The accumulation of various types of drug informatics data and computational approaches for drug repositioning can accelerate pharmaceutical research and development.However,the integration of multi-dimensional drug d...The accumulation of various types of drug informatics data and computational approaches for drug repositioning can accelerate pharmaceutical research and development.However,the integration of multi-dimensional drug data for precision repositioning remains a pressing challenge.Here,we propose a systematic framework named PIMD to predict drug therapeutic properties by integrating multi-dimensional data for drug repositioning.In PIMD,drug similarity networks(DSNs)based on chemical,pharmacological,and clinical data are fused into an integrated DSN(iDSN)composed of many clusters.Rather than simple fusion,PIMD offers a systematic way to annotate clusters.Unexpected drugs within clusters and drug pairs with a high iDSN similarity score are therefore identified to predict novel therapeutic uses.PIMD provides new insights into the universality,individuality,and complementarity of different drug properties by evaluating the contribution of each property data.To test the performance of PIMD,we use chemical,pharmacological,and clinical properties to generate an iDSN.Analyses of the contributions of each drug property indicate that this iDSN was driven by all data types and performs better than other DSNs.Within the top 20 recommended drug pairs,7 drugs have been reported to be repurposed.The source code for PIMD is available at https://github.com/Sepstar/PIMD/.展开更多
Let Fq be a finite field with q = pf elements,where p is an odd prime.Let N（a1x12 ＋ ···＋anxn2 = bx1 ···xs） denote the number of solutions（x1,...,xn） of the equation a1x12 ＋·&#...Let Fq be a finite field with q = pf elements,where p is an odd prime.Let N（a1x12 ＋ ···＋anxn2 = bx1 ···xs） denote the number of solutions（x1,...,xn） of the equation a1x12 ＋···＋ anxn2 = bx1 ···xs in Fnq,where n 5,s n,and ai ∈ F＊q,b ∈ F＊q.In this paper,we solve the problem which the present authors mentioned in an earlier paper,and obtain a reduction formula for the number of solutions of equation a1x21 ＋ ··· ＋ anxn2 = bx1 ···xs,where n 5,3 ≤ s n,under a certain restriction on coefficients.We also obtain an explicit formula for the number of solutions of equation a1x21 ＋ ··· ＋ anxn2 = bx1 ···xn-1 in Fqn under a restriction on n and q.展开更多
We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication....We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).展开更多
基金supported by the National Natural Science Foundation of China(Grant No.U1435222)the Program of International Sci-Tech Cooperation,China(Grant No.2014DFB30020)。
文摘The accumulation of various types of drug informatics data and computational approaches for drug repositioning can accelerate pharmaceutical research and development.However,the integration of multi-dimensional drug data for precision repositioning remains a pressing challenge.Here,we propose a systematic framework named PIMD to predict drug therapeutic properties by integrating multi-dimensional data for drug repositioning.In PIMD,drug similarity networks(DSNs)based on chemical,pharmacological,and clinical data are fused into an integrated DSN(iDSN)composed of many clusters.Rather than simple fusion,PIMD offers a systematic way to annotate clusters.Unexpected drugs within clusters and drug pairs with a high iDSN similarity score are therefore identified to predict novel therapeutic uses.PIMD provides new insights into the universality,individuality,and complementarity of different drug properties by evaluating the contribution of each property data.To test the performance of PIMD,we use chemical,pharmacological,and clinical properties to generate an iDSN.Analyses of the contributions of each drug property indicate that this iDSN was driven by all data types and performs better than other DSNs.Within the top 20 recommended drug pairs,7 drugs have been reported to be repurposed.The source code for PIMD is available at https://github.com/Sepstar/PIMD/.
基金Supported by the National Natural Science Foundation of China (Grant Nos.1097120510771100)
文摘Let Fq be a finite field with q = pf elements,where p is an odd prime.Let N（a1x12 ＋ ···＋anxn2 = bx1 ···xs） denote the number of solutions（x1,...,xn） of the equation a1x12 ＋···＋ anxn2 = bx1 ···xs in Fnq,where n 5,s n,and ai ∈ F＊q,b ∈ F＊q.In this paper,we solve the problem which the present authors mentioned in an earlier paper,and obtain a reduction formula for the number of solutions of equation a1x21 ＋ ··· ＋ anxn2 = bx1 ···xs,where n 5,3 ≤ s n,under a certain restriction on coefficients.We also obtain an explicit formula for the number of solutions of equation a1x21 ＋ ··· ＋ anxn2 = bx1 ···xn-1 in Fqn under a restriction on n and q.
文摘We continue our investigations on pointwise multipliers for Besov spaces of dominating mixed smoothness. This time we study the algebra property of the classes S_(p,q)~rB(R^d) with respect to pointwise multiplication. In addition, if p≤q, we are able to describe the space of all pointwise multipliers for S_(p,q)~rB(R^d).
