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  • image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/

    We introduce the notion of nonevasive reduction and show that for any monotone poset mapϕ:P→P, the simplicial complexΔ(P)NE-reduces toΔ(Q), for anyQ⊇Fixϕ.As a corollary, we prove that for any order-preserving mapϕ:P→Psatisfyingϕ(x)≥x, for anyx∈P, the simplicial complexΔ(P)collapses toΔ(ϕ(P)). We also obtain a generalization of Crapo's closure theorem.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ International Journa...arrow_drop_down
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    International Journal of Mathematics and Mathematical Sciences
    Article . 2006 . Peer-reviewed
    License: CC BY
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    arXiv.org e-Print Archive
    Other literature type . Preprint . 2005
    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    https://doi.org/10.48550/arxiv...
    Article . 2005
    License: arXiv Non-Exclusive Distribution
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ International Journa...arrow_drop_down
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      International Journal of Mathematics and Mathematical Sciences
      Article . 2006 . Peer-reviewed
      License: CC BY
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      arXiv.org e-Print Archive
      Other literature type . Preprint . 2005
      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
      https://doi.org/10.48550/arxiv...
      Article . 2005
      License: arXiv Non-Exclusive Distribution
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    Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality at each vertex. Unlike the classical model, the slack model naturally mods out projective transformations. It is inherently algebraic, arising as the positive part of a variety of a saturated determinantal ideal, and provides a new computational tool to study classical realizability problems for polytopes. We introduce the package SlackIdeals for Macaulay2, that provides methods for creating and manipulating slack matrices and slack ideals of convex polytopes and matroids. Slack ideals are often difficult to compute. To improve the power of the slack model, we develop two strategies to simplify computations: we scale as many entries of the slack matrix as possible to one; we then obtain a reduced slack model combining the slack variety with the more compact Grassmannian realization space model. This allows us to study slack ideals that were previously out of computational reach. As applications, we show that the well-known Perles polytope does not admit rational realizations and prove the non-realizability of a large quasi-simplicial sphere. Example 4 replaced

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Europe PubMed Centra...arrow_drop_down
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    https://link.springer.com/cont...
    Part of book or chapter of book
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    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/
    arXiv.org e-Print Archive
    Preprint . Other literature type . 2020
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    https://doi.org/10.1007/978-3-...
    Part of book or chapter of book . 2020 . Peer-reviewed
    License: Springer TDM
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    https://doi.org/10.48550/arxiv...
    Article . 2020
    License: arXiv Non-Exclusive Distribution
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      arXiv.org e-Print Archive
      Preprint . Other literature type . 2020
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      https://doi.org/10.1007/978-3-...
      Part of book or chapter of book . 2020 . Peer-reviewed
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      https://doi.org/10.48550/arxiv...
      Article . 2020
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    Authors: Amoussou-Guenou, Yackolley; del Pozzo, Antonella; Potop-Butucaru, Maria; Tucci-Piergiovanni, Sara;

    Tendermint-core blockchains (e.g. Cosmos) are considered today one of the most viable alternatives for the highly energy consuming proof-of-work blockchains such as Bitcoin and Ethereum. Their particularity is that they aim at offering strong consistency (no forks) in an open system combining two ingredients (i) a set of validators that generate blocks via a variant of Practical Byzantine Fault Tolerant (PBFT) consensus protocol and (ii) a selection strategy that dynamically selects nodes to be validators for the next block via a proof-of-stake mechanism. However,the exact assumptions on the system model under which Tendermint underlying algorithms are correct and the exact properties Tendermint verifies have never been formally analyzed. The contribution of this paper is two-fold. First, while formalizing Tendermint algorithms we precisely characterize the system model and the exact problem solved by Tendermint. We prove that in eventual synchronous systems a modified version of Tendermint solves (i) under additional assumptions, a variant of one-shot consensus for the validation of one single block and (ii) a variant of the repeated consensus problem for multiple blocks. These results hold even if the set of validators is hit by Byzantine failures, provided that for each one-shot consensus instance less than one third of the validators is Byzantine. Our second contribution relates to the fairness of the rewarding mechanism. It is common knowledge that in permisionless blockchain systems the main threat is the tragedy of commons that may yield the system to collapse if the rewarding mechanism is not adequate. Ad minimum the rewarding mechanism must be fair, i.e.distributing the rewards in proportion to the merit of participants. We prove, for the first time in blockchain systems, that in repeated-consensus based blockchains there exists an (eventual) fair rewarding mechanism if and only if the system is (eventual) synchronous. We also show that the original Tendermint rewarding is not fair, however, a modification of the original protocol makes it eventually fair.

    image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ INRIA a CCSD electro...arrow_drop_down
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    arXiv.org e-Print Archive
    Other literature type . Preprint . 2018
    https://doi.org/10.48550/arxiv...
    Article . 2018
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  • image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    Authors: Jerzy Brzeziński; G. Gambosi; Jacek Blazewicz;

    This paper deals with the problem of store-and-forward deadlock prevention in store-and-forward networks. The presented solution uses time stamping of all messages in the network, and a nonpreemptable message exchange mechanism. By combining these ideas, a new distributed flow control procedure is derived which guarantees that all messages are delivered to their own destinations, thus avoiding both deadlock and livelock without any message loss. It is shown that some properties of this procedure depend on the policy of the allocation of exchange buffers to nodes. On the one hand, an optimal allocation strategy is presented which results in a maximally optimal deadlock prevention procedure. The procedure is network sizeand topology-independent and allows unrestricted packet routing. On the other hand, the allocation of one exchange buffer per node is discussed, which, even if not optimal, makes the derived deadlock prevention procedure completely independent of network reconfigurations. The last feature is extremely important from the practical point of view and, therefore, such a solution is strongly recommended. When compared to store-and-forward deadlock prevention procedures described so far, which lack some or all of these desirable properties, the procedure presented here behaves favorably. However, it imposes other drawbacks, i.e., the possibility of extra hops as a result of exchange operations. It is argued that this drawback appears rarely in practice, and some strategies which aim at a reduction of it are proposed.

    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao IEEE Transactions on...arrow_drop_down
    image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
    IEEE Transactions on Communications
    Article . 1987 . Peer-reviewed
    License: IEEE Copyright
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      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao IEEE Transactions on...arrow_drop_down
      image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
      IEEE Transactions on Communications
      Article . 1987 . Peer-reviewed
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    This paper deals with the Extended Resource Constrained Project Scheduling Problem (ERCPSP) which is defined by events, nonrenewable resources and precedence constraints between pairs of events. The availability of a resource is depleted and replenished at the occurrence times of a set of events. The decision problem of ERCPSP consists of determining whether an instance has a feasible schedule or not. When there is only one nonrenewable resource, this problem is equivalent to find a feasible schedule that minimizes the number of resource units initially required. It generalizes the maximum cumulative cost problem and the two-machine maximum completion time flow-shop problem. In this paper, we consider this problem with some specific precedence constraints: parallel chains, series-parallel and interval order precedence constraints. For the first two cases, polynomial algorithms based on a linear decomposition of chains are proposed. For the third case, a polynomial algorithm is introduced to solve it. The priority between events is defined using the properties of interval orders.

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    RAIRO - Operations Research
    Article . 2021 . Peer-reviewed
    License: CC BY
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      image/svg+xml art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos Open Access logo, converted into svg, designed by PLoS. This version with transparent background. http://commons.wikimedia.org/wiki/File:Open_Access_logo_PLoS_white.svg art designer at PLoS, modified by Wikipedia users Nina, Beao, JakobVoss, and AnonMoos http://www.plos.org/ Hal; Mémoires en Sci...arrow_drop_down
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      RAIRO - Operations Research
      Article . 2021 . Peer-reviewed
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    Abstract Let U be a unital in PG ( 2 , q 2 ) , q = p h and let G be the group of projectivities of PG ( 2 , q 2 ) stabilizing U . In this paper we prove that U is a Buekenhout–Metz unital containing conics and q is odd if, and only if, there exists a point A of U such that the stabilizer of A in G contains an elementary Abelian p -group of order q 2 with no non-identity elations.

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    Discrete Mathematics
    Article . 2012 . Peer-reviewed
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      Discrete Mathematics
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  • Authors: Mohammed O. Assayony; Nur'Aini Abdul Rashid;

    Clustering protein sequences is becoming important in helping biologists analyze the large protein sequences produced by wet lab experiments. Graph based partitioning methods which is an important and stable algorithm in computer science can be used to cluster protein sequences such that each identified subgraph can be considered as a cluster. Each cluster represents a family of protein sequences or protein sequences that shared a common attribute. Since the size of protein sequence databases increases 1.5 times yearly, a fast and efficient graph based protein sequence clustering method is much needed. We proposed a parallel approach in graph-based clustering methods by improving the performance of an existing algorithm ProtClust by using parallel methods. We presented the design of a parallel method which will be the basis of our experiments for protein sequence clustering.

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    Abstract It has been proposed by Meyer, Kfouri and others to extend the so-called Nonstandard Logics of Programs approach (NLP henceforth) to recursive programs and denotational semantics in some natural way. The key step in doing NLP is selecting a semantics for programs (which, in the present paper, is denotational semantics) and then forming its KPU-absolute version. Absoluteness is a set theoretic property of logics. If a logic L is not absolute, then some formulas of L do not speak about the models of L , but about something else. If a logic has this strange property, then it is impossible to find a complete inference system for it, and this because of purely “administrative” reasons, which might not correspond to any of the inherent properties of the original situation we are modeling (in devising this logic etc.). This “administrative” incompleteness is only one of the undesirable side effects of nonabsoluteness. In NLP, the purpose of constructing and studying absolute versions of logics is aimed at, among other things, the removal of these undesirable properties. The absolute version of denotational semantics will turn out to be based on 2-sorted first order logic, or more concretely, on the usual nonstandard or weak second order logic. Some of the most relevant features of this logic are the ability to compare “realistic” existing program verification methods, create new, more powerful and still “realistic” ones, completeness etc., to mention only a very few.

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    Theoretical Computer Science
    Article . 1990 . Peer-reviewed
    License: Elsevier Non-Commercial
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      Theoretical Computer Science
      Article . 1990 . Peer-reviewed
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  • image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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    Journal of Symbolic Logic
    Article . 1971 . Peer-reviewed
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      Journal of Symbolic Logic
      Article . 1971 . Peer-reviewed
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450,094 Research products
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    We introduce the notion of nonevasive reduction and show that for any monotone poset mapϕ:P→P, the simplicial complexΔ(P)NE-reduces toΔ(Q), for anyQ⊇Fixϕ.As a corollary, we prove that for any order-preserving mapϕ:P→Psatisfyingϕ(x)≥x, for anyx∈P, the simplicial complexΔ(P)collapses toΔ(ϕ(P)). We also obtain a generalization of Crapo's closure theorem.

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    International Journal of Mathematics and Mathematical Sciences
    Article . 2006 . Peer-reviewed
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    arXiv.org e-Print Archive
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    https://doi.org/10.48550/arxiv...
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      https://doi.org/10.48550/arxiv...
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    Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality at each vertex. Unlike the classical model, the slack model naturally mods out projective transformations. It is inherently algebraic, arising as the positive part of a variety of a saturated determinantal ideal, and provides a new computational tool to study classical realizability problems for polytopes. We introduce the package SlackIdeals for Macaulay2, that provides methods for creating and manipulating slack matrices and slack ideals of convex polytopes and matroids. Slack ideals are often difficult to compute. To improve the power of the slack model, we develop two strategies to simplify computations: we scale as many entries of the slack matrix as possible to one; we then obtain a reduced slack model combining the slack variety with the more compact Grassmannian realization space model. This allows us to study slack ideals that were previously out of computational reach. As applications, we show that the well-known Perles polytope does not admit rational realizations and prove the non-realizability of a large quasi-simplicial sphere. Example 4 replaced

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    https://doi.org/10.1007/978-3-...
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