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  • 1
    Electronic Resource
    Electronic Resource
    On key storage in secure networks (1995)
    Springer
    Journal of cryptology 8 (1995), S. 189-200 
    Details
    ISSN: 1432-1378
    Keywords: Keys ; Secure networks ; Probabilistic construction
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science
    Notes: Abstract We consider systems where the keys for encrypting messages are derived from the pairwise intersections of sets of private keys issued to the users. We give improved bounds on the storage requirements of systems of this type for secure communication in a large network.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00191355
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  • 2
    Electronic Resource
    Electronic Resource
    Multiplicities of subgraphs (1996)
    Springer
    Combinatorica 16 (1996), S. 123-141 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 55 ; 05 C 35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A former conjecture of Burr and Rosta [1], extending a conjecture of Erdős [2], asserted that in any two-colouring of the edges of a large complete graph, the proportion of subgraphs isomorphic to a fixed graphG which are monochromatic is at least the proportion found in a random colouring. It is now known that the conjecture fails for some graphsG, includingG=K p forp≥4. We investigate for which graphsG the conjecture holds. Our main result is that the conjecture fails ifG containsK 4 as a subgraph, and in particular it fails for almost all graphs.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01300130
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  • 3
    Electronic Resource
    Electronic Resource
    Graph products and monochromatic multiplicities (1997)
    Springer
    Combinatorica 17 (1997), S. 125-134 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 35 ; 05 C 55
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Arcane two-edge-colourings of complete graphs were described in [13], in which there are significantly fewer monochromaticK r 's than in a random colouring (so disproving a conjecture of Erdős [2]). Jagger, Šťovíček and Thomason [7] showed that the same colourings have fewer monochromaticG's than do random colourings for any graphG containingK 4. The purpose of this note is to point out that these colourings are not as obscure as might appear. There is in fact a large, natural and easily described class of colourings of the above kind; the specific examples used in [13] and [7] fall into this class.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01196136
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  • 4
    Electronic Resource
    Electronic Resource
    Trees in tournaments (1991)
    Springer
    Combinatorica 11 (1991), S. 123-130 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 20 ; 05 C 35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Letf(n) be the smallest integer such that every tournament of orderf(n) contains every oriented tree of ordern. Sumner has just conjectures thatf(n)=2n−2, and F. K. Chung has shown thatf(n)≤(1+o(1))nlog2 n. Here we show thatf(n)≤12n andf(n)≤(4+o(1))n.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01206356
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  • 5
    Electronic Resource
    Electronic Resource
    Highly linked graphs (1996)
    Springer
    Combinatorica 16 (1996), S. 313-320 
    Details
    ISSN: 1439-6912
    Keywords: 05 C 40 ; 05 C 38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A graph with at least 2k vertices is said to bek-linked if, for any choices 1,...,s k ,t 1,...,t k of 2k distinct vertices there are vertex disjoint pathsP 1,...,P k withP i joinings i tot i , 1≤i≤k. Recently Robertson and Seymour [16] showed that a graphG isk-linked provided its vertex connectivityk(G) exceeds $$10k\sqrt {\log _2 k}$$ . We show here thatk(G)≥22k will do.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01261316
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  • 6
    Electronic Resource
    Electronic Resource
    The Structure of Hereditary Properties and Colourings of Random Graphs (2000)
    Springer
    Combinatorica 20 (2000), S. 173-202 
    Details
    ISSN: 1439-6912
    Keywords: AMS Subject Classification (1991) Classes:  05C80; 05C75, 05C15
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: in the probability space ? Second, does there exist a constant such that the -chromatic number of the random graph is almost surely ? The second question was posed by Scheinerman (SIAM J. Discrete Math. 5 (1992) 74–80). The two questions are closely related and, in the case p=1/2, have already been answered. Prömel and Steger (Contemporary Mathematics 147, Amer. Math. Soc., Providence, 1993, pp. 167-178), Alekseev (Discrete Math. Appl. 3 (1993) 191-199) and the authors ( Algorithms and Combinatorics 14 Springer-Verlag (1997) 70–78) provided an approximation which was used by the authors (Random Structures and Algorithms 6 (1995) 353–356) to answer the -chromatic question for p=1/2. However, the approximating properties that work well for p=1/2 fail completely for . In this paper we describe a class of properties that do approximate in , in the following sense: for any desired accuracy of approximation, there is a property in our class that approximates to this level of accuracy. As may be expected, our class includes the simple properties used in the case p=1/2. The main difficulty in answering the second of our two questions, that concerning the -chromatic number of , is that the number of small -graphs in has, in general, large variance. The variance is smaller if we replace by a simple approximation, but it is still not small enough. We overcome this by considering instead a very rigid non-hereditary subproperty of the approximating property; the variance of the number of small -graphs is small enough for our purpose, and the structure of is sufficiently restricted to enable us to show this by a fine analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004930070019
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  • 7
    Electronic Resource
    Electronic Resource
    Rotation numbers for complete tripartite graphs (1991)
    Springer
    Graphs and combinatorics 7 (1991), S. 153-163 
    Details
    ISSN: 1435-5914
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Arooted graph is a pair (G, x), whereG is a simple undirected graph andx ∈ V(G). IfG is rooted atx, then itsrotation number h(G, x) is the minimum number of edges in a graphF of the same order asG such that for allv ∈ V(F), we can find a copy ofG inF with the rootx atv. Rotation numbers for all complete bipartite graphs are now known (see [2], [4], [7]). In this paper we calculate rotation numbers for complete tripartite graphs with rootx in the largest vertex class.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01788140
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  • 8
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    REDX08608, a Novel, Potent and Selective, Reversible BTK Inhibitor with Efficacy and Equivalent Potency Against Wild-Type and Mutant C481S BTK (2016)
    American Society of Hematology
    Details
    Publication Date: 2016-12-02
    Description: Here we report the preclinical profile of REDX08608 our novel, potent and selective, reversible BTK inhibitor that is equipotent against wild-type and mutant C481S BTK. Bruton's tyrosine kinase (BTK) is a member of the src-related Tec family of cytoplasmic tyrosine kinases and plays a key role in the BCR signaling pathway, which is required for the development, activation and survival of B-cells. BTK is a clinically validated target to treat B-cell malignancies that are dependent on BCR signaling i.e.CLL and NHL with ibrutinib approved for the treatment of CLL, MCL and WM. Irreversible and covalent reversible BTK inhibitors such as ibrutinib, acalabrutinib and GS-4059 specifically target a cysteine residue C481 within BTK and mutations at this site clearly interfere with covalent drug binding. C481S, C481Y, C481R, C481F mutations have been reported and linked to cases of resistance that have emerged in patients with CLL progression following treatment with ibrutinib (Byrd2016, Inhye2016, Maddocks2015, Woaych2014). Redx reversible BTK inhibitor, REDX08608, aims to overcome this resistance mechanism by targeting both wild type and C481-mutated BTK. Redx have recently presented REDX06961 our BTK probe (Guisot2016, AACR#4795) and, following lead optimization, we are now disclosing REDX08608, our lead compound, a potent, reversible and selective BTK inhibitor, which displays an improved profile including superior pharmacokinetics. REDX08608, reversibly, inhibits WT and C481S BTK and displays nanomolar binding affinity and potency in biochemical and cellular-based assays. REDX08608 inhibits BTK signaling and growth in cell lines dependent on the BTK pathway such the OCI-LY10 ABC-DLBCL cell line. Importantly, REDX08608 also inhibits BTK signaling in primary CLL cells. In human whole blood and isolated human PBMCs, REDX08608 inhibits activation of B-cells at nanomolar concentrations measured by inhibition of immunoglobulin-induced CD69 in CD19+cells. REDX08608 is highly selective when tested against a panel of 468 kinases and exhibits improved target specificity with 〉100-fold selectivity against other Tec and Src kinase family members (ITK, TXK, BMX, TEC, BLK, CSK, FYN, HCK, LCK, SRC) and 〉400-fold selectivity against EGFR. REDX08608 was fully profiled through DMPK in vitro assays including metabolic stability, plasma stability, cytochrome P450 inhibition, PXR activation/cytochrome P450 activity, time dependent inhibition and cytochrome P450 reaction phenotyping. REDX08608 was shown to have an acceptable metabolic and plasma stability profile across species (mouse, rat, dog, monkey and human). REDX08608 displayed no evidence of PXR activation or time dependent inhibition. IC50s were determined for human cytochrome P450s (1A2, 2D6, 2C9, 2C19 and 3A4) and were all 〉10 µM. Good exposure, oral bioavailability and half-life were demonstrated for REDX08608 in mouse, rat and dog, with dose linearity assessment performed in mouse (F = 73-100%, CL= 11% liver blood flow in mice; F = 55-84%, CL = 28% liver blood flow in rat; F = 85%, CL= 10% liver blood flow in dog). In vivo efficacy studies in preclinical models will also be disclosed. In conclusion, REDX08608 is a potent and selective, reversible BTK inhibitor with efficacy in lymphoma cell lines that offers the potential to target both wild-type BTK and an important emerging resistance mechanism in patients with CLL progression following ibrutinib-treatment. Disclosures Guisot: Redx Oncology Ltd - Redx Pharma Plc: Employment. Best:Redx Oncology Ltd - Redx Pharma Plc: Employment. Wright:Redx Oncology Ltd - Redx Pharma Plc: Employment. Thomason:Redx Oncology Ltd - Redx Pharma Plc: Employment. Woyach:Acerta: Research Funding; Karyopharm: Research Funding; Morphosys: Research Funding. Abet:Redx Oncology Ltd - Redx Pharma Plc: Employment. Castagna:Redx Oncology Ltd - Redx Pharma Plc: Employment. Cousin:Redx Oncology Ltd - Redx Pharma Plc: Employment. Emmerich:Redx Oncology Ltd - Redx Pharma Plc: Employment. Ho:Redx Oncology Ltd - Redx Pharma Plc: Employment. Kelly:Redx Oncology Ltd - Redx Pharma Plc: Employment. King-Tours:Redx Oncology Ltd - Redx Pharma Plc: Employment. Lyons:Redx Oncology Ltd - Redx Pharma Plc: Employment. Muller:Redx Oncology Ltd - Redx Pharma Plc: Employment. Refuerzo:Redx Oncology Ltd - Redx Pharma Plc: Employment. Sargent:Redx Oncology Ltd - Redx Pharma Plc: Employment. Talab:Redx Oncology Ltd - Redx Pharma Plc: Employment. Bingham:Redx Oncology Ltd - Redx Pharma Plc: Employment. Phillips:Redx Oncology Ltd - Redx Pharma Plc: Employment. Armer:Redx Oncology Ltd - Redx Pharma Plc: Employment.
    Print ISSN: 0006-4971
    Electronic ISSN: 1528-0020
    Topics: Biology , Medicine
    Published by American Society of Hematology
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  • 9
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    Discovery of Novel 3-Quinoline Carboxamides as Potent, Selective, and Orally Bioavailable Inhibitors of Ataxia Telangiectasia Mutated (ATM) Kinase (2016)
    American Chemical Society
    Details
    Publication Date: 2016-06-16
    Print ISSN: 0022-2623
    Electronic ISSN: 1520-4804
    Topics: Chemistry and Pharmacology , Medicine
    Published by American Chemical Society
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  • 10
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    A Disproof of a Conjecture of Erdős in Ramsey Theory (1989)
    Oxford University Press
    Details
    Publication Date: 1989-04-01
    Print ISSN: 0024-6107
    Electronic ISSN: 1469-7750
    Topics: Mathematics
    Published by Oxford University Press
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