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

Finite-State Dimension and Lossy Decompressors

This paper examines information-theoretic questions regarding the difficulty of compressing data versus the difficulty of decompressing data and the role that information loss plays in this interaction. Finite-state compression and decompression are shown to be of equivalent difficulty, even when the decompressors are allowed to be lossy. Inspired by Kolmogorov complexity, this paper defines the optimal *decompression *ratio achievable on an infinite sequence by finite-state decompressors (that is, finite-state transducers outputting the sequence in question). It is shown that the optimal compression ratio achievable on a sequence S by any *information lossless* finite state compressor, known as the finite-state dimension of S, is equal to the optimal decompression ratio achievable on S by any finite-state decompressor. This result implies a new decompression characterization of finite-state dimension in terms of lossy finite-state transducers.Comment: We found that Theorem 3.11, which was basically the motive for this paper, was already proven by Sheinwald, Ziv, and Lempel in 1991 and 1995 paper

Aortic Root Replacement With Biological Valved Conduits

none9The execution of Bentall procedures using biological valved conduits is expanding owing to the increased incidence of aortic valve and root diseases in the aging population. To review the available data, a systematic search identified 29 studies with a total of 3,298 patients. Although evidence on short-term results suggested favorable outcomes after biological Bentall operations, data beyond 5 years are limited and highlight the urgent need for further investigations with longer follow-up.openCastrovinci, Sebastiano; Tian, David H; Murana, Giacomo; Cefarelli, Mariano; Berretta, Paolo; Alfonsi, Jacopo; Yan, Tristan D; Di Bartolomeo, Roberto; Di Eusanio, MarcoCastrovinci, Sebastiano; Tian, David H; Murana, Giacomo; Cefarelli, Mariano; Berretta, Paolo; Alfonsi, Jacopo; Yan, Tristan D; Di Bartolomeo, Roberto; Di Eusanio, Marc

Optimal Information Encoding in Chemical Reaction Networks

Discrete chemical reaction networks formalize the interactions of molecular species in a well-mixed solution as stochastic events. Given their basic mathematical and physical role, the computational power of chemical reaction networks has been widely studied in the molecular programming and distributed computing communities. While for Turing-universal systems there is a universal measure of optimal information encoding based on Kolmogorov complexity, chemical reaction networks are not Turing universal unless error and unbounded molecular counts are permitted. Nonetheless, here we show that the optimal number of reactions to generate a specific count x ? ? with probability 1 is asymptotically equal to a "space-aware" version of the Kolmogorov complexity of x, defined as K?s(x) = min_p {|p|/log|p| + log(space(?(p))) : ?(p) = x}, where p is a program for universal Turing machine ?. This version of Kolmogorov complexity incorporates not just the length of the shortest program for generating x, but also the space usage of that program. Probability 1 computation is captured by the standard notion of stable computation from distributed computing, but we limit our consideration to chemical reaction networks obeying a stronger constraint: they "know when they are done" in the sense that they produce a special species to indicate completion. As part of our results, we develop a module for encoding and unpacking any b bits of information via O(b/log{b}) reactions, which is information-theoretically optimal for incompressible information. Our work provides one answer to the question of how succinctly chemical self-organization can be encoded - in the sense of generating precise molecular counts of species as the desired state

Who Are the Remaining Uninsured and Why Haven't They Signed Up for Coverage? Findings from the Commonwealth Fund Affordable Care Act Tracking Survey, FebruaryApril 2016

The number of uninsured people in the United States has declined by an estimated 20 million since the Affordable Care Act went into effect in 2010. Yet, an estimated 24 million people still lack health insurance. Goal: To examine the characteristics of the remaining uninsured adults and their reasons for not enrolling in marketplace plans or Medicaid. Methods: Analysis of the Commonwealth Fund ACA Tracking Survey, February–April 2016. Key findings and conclusions: There have been notable shifts in the demographic composition of the uninsured since the law's major coverage expansions went into effect in 2014. Latinos have become a growing share of the uninsured, rising from 29 percent in 2013 to 40 percent in 2016. Whites have become a declining share, falling from half the uninsured in 2013 to 41 percent in 2016. The uninsured are very poor: 39 percent of uninsured adults have incomes below the federal poverty level, twice the rate of their overall representation in the adult population. Of uninsured adults who are aware of the marketplaces or who have tried to enroll for coverage, the majority point to affordability concerns as a reason for not signing up

EPR and Structural Characterization of Water-Soluble Mn2+-Doped Si Nanoparticles.

Water-soluble poly(allylamine) Mn2+-doped Si (SiMn) nanoparticles (NPs) were prepared and show promise for biologically related applications. The nanoparticles show both strong photoluminescence and good magnetic resonance contrast imaging. The morphology and average diameter were obtained through transmission electron microscopy (TEM) and high-resolution transmission electron microscopy (HRTEM); spherical crystalline Si NPs with an average diameter of 4.2 ± 0.7 nm were observed. The doping maximum obtained through this process was an average concentration of 0.4 ± 0.3% Mn per mole of Si. The water-soluble SiMn NPs showed a strong photoluminescence with a quantum yield up to 13%. The SiMn NPs had significant T1 contrast with an r1 relaxivity of 11.1 ± 1.5 mM-1 s-1 and r2 relaxivity of 32.7 ± 4.7 mM-1 s-1 where the concentration is in mM of Mn2+. Dextran-coated poly(allylamine) SiMn NPs produced NPs with T1 and T2 contrast with a r1 relaxivity of 27.1 ± 2.8 mM-1 s-1 and r2 relaxivity of 1078.5 ± 1.9 mM-1 s-1. X-band electron paramagnetic resonance spectra are fit with a two-site model demonstrating that there are two types of Mn2+ in these NP's. The fits yield hyperfine splittings (A) of 265 and 238 MHz with significant zero field splitting (D and E terms). This is consistent with Mn in sites of symmetry lower than tetrahedral due to the small size of the NP's