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 $\textsf{NP}$, and the problem "is a network subset atomic with respect to a given atom set" is strongly $\textsf{NP}$-$\textsf{Complete}$. 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 $\textbf{polynomial-time algorithm}$ to decide whether a given network is reachably atomic, improving upon the result of Adleman et al. that the problem is $\textbf{decidable}$. We show that the reachability problem for reachably atomic networks is $\textsf{Pspace}$-$\textsf{Complete}$. 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