply Kreck's modified surgery and a special case of Crowley's $Q$-form conjecture, proven by Nagy, to compute the inertia groups of these manifolds. In the cases $n=4,8$, our results recover unpublished work of Crowley--Nagy and Crowley--Olbermann. In contrast, we show that the the homotopy and concordance inertia groups of $(n-1)$-connected, smooth, closed, oriented $2n$-manifolds with $n \geq 3$ always vanish.Comment: 33 pages; comments welcome

Systemic similarity analysis of compatibility drug-induced multiple pathway patterns _in vivo_

A major challenge in post-genomic research is to understand how physiological and pathological phenotypes arise from the networks of expressed genes and to develop powerful tools for translating the information exchanged between gene and the organ system networks. Although different expression modules may contribute independently to different phenotypes, it is difficult to interpret microarray experimental results at the level of single gene associations. The global effects and response pathways of small molecules in cells have been investigated, but the quantitative details of the activation mechanisms of multiple pathways _in vivo_ are not well understood. Similar response networks indicate similar modes of action, and gene networks may appear to be similar despite differences in the behaviour of individual gene groups. Here we establish the method for assessing global effect spectra of the complex signaling forms using Global Similarity Index (GSI) in cosines vector included angle. Our approach provides quantitative multidimensional measures of genes expression profile based on drug-dependent phenotypic alteration _in vivo_. These results make a starting point for identifying relationships between GSI at the molecular level and a step toward phenotypic outcomes at a system level to predict action of unknown compounds and any combination therapy

Numerical study of hydraulic fracturing fracture area changing rules in underground coal mine

To investigate the relationship between the fractured area created by hydraulic fracturing and various fracturing parameters of underground coal mines, we applied fracture and porous media fluid-solid coupling theory to establish a numerical model of hydraulic fracturing. Three-dimensional numerical simulation of hydraulic fracturing of K1 coal seam in a coalmine was performed using the proposed numerical model. We examined the relations between the fractured area and the injection volume, injection rate, and viscosity of the fracturing fluid. The results showed that the fractured area increased with increasing injection rate, however, the extension rate slowed down; the fractured area initially increased then decreased with increasing viscosity; the fractured area increases rapidly with the increase of the water injection volume at the beginning, then begin to slow, eventually approximate linear growth

Experimental study on characteristics of self-excited oscillation pulsed water jet

To promote the application of self-excited oscillation pulsed water jet in various fields, various characteristics of self-excited oscillation pulsed water jet were studied experimentally. A test system of self-excited oscillation pulsed water jet characteristics was designed, and it is composed of pulsed jet producer devices, particle image velocity (PIV) measuring system, pressure pulse test device and the confining pressure cavity suitable for a PIV test. The characteristics of flow field, pressure oscillation, pulsed cavitation and acoustic shock of pulsed jet were researched. The results showed that the axis velocity vector at nozzle outlet changes periodically, and gradually becomes smaller away from the nozzle. The peak pressure of self-excited oscillation pulsed water jet is 2.5 times higher than the common continuous jet. The wave crest and the wave trough of pulsed jet are not completely symmetric. As the pump pressure increases, the length of bubble cloud increases, and it first increases and then decreases with confining pressure increasing. The vibration acceleration of sonic boom increases and then decreases as pump pressure increases, and decreases steadily with confining pressure increasing

High-dimensional quantum key distribution based on mutually partially unbiased bases

We propose a practical high-dimensional quantum key distribution protocol based on mutually partially unbiased bases utilizing transverse modes of light. In contrast to conventional protocols using mutually unbiased bases, our protocol uses Laguerre-Gaussian and Hermite-Gaussian modes of the same mode order as two mutually partially unbiased bases for encoding, which leads to a scheme free from mode-dependent diffraction in long-distance channels. Since only linear and passive optical elements are needed, our experimental implementation significantly simplifies qudit generation and state measurement. Since this protocol differs from conventional protocols using mutually unbiased bases, we provide a security analysis of our protocol