Linear Programming Relaxations for Goldreich's Generators over Non-Binary Alphabets

Goldreich suggested candidates of one-way functions and pseudorandom generators included in $\mathsf{NC}^0$. It is known that randomly generated Goldreich's generator using $(r-1)$-wise independent predicates with $n$ input variables and $m=C n^{r/2}$ output variables is not pseudorandom generator with high probability for sufficiently large constant $C$. Most of the previous works assume that the alphabet is binary and use techniques available only for the binary alphabet. In this paper, we deal with non-binary generalization of Goldreich's generator and derives the tight threshold for linear programming relaxation attack using local marginal polytope for randomly generated Goldreich's generators. We assume that $u(n)\in \omega(1)\cap o(n)$ input variables are known. In that case, we show that when $r\ge 3$, there is an exact threshold $\mu_\mathrm{c}(k,r):=\binom{k}{r}^{-1}\frac{(r-2)^{r-2}}{r(r-1)^{r-1}}$ such that for $m=\mu\frac{n^{r-1}}{u(n)^{r-2}}$, the LP relaxation can determine linearly many input variables of Goldreich's generator if $\mu>\mu_\mathrm{c}(k,r)$, and that the LP relaxation cannot determine $\frac1{r-2} u(n)$ input variables of Goldreich's generator if $\mu<\mu_\mathrm{c}(k,r)$. This paper uses characterization of LP solutions by combinatorial structures called stopping sets on a bipartite graph, which is related to a simple algorithm called peeling algorithm.Comment: 14 pages, 1 figur

Purification and immunochemical characterization of alpha-fetoprotein from rat fetal serum and liver

Two alpha1-globulin bands of fetal serum with relative mobilities against bromophenol blue of 0.55 and 0.58 on 7% polyacrylamide gel electrophoresis reacted with a monospecific rabbit antiserum to alpha-fetoprotein (AFP). The former globulin band was clearly detected in the fetal liver supernatant. AFP was immunochemically purified from both the fetal serum and liver, and their electrophoretic and immunochemical properties were compared. Liver AFP purified by immunoadsorbent column yielded electrophoretic mobilities and relative amounts of the two electrophoretically distinct components identical with the purified serum AFP. The immunological reactivity of the two components of the purified preparations from serum and liver against the monospecific anti-AFP serum was also indistinguishable. After the removal of the sialic acid residues from purified serum and liver AFP by treatment with neuraminidase for 6 to 12 hr, disc electrophoretic patterns on 5% polyacrylamide gel and immunoelectrophoretic patterns of the treated AFP were found to be closely similar in both preparations. It may be possible to conclude that serum and liver AFP are structurally indistinguishable and probably identical.</p

Clinical Applica­tion of Sialic Acid I. On Serum Sialic Acid Contents in Patients

1) The contents of sialic acid in patients of various diseases sera were determined and increases of it were noticed in several diseases. 2) Sialic acid contents ranged between 50 and 100 mg./dl. in the normal serum. 3) But in the pathological serum, it ranged between 90 and 170 mg./dl. in cancer patients, between 80 and 110 mg./dl. in peptic ulcer, between 75 and 135 mg./dl. in arachnoiditis, and between 90 and 120 mg./dl. in epilepsy. 4) In other several diseases, sialic acid contents were determined.</p

Evaluation of the effectiveness of X-ray protective aprons in experimental and practical fields

Few practical evaluation studies have been conducted on X-ray protective aprons in workplaces. We examined the effects of exchanging the protective apron type with regard to exposure reduction in experimental and practical fields, and discuss the effectiveness of X-ray protective aprons. Experimental field evaluations were performed by the measurement of the X-ray transmission rates of protective aprons. Practical field evaluations were performed by the estimation of the differences in the transit doses before and after the apron exchange. A 0.50-mm lead-equivalent-thick non-lead apron had the lowest transmission rate among the 7 protective aprons, but weighed 10.9 kg and was too heavy. The 0.25 and 0.35-mm lead-equivalent-thick non-lead aprons differed little in the practical field of interventional radiology. The 0.35-mm lead apron had lower X-ray transmission rates and transit doses than the 0.25-mm lead-equivalent-thick non-lead apron, and each of these differences exceeded 8 % in the experimental field and approximately 0.15 mSv/month in the practical field of computed tomography (p < 0.01). Therefore, we concluded that the 0.25-mm lead-equivalent-thick aprons and 0.35-mm lead apron are effective for interventional radiology operators and computed tomography nurses, respectively

Issues for application of virtual microscopy to cytoscreening, perspectives based on questionnaire to Japanese cytotechnologists

To clarify the issues associated with the applications of virtual microscopy to the daily cytology slide screening, we conducted a survey at a slide conference of cytology. The survey was conducted specifically to the Japanese cytology technologists who use microscopes on a routine basis. Virtual slides (VS) were prepared from cytology slides using NanoZoomer (Hamamatsu Photonics, Japan), which is capable of adjusting focus on any part of the slide. A total of ten layers were scanned from the same slides, with 2 micrometer intervals. To simulate the cytology slide screening, no marker points were created. The total data volume of six slides was approximately 25 Giga Bytes. The slides were stored on the Windows 2003 Server, and were made accessible on the web to the cytology technologists. Most cytotechnologists answered "Satisfied" or "Acceptable" to the VS resolution and drawing speed, and "Dissatisfied" to the operation speed. To the ten layered focus, an answer "insufficient" was slightly more frequent than the answer "sufficient", while no one answered "fewer is acceptable" or "no need for depth". As for the use of cytology slide screening, answers "usable, but requires effort" and "not usable" were about equal in number. In a Japanese cytology meeting, a unique VS system has been used in slide conferences with markings to the discussion point for years. Therefore, Japanese cytotechnologists are relatively well accustomed to the use of VS, and the survey results showed that they regarded VS more positively than we expected. Currently, VS has the acceptable resolution and drawing speed even on the web. Most cytotechnologists regard the focusing capability crucial for cytology slide screening, but the consequential enlargement of data size, longer scanning time, and slower drawing speed are the issues that are yet to be resolved