Randomized comparison of the effects of the vitamin D(3 )adequate intake versus 100 mcg (4000 IU) per day on biochemical responses and the wellbeing of patients

BACKGROUND: For adults, vitamin D intake of 100 mcg (4000 IU)/day is physiologic and safe. The adequate intake (AI) for older adults is 15 mcg (600 IU)/day, but there has been no report focusing on use of this dose. METHODS: We compared effects of these doses on biochemical responses and sense of wellbeing in a blinded, randomized trial. In Study 1, 64 outpatients (recruited if summer 2001 25(OH)D <61 nmol/L) were given 15 or 100 mcg/day vitamin D in December 2001. Biochemical responses were followed at subsequent visits that were part of clinical care; 37 patients completed a wellbeing questionnaire in December 2001 and February 2002. Subjects for Study 2 were recruited if their 25(OH)D was <51 nmol/L in summer 2001. 66 outpatients were given vitamin D; 51 completed a wellbeing questionnaire in both December 2002 and February 2003. RESULTS: In Study 1, basal summer 25-hydroxyvitamin D [25(OH)D] averaged 48 ± 9 (SD) nmol/L. Supplementation for more than 6 months produced mean 25(OH)D levels of 79 ± 30 nmol/L for the 15 mcg/day group, and 112 ± 41 nmol/L for the 100 mcg/day group. Both doses lowered plasma parathyroid hormone with no effect on plasma calcium. Between December and February, wellbeing score improved more for the 100-mcg/day group than for the lower-dosed group (1-tail Mann-Whitney p = 0.036). In Study 2, 25(OH)D averaged 39 ± 9 nmol/L, and winter wellbeing scores improved with both doses of vitamin D (two-tail p < 0.001). CONCLUSION: The highest AI for vitamin D brought summertime 25(OH)D to >40 nmol/L, lowered PTH, and its use was associated with improved wellbeing. The 100 mcg/day dose produced greater responses. Since it was ethically necessary to provide a meaningful dose of vitamin D to these insufficient patients, we cannot rule out a placebo wellbeing response, particularly for those on the lower dose. This work confirms the safety and efficacy of both 15 and 100 mcg/day vitamin D(3 )in patients who needed additional vitamin D

Quasi-Optimal SNARGs via Linear Multi-Prover Interactive Proofs

Succinct non-interactive arguments (SNARGs) enable verifying NP computations with significantly less complexity than that required for classical NP verification. In this work, we focus on simultaneously minimizing the proof size and the prover complexity of SNARGs. Concretely, for a security parameter $\lambda$, we measure the asymptotic cost of achieving soundness error $2^{-\lambda}$ against provers of size $2^\lambda$. We say a SNARG is quasi-optimally succinct if its proof length is $\tilde{O}(\lambda)$, and that it is quasi-optimal, if moreover, its prover complexity is only polylogarithmically greater than the running time of the classical NP prover. We show that this definition is the best we could hope for assuming that NP does not have succinct proofs. Our definition strictly strengthens the previous notion of quasi-optimality introduced in the work of Boneh et al. (Eurocrypt 2017). This work gives the first quasi-optimal SNARG for Boolean circuit satisfiability from a concrete cryptographic assumption. Our construction takes a two-step approach. The first is an information-theoretic construction of a quasi-optimal linear multi-prover interactive proof (linear MIP) for circuit satisfiability. Then, we describe a generic cryptographic compiler that transforms our quasi-optimal linear MIP into a quasi-optimal SNARG by relying on the notion of linear-only vector encryption over rings introduced by Boneh et al. Combining these two primitives yields the first quasi-optimal SNARG based on linear-only vector encryption. Moreover, our linear MIP construction leverages a new robust circuit decomposition primitive that allows us to decompose a circuit satisfiability instance into several smaller circuit satisfiability instances. This primitive may be of independent interest. Finally, we consider (designated-verifier) SNARGs that provide optimal succinctness for a non-negligible soundness error. Concretely, we put forward the notion of 1-bit SNARGs that achieve soundness error 1/2 with only one bit of proof. We first show how to build 1-bit SNARGs from indistinguishability obfuscation, and then show that 1-bit SNARGs also suffice for realizing a form of witness encryption. The latter result highlights a two-way connection between the soundness of very succinct argument systems and powerful forms of encryption