Computing the Rank Profile Matrix

The row (resp. column) rank profile of a matrix describes the staircase shape of its row (resp. column) echelon form. In an ISSAC'13 paper, we proposed a recursive Gaussian elimination that can compute simultaneously the row and column rank profiles of a matrix as well as those of all of its leading sub-matrices, in the same time as state of the art Gaussian elimination algorithms. Here we first study the conditions making a Gaus-sian elimination algorithm reveal this information. Therefore, we propose the definition of a new matrix invariant, the rank profile matrix, summarizing all information on the row and column rank profiles of all the leading sub-matrices. We also explore the conditions for a Gaussian elimination algorithm to compute all or part of this invariant, through the corresponding PLUQ decomposition. As a consequence, we show that the classical iterative CUP decomposition algorithm can actually be adapted to compute the rank profile matrix. Used, in a Crout variant, as a base-case to our ISSAC'13 implementation, it delivers a significant improvement in efficiency. Second, the row (resp. column) echelon form of a matrix are usually computed via different dedicated triangular decompositions. We show here that, from some PLUQ decompositions, it is possible to recover the row and column echelon forms of a matrix and of any of its leading sub-matrices thanks to an elementary post-processing algorithm

Computing a Lattice Basis Revisited

International audienc

Processing Succinct Matrices and Vectors

We study the complexity of algorithmic problems for matrices that are represented by multi-terminal decision diagrams (MTDD). These are a variant of ordered decision diagrams, where the terminal nodes are labeled with arbitrary elements of a semiring (instead of 0 and 1). A simple example shows that the product of two MTDD-represented matrices cannot be represented by an MTDD of polynomial size. To overcome this deficiency, we extended MTDDs to MTDD_+ by allowing componentwise symbolic addition of variables (of the same dimension) in rules. It is shown that accessing an entry, equality checking, matrix multiplication, and other basic matrix operations can be solved in polynomial time for MTDD_+-represented matrices. On the other hand, testing whether the determinant of a MTDD-represented matrix vanishes PSPACE$-complete, and the same problem is NP-complete for MTDD_+-represented diagonal matrices. Computing a specific entry in a product of MTDD-represented matrices is #P-complete.Comment: An extended abstract of this paper will appear in the Proceedings of CSR 201

Structure of the Afferent Terminals in Terminal Ganglion of a Cricket and Persistent Homology

We use topological data analysis to investigate the three dimensional spatial structure of the locus of afferent neuron terminals in crickets Acheta domesticus. Each afferent neuron innervates a filiform hair positioned on a cercus: a protruding appendage at the rear of the animal. The hairs transduce air motion to the neuron signal that is used by a cricket to respond to the environment. We stratify the hairs (and the corresponding afferent terminals) into classes depending on hair length, along with position. Our analysis uncovers significant structure in the relative position of these terminal classes and suggests the functional relevance of this structure. Our method is very robust to the presence of significant experimental and developmental noise. It can be used to analyze a wide range of other point cloud data sets

Class A Orphans in GtoPdb v.2023.1

Table 1 lists a number of putative GPCRs identified by NC-IUPHAR [161], for which preliminary evidence for an endogenous ligand has been published, or for which there exists a potential link to a disease, or disorder. These GPCRs have recently been reviewed in detail [121]. The GPCRs in Table 1 are all Class A, rhodopsin-like GPCRs. Class A orphan GPCRs not listed in Table 1 are putative GPCRs with as-yet unidentified endogenous ligands.Table 1: Class A orphan GPCRs with putative endogenous ligands GPR3GPR4GPR6GPR12GPR15GPR17GPR20 GPR22GPR26GPR31GPR34GPR35GPR37GPR39 GPR50GPR63GPR65GPR68GPR75GPR84GPR87 GPR88GPR132GPR149GPR161GPR183LGR4LGR5 LGR6MAS1MRGPRDMRGPRX1MRGPRX2P2RY10TAAR2 In addition the orphan receptors GPR18, GPR55 and GPR119 which are reported to respond to endogenous agents analogous to the endogenous cannabinoid ligands have been grouped together (GPR18, GPR55 and GPR119)

Class A Orphans (version 2020.5) in the IUPHAR/BPS Guide to Pharmacology Database

Table 1 lists a number of putative GPCRs identified by NC-IUPHAR [194], for which preliminary evidence for an endogenous ligand has been published, or for which there exists a potential link to a disease, or disorder. These GPCRs have recently been reviewed in detail [150]. The GPCRs in Table 1 are all Class A, rhodopsin-like GPCRs. Class A orphan GPCRs not listed in Table 1 are putative GPCRs with as-yet unidentified endogenous ligands.Table 1: Class A orphan GPCRs with putative endogenous ligands GPR3 GPR4 GPR6 GPR12 GPR15 GPR17 GPR20 GPR22 GPR26 GPR31 GPR34 GPR35 GPR37 GPR39 GPR50 GPR63 GRP65 GPR68 GPR75 GPR84 GPR87 GPR88 GPR132 GPR149 GPR161 GPR183 LGR4 LGR5 LGR6 MAS1 MRGPRD MRGPRX1 MRGPRX2 P2RY10 TAAR2 In addition the orphan receptors GPR18, GPR55 and GPR119 which are reported to respond to endogenous agents analogous to the endogenous cannabinoid ligands have been grouped together (GPR18, GPR55 and GPR119)

Class A Orphans in GtoPdb v.2022.3

Table 1 lists a number of putative GPCRs identified by NC-IUPHAR [161], for which preliminary evidence for an endogenous ligand has been published, or for which there exists a potential link to a disease, or disorder. These GPCRs have recently been reviewed in detail [121]. The GPCRs in Table 1 are all Class A, rhodopsin-like GPCRs. Class A orphan GPCRs not listed in Table 1 are putative GPCRs with as-yet unidentified endogenous ligands.Table 1: Class A orphan GPCRs with putative endogenous ligands GPR3GPR4GPR6GPR12GPR15GPR17GPR20 GPR22GPR26GPR31GPR34GPR35GPR37GPR39 GPR50GPR63GPR65GPR68GPR75GPR84GPR87 GPR88GPR132GPR149GPR161GPR183LGR4LGR5 LGR6MAS1MRGPRDMRGPRX1MRGPRX2P2RY10TAAR2 In addition the orphan receptors GPR18, GPR55 and GPR119 which are reported to respond to endogenous agents analogous to the endogenous cannabinoid ligands have been grouped together (GPR18, GPR55 and GPR119)

Class A Orphans in GtoPdb v.2021.3

Table 1 lists a number of putative GPCRs identified by NC-IUPHAR [161], for which preliminary evidence for an endogenous ligand has been published, or for which there exists a potential link to a disease, or disorder. These GPCRs have recently been reviewed in detail [121]. The GPCRs in Table 1 are all Class A, rhodopsin-like GPCRs. Class A orphan GPCRs not listed in Table 1 are putative GPCRs with as-yet unidentified endogenous ligands.Table 1: Class A orphan GPCRs with putative endogenous ligands GPR3GPR4GPR6GPR12GPR15GPR17GPR20 GPR22GPR26GPR31GPR34GPR35GPR37GPR39 GPR50GPR63GRP65GPR68GPR75GPR84GPR87 GPR88GPR132GPR149GPR161GPR183LGR4LGR5 LGR6MAS1MRGPRDMRGPRX1MRGPRX2P2RY10TAAR2 In addition the orphan receptors GPR18, GPR55 and GPR119 which are reported to respond to endogenous agents analogous to the endogenous cannabinoid ligands have been grouped together (GPR18, GPR55 and GPR119)

Class A Orphans (version 2019.4) in the IUPHAR/BPS Guide to Pharmacology Database

Table 1 lists a number of putative GPCRs identified by NC-IUPHAR [191], for which preliminary evidence for an endogenous ligand has been published, or for which there exists a potential link to a disease, or disorder. These GPCRs have recently been reviewed in detail [148]. The GPCRs in Table 1 are all Class A, rhodopsin-like GPCRs. Class A orphan GPCRs not listed in Table 1 are putative GPCRs with as-yet unidentified endogenous ligands.Table 1: Class A orphan GPCRs with putative endogenous ligands GPR3GPR4GPR6GPR12GPR15GPR17GPR20 GPR22GPR26GPR31GPR34GPR35GPR37GPR39 GPR50GPR63GRP65GPR68GPR75GPR84GPR87 GPR88GPR132GPR149GPR161GPR183LGR4LGR5 LGR6MAS1MRGPRDMRGPRX1MRGPRX2P2RY10TAAR2 In addition the orphan receptors GPR18, GPR55 and GPR119 which are reported to respond to endogenous agents analogous to the endogenous cannabinoid ligands have been grouped together (GPR18, GPR55 and GPR119)

Rapid PCR analysis of the St14 (DXS52) VNTR.

Introduction: Some segments of the human genome exhibit polymorphism due to a variable number of tandem repeats (VNTR). The enzymatic amplification of VNTR loci can allow for rapid analysis and discrimination of closely sized alleles. We report a PCR-based method for analysis of the highl