Stereoviews of the active-site cavities on the zinc acetate-bound (top) and apo structure (bottom... more Stereoviews of the active-site cavities on the zinc acetate-bound (top) and apo structure (bottom) of XcTcmJ from Xanthomonas campestris. Solvent-accessible surface is shown and was rendered using PyMOL (DeLano Scientific). Residues surrounding the cavities were determined with CASTp and rendered in yellow for the zinc acetate-bound (top) and cyan for the apo structures with these residues labeled. The surface of the bound zinc (orange) interacting with the acetate (ACT) ligand is shown on the upper surface.
We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann in their computa... more We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann in their computational study of energy-minimizing particle configurations in Euclidean space. In particular, using the Poisson summation formula we reformulate formal duality as a combinatorial phenomenon in finite abelian groups. We give new examples related to Gauss sums and make some progress towards classifying formally dual configurations.
We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from lin... more We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic projective spaces and the octonionic projective plane. The most noteworthy cases are 15-point simplices in HP 2 and 27-point simplices in OP 2 , both of which are the largest simplices and the smallest 2-designs possible in their respective spaces. These codes are all universally optimal, by a theorem of Cohn and Kumar. We also show the existence of several positive-dimensional families of simplices in the Grassmannians of subspaces of R n with n ≤ 8; close numerical approximations to these families had been found by Conway, Hardin, and Sloane, but no proof of existence was known. Our existence proofs are computer-assisted, and the main tool is a variant of the Newton-Kantorovich theorem. This effective implicit function theorem shows, in favorable conditions, that every approximate solution to a set of polynomial equations has a nearby exact solution. Finally, we also exhibit a few explicit codes, including a configuration of 39 points in OP 2 that form a maximal system of mutually unbiased bases. This is the last tight code in OP 2 whose existence had been previously conjectured but not resolved.
Journal of Computational and Applied Mathematics, May 1, 2005
We propose a triangulation-based partitioning algorithm, TRIOPT, for solving low-dimensional boun... more We propose a triangulation-based partitioning algorithm, TRIOPT, for solving low-dimensional bound-constrained black box global optimization problems. The method starts by forming a Delaunay triangulation of a given set of samples in the feasible domain, and then, it assesses the simplices (partitions) obtained for re-partitioning. Function values at the vertices of each partition are mapped into the zero one interval by a nonlinear transformation function and their aggregate entropy is calculated. Based on this entropy, partitions that hold a promise of containing the global optimum are re-partitioned according to different triangular splitting strategies, forming new partitions. These strategies are efficient in terms of the number of new function evaluations required per new partition.A novelty in the search scheme proposed here is that once a partition narrows down to a small size, its vertices are eliminated from the available sample set. This changes global information on the best solution and triggers a re-calculation of transformed values. Hence, revised entropies change the direction of the search to new areas. The latter scheme leads to a dynamic parallel search policy which is based on an entropy cut. The tree adopts flexible breadth depending on the status of the search. In the experimental results it is demonstrated that TRIOPTs performance is compatible and often better than that of a well-known response surface methodology and two other efficient black box partitioning approaches proposed for global optimization.
We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of ... more We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a representation are in bijection with K3 surfaces (up to suitable equivalence) whose Néron-Severi lattice contains a given lattice. An immediate consequence is that the corresponding moduli spaces of these lattice-polarized K3 surfaces are all unirational. Our constructions also produce many fixed-point-free automorphisms of positive entropy on K3 surfaces in various families associated to these representations, giving a natural extension of recent work of Oguiso.
We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,1/4) sp... more We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23,4600,1/3) spherical code.
The structure of LP2179, a member of the PF08866 (DUF1831) family, suggests a novel + fold compri... more The structure of LP2179, a member of the PF08866 (DUF1831) family, suggests a novel + fold comprising two -sheets packed against a single helix. A remote structural similarity to two other uncharacterized protein families specific to the Bacillus genus (PF08868 and PF08968), as well as to prokaryotic S-adenosylmethionine decarboxylases, is consistent with a role in amino-acid metabolism. Genomic neighborhood analysis of LP2179 supports this functional assignment, which might also then be extended to PF08868 and PF08968.
ECX21941 represents a very large family (over 600 members) of novel, ocean metagenomespecific pro... more ECX21941 represents a very large family (over 600 members) of novel, ocean metagenomespecific proteins identified by clustering of the dataset from the Global Ocean Sampling expedition. The crystal structure of ECX21941 reveals unexpected similarity to Sm/LSm proteins, which are important RNA-binding proteins, despite no detectable sequence similarity. The ECX21941 protein assembles as a homopentamer in solution and in the crystal structure when expressed in Escherichia coli and represents the first pentameric structure for this Sm/LSm family of proteins, although the actual oligomeric form in vivo is currently not known. The genomic neighborhood analysis of ECX21941 and its homologs combined with sequence similarity searches suggest a cyanophage origin for this protein. The specific functions of members of this family are unknown, but our structure analysis of ECX21941 indicates nucleic acid-binding capabilities and suggests a role in RNA and/or DNA processing.
SsgA-like proteins (SALPs) are a family of homologous cell division-related proteins that occur e... more SsgA-like proteins (SALPs) are a family of homologous cell division-related proteins that occur exclusively in morphologically complex actinomycetes. We show that SsgB, a subfamily of SALPs, is the archetypal SALP that is functionally conserved in all sporulating actinomycetes. Sporulation-specific cell division of Streptomyces coelicolor ssgB mutants is restored by introduction of distant ssgB orthologues from other actinomycetes. Interestingly, the number of septa (and spores) of the complemented null mutants is dictated by the specific ssgB orthologue that is expressed. The crystal structure of the SsgB from Thermobifida fusca was determined at 2.6 A resolution and represents the first structure for this family. The structure revealed similarities to a class of eukaryotic…
Cotton leaf curl disease (CLCuD) is caused by several distinct begomovirus species in association... more Cotton leaf curl disease (CLCuD) is caused by several distinct begomovirus species in association with disease-specific betasatellite essential for induction of disease symptoms. CLCuD is a serious threat for the cultivation of cotton (Gossypium sp.) and several species in the family Malvaceae. In this study, RNAi-based approach was applied to generate transgenic cotton (Gossypium hirsutum) plants resistant to Cotton leaf curl Rajasthan virus (CLCuRV). An intron hairpin (ihp) RNAi construct capable of expressing dsRNA homologous to the intergenic region (IR) of CLCuRV was designed and developed. Following Agrobacterium tumefaciens-mediated transformation of cotton (G. hirsutum cv. Narasimha) plants with the designed ihpRNAi construct, a total of 9 independent lines of transformed cotton were obtained. The presence of the potential stretch of IR in the transformed cotton was confirmed by PCR coupled with Southern hybridization. Upon inoculation with viruliferous whiteflies, the trans...
A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated ... more A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times. The FNIG process is also derived as the limit of a fractional ARIMA processes. Finally, the NIG densities are shown to solve the relativistic diffusion equation from statistical physics.
Proteins Structure Function and Bioinformatics, Jan 11, 2007
BtDyP from Bacteroides thetaiotaomicron (strain VPI-5482) and TyrA from Shewanella oneidensis are... more BtDyP from Bacteroides thetaiotaomicron (strain VPI-5482) and TyrA from Shewanella oneidensis are dye-decolorizing peroxidases (DyPs), members of a new family of heme-dependent peroxidases recently identified in fungi and bacteria. Here, we report the crystal structures of BtDyP and TyrA at 1.6 and 2.7 A, respectively. BtDyP assembles into a hexamer, while TyrA assembles into a dimer; the dimerization interface is conserved between the two proteins. Each monomer exhibits a two-domain, alpha+beta ferredoxin-like fold. A site for heme binding was identified computationally, and modeling of a heme into the proposed active site allowed for identification of residues likely to be functionally important. Structural and sequence comparisons with other DyPs demonstrate a conservation of putative heme-binding residues, including an absolutely conserved histidine. Isothermal titration calorimetry experiments confirm heme binding, but with a stoichiometry of 0.3:1 (heme:protein).(c) 2007 Wiley-Liss, Inc.
Stereoviews of the active-site cavities on the zinc acetate-bound (top) and apo structure (bottom... more Stereoviews of the active-site cavities on the zinc acetate-bound (top) and apo structure (bottom) of XcTcmJ from Xanthomonas campestris. Solvent-accessible surface is shown and was rendered using PyMOL (DeLano Scientific). Residues surrounding the cavities were determined with CASTp and rendered in yellow for the zinc acetate-bound (top) and cyan for the apo structures with these residues labeled. The surface of the bound zinc (orange) interacting with the acetate (ACT) ligand is shown on the upper surface.
We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann in their computa... more We study the notion of formal duality introduced by Cohn, Kumar, and Sch\"urmann in their computational study of energy-minimizing particle configurations in Euclidean space. In particular, using the Poisson summation formula we reformulate formal duality as a combinatorial phenomenon in finite abelian groups. We give new examples related to Gauss sums and make some progress towards classifying formally dual configurations.
We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from lin... more We find many tight codes in compact spaces, i.e., optimal codes whose optimality follows from linear programming bounds. In particular, we show the existence (and abundance) of several hitherto unknown families of simplices in quaternionic projective spaces and the octonionic projective plane. The most noteworthy cases are 15-point simplices in HP 2 and 27-point simplices in OP 2 , both of which are the largest simplices and the smallest 2-designs possible in their respective spaces. These codes are all universally optimal, by a theorem of Cohn and Kumar. We also show the existence of several positive-dimensional families of simplices in the Grassmannians of subspaces of R n with n ≤ 8; close numerical approximations to these families had been found by Conway, Hardin, and Sloane, but no proof of existence was known. Our existence proofs are computer-assisted, and the main tool is a variant of the Newton-Kantorovich theorem. This effective implicit function theorem shows, in favorable conditions, that every approximate solution to a set of polynomial equations has a nearby exact solution. Finally, we also exhibit a few explicit codes, including a configuration of 39 points in OP 2 that form a maximal system of mutually unbiased bases. This is the last tight code in OP 2 whose existence had been previously conjectured but not resolved.
Journal of Computational and Applied Mathematics, May 1, 2005
We propose a triangulation-based partitioning algorithm, TRIOPT, for solving low-dimensional boun... more We propose a triangulation-based partitioning algorithm, TRIOPT, for solving low-dimensional bound-constrained black box global optimization problems. The method starts by forming a Delaunay triangulation of a given set of samples in the feasible domain, and then, it assesses the simplices (partitions) obtained for re-partitioning. Function values at the vertices of each partition are mapped into the zero one interval by a nonlinear transformation function and their aggregate entropy is calculated. Based on this entropy, partitions that hold a promise of containing the global optimum are re-partitioned according to different triangular splitting strategies, forming new partitions. These strategies are efficient in terms of the number of new function evaluations required per new partition.A novelty in the search scheme proposed here is that once a partition narrows down to a small size, its vertices are eliminated from the available sample set. This changes global information on the best solution and triggers a re-calculation of transformed values. Hence, revised entropies change the direction of the search to new areas. The latter scheme leads to a dynamic parallel search policy which is based on an entropy cut. The tree adopts flexible breadth depending on the status of the search. In the experimental results it is demonstrated that TRIOPTs performance is compatible and often better than that of a well-known response surface methodology and two other efficient black box partitioning approaches proposed for global optimization.
We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of ... more We study moduli spaces of lattice-polarized K3 surfaces in terms of orbits of representations of algebraic groups. In particular, over an algebraically closed field of characteristic 0, we show that in many cases, the nondegenerate orbits of a representation are in bijection with K3 surfaces (up to suitable equivalence) whose Néron-Severi lattice contains a given lattice. An immediate consequence is that the corresponding moduli spaces of these lattice-polarized K3 surfaces are all unirational. Our constructions also produce many fixed-point-free automorphisms of positive entropy on K3 surfaces in various families associated to these representations, giving a natural extension of recent work of Oguiso.
We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,1/4) sp... more We use techniques of Bannai and Sloane to give a new proof that there is a unique (22,891,1/4) spherical code; this result is implicit in a recent paper by Cuypers. We also correct a minor error in the uniqueness proof given by Bannai and Sloane for the (23,4600,1/3) spherical code.
The structure of LP2179, a member of the PF08866 (DUF1831) family, suggests a novel + fold compri... more The structure of LP2179, a member of the PF08866 (DUF1831) family, suggests a novel + fold comprising two -sheets packed against a single helix. A remote structural similarity to two other uncharacterized protein families specific to the Bacillus genus (PF08868 and PF08968), as well as to prokaryotic S-adenosylmethionine decarboxylases, is consistent with a role in amino-acid metabolism. Genomic neighborhood analysis of LP2179 supports this functional assignment, which might also then be extended to PF08868 and PF08968.
ECX21941 represents a very large family (over 600 members) of novel, ocean metagenomespecific pro... more ECX21941 represents a very large family (over 600 members) of novel, ocean metagenomespecific proteins identified by clustering of the dataset from the Global Ocean Sampling expedition. The crystal structure of ECX21941 reveals unexpected similarity to Sm/LSm proteins, which are important RNA-binding proteins, despite no detectable sequence similarity. The ECX21941 protein assembles as a homopentamer in solution and in the crystal structure when expressed in Escherichia coli and represents the first pentameric structure for this Sm/LSm family of proteins, although the actual oligomeric form in vivo is currently not known. The genomic neighborhood analysis of ECX21941 and its homologs combined with sequence similarity searches suggest a cyanophage origin for this protein. The specific functions of members of this family are unknown, but our structure analysis of ECX21941 indicates nucleic acid-binding capabilities and suggests a role in RNA and/or DNA processing.
SsgA-like proteins (SALPs) are a family of homologous cell division-related proteins that occur e... more SsgA-like proteins (SALPs) are a family of homologous cell division-related proteins that occur exclusively in morphologically complex actinomycetes. We show that SsgB, a subfamily of SALPs, is the archetypal SALP that is functionally conserved in all sporulating actinomycetes. Sporulation-specific cell division of Streptomyces coelicolor ssgB mutants is restored by introduction of distant ssgB orthologues from other actinomycetes. Interestingly, the number of septa (and spores) of the complemented null mutants is dictated by the specific ssgB orthologue that is expressed. The crystal structure of the SsgB from Thermobifida fusca was determined at 2.6 A resolution and represents the first structure for this family. The structure revealed similarities to a class of eukaryotic…
Cotton leaf curl disease (CLCuD) is caused by several distinct begomovirus species in association... more Cotton leaf curl disease (CLCuD) is caused by several distinct begomovirus species in association with disease-specific betasatellite essential for induction of disease symptoms. CLCuD is a serious threat for the cultivation of cotton (Gossypium sp.) and several species in the family Malvaceae. In this study, RNAi-based approach was applied to generate transgenic cotton (Gossypium hirsutum) plants resistant to Cotton leaf curl Rajasthan virus (CLCuRV). An intron hairpin (ihp) RNAi construct capable of expressing dsRNA homologous to the intergenic region (IR) of CLCuRV was designed and developed. Following Agrobacterium tumefaciens-mediated transformation of cotton (G. hirsutum cv. Narasimha) plants with the designed ihpRNAi construct, a total of 9 independent lines of transformed cotton were obtained. The presence of the potential stretch of IR in the transformed cotton was confirmed by PCR coupled with Southern hybridization. Upon inoculation with viruliferous whiteflies, the trans...
A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated ... more A fractional normal inverse Gaussian (FNIG) process is a fractional Brownian motion subordinated to an inverse Gaussian process. This paper shows how the FNIG process emerges naturally as the limit of a random walk with correlated jumps separated by i.i.d. waiting times. Similarly, we show that the NIG process, a Brownian motion subordinated to an inverse Gaussian process, is the limit of a random walk with uncorrelated jumps separated by i.i.d. waiting times. The FNIG process is also derived as the limit of a fractional ARIMA processes. Finally, the NIG densities are shown to solve the relativistic diffusion equation from statistical physics.
Proteins Structure Function and Bioinformatics, Jan 11, 2007
BtDyP from Bacteroides thetaiotaomicron (strain VPI-5482) and TyrA from Shewanella oneidensis are... more BtDyP from Bacteroides thetaiotaomicron (strain VPI-5482) and TyrA from Shewanella oneidensis are dye-decolorizing peroxidases (DyPs), members of a new family of heme-dependent peroxidases recently identified in fungi and bacteria. Here, we report the crystal structures of BtDyP and TyrA at 1.6 and 2.7 A, respectively. BtDyP assembles into a hexamer, while TyrA assembles into a dimer; the dimerization interface is conserved between the two proteins. Each monomer exhibits a two-domain, alpha+beta ferredoxin-like fold. A site for heme binding was identified computationally, and modeling of a heme into the proposed active site allowed for identification of residues likely to be functionally important. Structural and sequence comparisons with other DyPs demonstrate a conservation of putative heme-binding residues, including an absolutely conserved histidine. Isothermal titration calorimetry experiments confirm heme binding, but with a stoichiometry of 0.3:1 (heme:protein).(c) 2007 Wiley-Liss, Inc.
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Papers by Abhinav Kumar