Efficient Homomorphic Comparison Methods with Optimal Complexity

Comparison of two numbers is one of the most frequently used operations, but it has been a challenging task to efficiently compute the comparison function in homomorphic encryption (HE) which basically support addition and multiplication. Recently, Cheon et al. (Asiacrypt 2019) introduced a new approximate representation of the comparison function with a rational function, and showed that this rational function can be evaluated by an iterative algorithm. Due to this iterative feature, their method achieves a logarithmic computational complexity compared to previous polynomial approximation methods; however, the computational complexity is still not optimal, and the algorithm is quite slow for large-bit inputs in HE implementation. In this work, we propose new comparison methods with optimal asymptotic complexity based on composite polynomial approximation. The main idea is to systematically design a constant-degree polynomial $f$ by identifying the \emph{core properties} to make a composite polynomial $f\circ f \circ \cdots \circ f$ get close to the sign function (equivalent to the comparison function) as the number of compositions increases. We additionally introduce an acceleration method applying a mixed polynomial composition $f\circ \cdots \circ f\circ g \circ \cdots \circ g$ for some other polynomial $g$ with different properties instead of $f\circ f \circ \cdots \circ f$. Utilizing the devised polynomials $f$ and $g$, our new comparison algorithms only require $\Theta(\log(1/\epsilon)) + \Theta(\log\alpha)$ computational complexity to obtain an approximate comparison result of $a,b\in[0,1]$ satisfying $|a-b|\ge \epsilon$ within $2^{-\alpha}$ error. The asymptotic optimality results in substantial performance enhancement: our comparison algorithm on encrypted $20$-bit integers for $\alpha = 20$ takes $1.43$ milliseconds in amortized running time, which is $30$ times faster than the previous work

Magnetism, FeS colloids, and Origins of Life

A number of features of living systems: reversible interactions and weak bonds underlying motor-dynamics; gel-sol transitions; cellular connected fractal organization; asymmetry in interactions and organization; quantum coherent phenomena; to name some, can have a natural accounting via $physical$ interactions, which we therefore seek to incorporate by expanding the horizons of `chemistry-only' approaches to the origins of life. It is suggested that the magnetic 'face' of the minerals from the inorganic world, recognized to have played a pivotal role in initiating Life, may throw light on some of these issues. A magnetic environment in the form of rocks in the Hadean Ocean could have enabled the accretion and therefore an ordered confinement of super-paramagnetic colloids within a structured phase. A moderate H-field can help magnetic nano-particles to not only overcome thermal fluctuations but also harness them. Such controlled dynamics brings in the possibility of accessing quantum effects, which together with frustrations in magnetic ordering and hysteresis (a natural mechanism for a primitive memory) could throw light on the birth of biological information which, as Abel argues, requires a combination of order and complexity. This scenario gains strength from observations of scale-free framboidal forms of the greigite mineral, with a magnetic basis of assembly. And greigite's metabolic potential plays a key role in the mound scenario of Russell and coworkers-an expansion of which is suggested for including magnetism.Comment: 42 pages, 5 figures, to be published in A.R. Memorial volume, Ed Krishnaswami Alladi, Springer 201

Magnetic Iron Oxide Nanoparticles: Synthesis and Surface Functionalization Strategies

Surface functionalized magnetic iron oxide nanoparticles (NPs) are a kind of novel functional materials, which have been widely used in the biotechnology and catalysis. This review focuses on the recent development and various strategies in preparation, structure, and magnetic properties of naked and surface functionalized iron oxide NPs and their corresponding application briefly. In order to implement the practical application, the particles must have combined properties of high magnetic saturation, stability, biocompatibility, and interactive functions at the surface. Moreover, the surface of iron oxide NPs could be modified by organic materials or inorganic materials, such as polymers, biomolecules, silica, metals, etc. The problems and major challenges, along with the directions for the synthesis and surface functionalization of iron oxide NPs, are considered. Finally, some future trends and prospective in these research areas are also discussed

A genetic cause of Alzheimer disease: mechanistic insights from Down syndrome

Down syndrome, caused by an extra copy of chromosome 21, is associated with a greatly increased risk of early onset Alzheimer disease. It is thought that this risk is conferred by the presence of three copies of the gene encoding amyloid precursor protein (APP), an Alzheimer risk factor, although the possession of extra copies of other chromosome 21 genes may also play a role. Further study of the mechanisms underlying the development of Alzheimer disease in Down syndrome could provide insights into the mechanisms that cause dementia in the general population

Ustekinumab as Induction and Maintenance Therapy for Crohn’s Disease

BACKGROUND Ustekinumab, a monoclonal antibody to the p40 subunit of interleukin-12 and inter-leukin-23, was evaluated as an intravenous induction therapy in two populations with moderately to severely active Crohn’s disease. Ustekinumab was also evaluated as subcutaneous maintenance therapy. METHODS We randomly assigned patients to receive a single intravenous dose of ustekinumab (either 130 mg or approximately 6 mg per kilogram of body weight) or placebo in two induction trials. The UNITI-1 trial included 741 patients who met the criteria for primary or secondary nonresponse to tumor necrosis factor (TNF) antagonists or had unacceptable side effects. The UNITI-2 trial included 628 patients in whom conventional therapy failed or unacceptable side effects occurred. Patients who completed these induction trials then participated in IM-UNITI, in which the 397 patients who had a response to ustekinumab were randomly assigned to receive subcutaneous maintenance injections of 90 mg of ustekinumab (either every 8 weeks or every 12 weeks) or placebo. The primary end point for the induction trials was a clinical response at week 6 (defined as a decrease from baseline in the Crohn’s Disease Activity Index [CDAI] score of ≥100 points or a CDAI score <150). The primary end point for the maintenance trial was remission at week 44 (CDAI score <150). RESULTS The rates of response at week 6 among patients receiving intravenous ustekinumab at a dose of either 130 mg or approximately 6 mg per kilogram were significantly higher than the rates among patients receiving placebo (in UNITI-1, 34.3%, 33.7%, and 21.5%, respectively, with P≤0.003 for both comparisons with placebo; in UNITI-2, 51.7%, 55.5%, and 28.7%, respectively, with P<0.001 for both doses). In the groups receiving maintenance doses of ustekinumab every 8 weeks or every 12 weeks, 53.1% and 48.8%, respectively, were in remission at week 44, as compared with 35.9% of those receiving placebo (P = 0.005 and P = 0.04, respectively). Within each trial, adverse-event rates were similar among treatment groups. CONCLUSIONS Among patients with moderately to severely active Crohn’s disease, those receiving intravenous ustekinumab had a significantly higher rate of response than did those receiving placebo. Subcutaneous ustekinumab maintained remission in patients who had a clinical response to induction therapy. (Funded by Janssen Research and Development; ClinicalTrials.gov numbers, NCT01369329, NCT01369342, and NCT01369355.

Monitoring methionine sulfoxide with stereospecific mechanism-based fluorescent sensors

Methionine can be reversibly oxidized to methionine sulfoxide (MetO) under physiological and pathophysiological conditions, but its use as a redox marker suffers from the lack of tools to detect and quantify MetO within cells. In this work, we created a pair of complementary stereospecific genetically-encoded mechanism-based ratiometric fluorescent sensors of MetO by inserting a circularly yellow fluorescent protein between yeast methionine sulfoxide reductases and thioredoxins. The two sensors, named MetSOx and MetROx for their ability to detect S and R-forms of MetO, respectively, were utilized for targeted analysis of protein oxidation, regulation and repair, as well as for monitoring MetO in bacterial and mammalian cells, analyzing compartment-specific changes in MetO, and examining responses to physiological stimuli