130 research outputs found
Need Polynomial Systems Be Doubly-Exponential?
Polynomial Systems, or at least their algorithms, have the reputation of
being doubly-exponential in the number of variables [Mayr and Mayer, 1982],
[Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that
number of zeros of a zero-dimensional system is singly-exponential in the
number of variables. How should this contradiction be reconciled?
We first note that [Mayr and Ritscher, 2013] shows that the doubly
exponential nature of Gr\"{o}bner bases is with respect to the dimension of the
ideal, not the number of variables. This inspires us to consider what can be
done for Cylindrical Algebraic Decomposition which produces a
doubly-exponential number of polynomials of doubly-exponential degree.
We review work from ISSAC 2015 which showed the number of polynomials could
be restricted to doubly-exponential in the (complex) dimension using McCallum's
theory of reduced projection in the presence of equational constraints. We then
discuss preliminary results showing the same for the degree of those
polynomials. The results are under primitivity assumptions whose importance we
illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text
overlap with arXiv:1605.0249
Computational Complexity of Atomic Chemical Reaction Networks
Informally, a chemical reaction network is "atomic" if each reaction may be
interpreted as the rearrangement of indivisible units of matter. There are
several reasonable definitions formalizing this idea. We investigate the
computational complexity of deciding whether a given network is atomic
according to each of these definitions.
Our first definition, primitive atomic, which requires each reaction to
preserve the total number of atoms, is to shown to be equivalent to mass
conservation. Since it is known that it can be decided in polynomial time
whether a given chemical reaction network is mass-conserving, the equivalence
gives an efficient algorithm to decide primitive atomicity.
Another definition, subset atomic, further requires that all atoms are
species. We show that deciding whether a given network is subset atomic is in
, and the problem "is a network subset atomic with respect to a
given atom set" is strongly -.
A third definition, reachably atomic, studied by Adleman, Gopalkrishnan et
al., further requires that each species has a sequence of reactions splitting
it into its constituent atoms. We show that there is a to decide whether a given network is reachably atomic, improving
upon the result of Adleman et al. that the problem is . We
show that the reachability problem for reachably atomic networks is
-.
Finally, we demonstrate equivalence relationships between our definitions and
some special cases of another existing definition of atomicity due to Gnacadja
Programmability of Chemical Reaction Networks
Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior
A Linear Algebra Approach for Detecting Binomiality of Steady State Ideals of Reversible Chemical Reaction Networks
Motivated by problems from Chemical Reaction Network Theory, we investigate
whether steady state ideals of reversible reaction networks are generated by
binomials. We take an algebraic approach considering, besides concentrations of
species, also rate constants as indeterminates. This leads us to the concept of
unconditional binomiality, meaning binomiality for all values of the rate
constants. This concept is different from conditional binomiality that applies
when rate constant values or relations among rate constants are given. We start
by representing the generators of a steady state ideal as sums of binomials,
which yields a corresponding coefficient matrix. On these grounds we propose an
efficient algorithm for detecting unconditional binomiality. That algorithm
uses exclusively elementary column and row operations on the coefficient
matrix. We prove asymptotic worst case upper bounds on the time complexity of
our algorithm. Furthermore, we experimentally compare its performance with
other existing methods
Universal scaling in the branching of the Tree of Life
Understanding the patterns and processes of diversification of life in the
planet is a key challenge of science. The Tree of Life represents such
diversification processes through the evolutionary relationships among the
different taxa, and can be extended down to intra-specific relationships. Here
we examine the topological properties of a large set of interspecific and
intraspecific phylogenies and show that the branching patterns follow
allometric rules conserved across the different levels in the Tree of Life, all
significantly departing from those expected from the standard null models. The
finding of non-random universal patterns of phylogenetic differentiation
suggests that similar evolutionary forces drive diversification across the
broad range of scales, from macro-evolutionary to micro-evolutionary processes,
shaping the diversity of life on the planet.Comment: 6 pages + 19 of Supporting Informatio
Expanding the Repertoire of Modified Vaccinia Ankara-Based Vaccine Vectors via Genetic Complementation Strategies
nkara (MVA) is a safe, highly attenuated orthopoxvirus that is being developed as a recombinant vaccine vector for immunization against a number of infectious diseases and cancers. However, the expression by MVA vectors of large numbers of poxvirus antigens, which display immunodominance over vectored antigens-of-interest for the priming of T cell responses, and the induction of vector-neutralizing antibodies, which curtail the efficacy of subsequent booster immunizations, remain as significant impediments to the overall utility of such vaccines. Thus, genetic approaches that enable the derivation of MVA vectors that are antigenically less complex may allow for rational improvement of MVA-based vaccines. during infection, and that the processes governing the generation of antiviral antibody responses are more readily saturated by viral antigen than are those that elicit CD8+ T cell responses. deletion, enables the generation of novel replication-defective MVA mutants and expands the repertoire of genetic viral variants that can now be explored as improved vaccine vectors
Spermidine Promotes Human Hair Growth and Is a Novel Modulator of Human Epithelial Stem Cell Functions
This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited
Phylogeography of Sardinian Cave Salamanders (Genus Hydromantes) Is Mainly Determined by Geomorphology
Detecting the factors that determine the interruption of gene flow between populations is key to understanding how speciation occurs. In this context, caves are an excellent system for studying processes of colonization, differentiation and speciation, since they represent discrete geographical units often with known geological histories. Here, we asked whether discontinuous calcareous areas and cave systems represent major barriers to gene flow within and among the five species of Sardinian cave salamanders (genus Hydromantes) and whether intraspecific genetic structure parallels geographic distance within and among caves. We generated mitochondrial cytochrome b gene sequences from 184 individuals representing 48 populations, and used a Bayesian phylogeographic approach to infer possible areas of cladogenesis for these species and reconstruct historical and current dispersal routes among distinct populations. Our results show deep genetic divergence within and among all Sardinian cave salamander species, which can mostly be attributed to the effects of mountains and discontinuities in major calcareous areas and cave systems acting as barriers to gene flow. While these salamander species can also occur outside caves, our results indicate that there is a very poor dispersal of these species between separate cave systems
Indistinguishability Obfuscation Without Maps: Attacks and Fixes for Noisy Linear FE
Candidates of Indistinguishability Obfuscation (iO) can be categorized as ``direct\u27\u27 or ``bootstrapping based\u27\u27. Direct constructions rely on high degree multilinear maps [GGH13,GGHRSW13] and provide heuristic guarantees, while bootstrapping based constructions [LV16,Lin17,LT17,AJLMS19,Agr19,JLMS19] rely, in the best case, on bilinear maps as well as new variants of the Learning With Errors (LWE) assumption and pseudorandom generators. Recent times have seen exciting progress in the construction of indistinguishability obfuscation (iO) from bilinear maps (along with other assumptions) [LT17,AJLMS19,JLMS19,Agr19].
As a notable exception, a recent work by Agrawal [Agr19] provided a construction for iO without using any maps. This work identified a new primitive, called Noisy Linear Functional Encryption (NLinFE) that provably suffices for iO and gave a direct construction of NLinFE from new assumptions on lattices. While a preliminary cryptanalysis for the new assumptions was provided in the original work, the author admitted the necessity of performing significantly more cryptanalysis before faith could be placed in the security of the scheme. Moreover, the author did not suggest concrete parameters for the construction.
In this work, we fill this gap by undertaking the task of thorough cryptanalytic study of NLinFE. We design two attacks that let the adversary completely break the security of the scheme. To achieve this, we develop new cryptanalytic techniques which (we hope) will inform future designs of the primitive of NLinFE.
From the knowledge gained by our cryptanalytic study, we suggest modifications to the scheme. We provide a new scheme which overcomes the vulnerabilities identified before. We also provide a thorough analysis of all the security aspects of this scheme and argue why plausible attacks do not work. We additionally provide concrete parameters with which the scheme may be instantiated. We believe the security of NLinFE stands on significantly firmer footing as a result of this work
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