Finite-Length Scaling of Polar Codes

Consider a binary-input memoryless output-symmetric channel $W$. Such a channel has a capacity, call it $I(W)$, and for any $R<I(W)$ and strictly positive constant $P_{\rm e}$ we know that we can construct a coding scheme that allows transmission at rate $R$ with an error probability not exceeding $P_{\rm e}$. Assume now that we let the rate $R$ tend to $I(W)$ and we ask how we have to "scale" the blocklength $N$ in order to keep the error probability fixed to $P_{\rm e}$. We refer to this as the "finite-length scaling" behavior. This question was addressed by Strassen as well as Polyanskiy, Poor and Verdu, and the result is that $N$ must grow at least as the square of the reciprocal of $I(W)-R$. Polar codes are optimal in the sense that they achieve capacity. In this paper, we are asking to what degree they are also optimal in terms of their finite-length behavior. Our approach is based on analyzing the dynamics of the un-polarized channels. The main results of this paper can be summarized as follows. Consider the sum of Bhattacharyya parameters of sub-channels chosen (by the polar coding scheme) to transmit information. If we require this sum to be smaller than a given value $P_{\rm e}>0$, then the required block-length $N$ scales in terms of the rate $R < I(W)$ as $N \geq \frac{\alpha}{(I(W)-R)^{\underline{\mu}}}$, where $\alpha$ is a positive constant that depends on $P_{\rm e}$ and $I(W)$, and $\underline{\mu} = 3.579$. Also, we show that with the same requirement on the sum of Bhattacharyya parameters, the block-length scales in terms of the rate like $N \leq \frac{\beta}{(I(W)-R)^{\overline{\mu}}}$, where $\beta$ is a constant that depends on $P_{\rm e}$ and $I(W)$, and $\overline{\mu}=6$.Comment: In IEEE Transactions on Information Theory, 201

Vaccination of rainbow trout against Streptococcus iniae infection: comparison of different routes of administration and different vaccines

Antibody production and clinical efficacy (relative percent survival RPS) were measured in 40±5g rainbow trout after immunization with two types of Streptococcus iniae vaccines consisting of formalin killed cells (FKC) and FKC enriched with the bacterial extracellular products (ECP) administered by intraperitoneal (i.p), immersion and oral routes at 16±1°C for 18 weeks. No significant difference was found in antibody levels among the fish i.p immunized with FKC enriched with ECP plus Freunds' adjuvant (FA), FKC plus FA and FKC vaccines (P>0.05), whilst the antibody production was significantly higher in these three groups than fish immunized by immersion and oral routes of FKC and FKC enriched ECP (P0.05). The RPSs ranging 82.6-100, 73.9-95 and 73.9-91.7% were obtained in the fish intraperitoneally immunized with FKC enriched ECP plus FA, FKC plus FA and FKC vaccines, respectively, compared to 0% survival for the control fish. Also, RPS in fish vaccinated by the immersion route was in the range 45.8-30.4% after 18 weeks post-vaccination. Efficacy of oral vaccination of fish with FKC plus ECP was in range of 8.7-29% and that of fish orally vaccinated with FKC resulted in 8.7-20.8% protection

Application of superconducting coils to the NASA prototype magnetic balance

Application of superconducting coils to a general purpose magnetic balance was studied. The most suitable currently available superconducting cable for coils appears to be a bundle of many fine wires which are transposed and are mechanically confined. Sample coils were tested at central fields up to .5 Tesla, slewing rates up to 53 Tesla/ sec and frequencies up to 30 Hz. The ac losses were measured from helium boil-off and were approximately 20% higher than those calculated. Losses were dominated by hysteresis and a model for loss calculation which appears suitable for design purposes is presented along with computer listings. Combinations of two coils were also tested and interaction losses are reported. Two feasible geometries are also presented for prototype magnetic balance using superconductors

Evaluation of the toxicity of magnetite (Fe3O4) nanoparticle aqueous suspensions on bio-indices of sea water (barnacle) and fresh water (rotifer)

Due to the inevitable achievement of nanoparticles to aquatic ecosystems, the limitation of existing reports, and the inadequate understanding of their possible biological reactions with aquatic organisms, this study in the pioneering step was aimed to toxicity assessment of aqueous suspension of chemical magnetic nanoparticles (Fe3O4) in zooplanktonic species such as barnacle larvae Amphibalanus amphitrite (sea water index) and rotifer Brachionus rotundiformis (fresh water index). For this purpose, serial concentrations (0, 10, 50, 100, 200, 500 mg / l) of magnetite nanoparticles were prepared in 24 well plates with 5 replicates. After that, the zooplanktons (50 barnacle nauplii and 20 neonate rotifer to each well) were introduced to plates and the sensitivity of the samples were evaluated for the toxicity of nanoparticles at a time interval of 12-48 hours. The results of this study showed that the toxicity effects of chemical magnetite nanoparticles on barnacle nauplii larvae and neonate rotifer were increased with increasing time and concentration of magnetite nanoparticles. Differences between control and treatment groups were significant (P1000 mg/l). Regardless of species variation in barnacles and rotifers, according to the results, magnetite nanoparticles are in the group of non-toxic contaminants for these zooplanktonic organisms

The efficacy and safety of ketamine for depression in patients with cancer: A systematic review

Management of depression in the oncology population includes supportive psychotherapeutic interventions with or without psychotropic medication, which take time to demonstrate effectiveness. Fast-acting interventions, like ketamine, can provide a rapid antidepressant effect; however, there has been limited research on effects of ketamine among cancer patients. The objective of this review is to provide an overview of research on the efficacy and safety of ketamine on depression in patients with cancer. We reviewed the published literature in MEDLINE® (via PubMed®), EMBASE, and Scopus from 1 January 1982 to 20 October 2022. We screened the retrieved abstracts against inclusion criteria and conducted a full-text review of eligible studies. Following extraction of data from included studies, we used a framework analysis approach to summarize the evidence on using ketamine in patients with cancer. All 5 included studies were randomized clinical trials conducted in inpatient settings in China. In all included studies ketamine was administered intravenously. Three studies used only racemic ketamine, and two studies used both S-ketamine and racemic ketamine. All included studies reported ketamine a tolerable and effective drug to control depression symptoms. Included studies showed administration of sub-anesthesia ketamine significantly improves postoperative depression among patients with cancer. [Abstract copyright: © 2023 The Author(s).