Facial structures for various notions of positivity and applications to the theory of entanglement

In this expository note, we explain facial structures for the convex cones consisting of positive linear maps, completely positive linear maps, decomposable positive linear maps between matrix algebras, respectively. These will be applied to study the notions of entangled edge states with positive partial transposes and optimality of entanglement witnesses.Comment: An expository note. Section 7 and Section 8 have been enlarge

Security bound of two-bases quantum key-distribution protocols using qudits

We investigate the security bounds of quantum cryptographic protocols using $d$-level systems. In particular, we focus on schemes that use two mutually unbiased bases, thus extending the BB84 quantum key distribution scheme to higher dimensions. Under the assumption of general coherent attacks, we derive an analytic expression for the ultimate upper security bound of such quantum cryptography schemes. This bound is well below the predictions of optimal cloning machines. The possibility of extraction of a secret key beyond entanglement distillation is discussed. In the case of qutrits we argue that any eavesdropping strategy is equivalent to a symmetric one. For higher dimensions such an equivalence is generally no longer valid.Comment: 12 pages, 2 figures, to appear in Phys. Rev.

Quantitative analysis of cell types during growth and morphogenesis in Hydra

Tissue maceration was used to determine the absolute number and the distribution of cell types in Hydra. It was shown that the total number of cells per animal as well as the distribution of cells vary depending on temperature, feeding conditions, and state of growth. During head and foot regeneration and during budding the first detectable change in the cell distribution is an increase in the number of nerve cells at the site of morphogenesis. These results and the finding that nerve cells are most concentrated in the head region, diminishing in density down the body column, are discussed in relation to tissue polarity

Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

On Approximately Symmetric Informationally Complete Positive Operator-Valued Measures and Related Systems of Quantum States

We address the problem of constructing positive operator-valued measures (POVMs) in finite dimension $n$ consisting of $n^2$ operators of rank one which have an inner product close to uniform. This is motivated by the related question of constructing symmetric informationally complete POVMs (SIC-POVMs) for which the inner products are perfectly uniform. However, SIC-POVMs are notoriously hard to construct and despite some success of constructing them numerically, there is no analytic construction known. We present two constructions of approximate versions of SIC-POVMs, where a small deviation from uniformity of the inner products is allowed. The first construction is based on selecting vectors from a maximal collection of mutually unbiased bases and works whenever the dimension of the system is a prime power. The second construction is based on perturbing the matrix elements of a subset of mutually unbiased bases. Moreover, we construct vector systems in \C^n which are almost orthogonal and which might turn out to be useful for quantum computation. Our constructions are based on results of analytic number theory.Comment: 29 pages, LaTe

Information-bit error rate and false positives in an MDS code

In this paper, a refinement of the weight distribution in an MDS code is computed. Concretely, the number of codewords with a fixed amount of nonzero bits in both information and redundancy parts is obtained. This refinement improves the theoretical approximation of the information-bit and -symbol error rate, in terms of the channel bit-error rate, in a block transmission through a discrete memoryless channel. Since a bounded distance reproducing encoder is assumed, the computation of the here-called false positive (a decoding failure with no information-symbol error) is provided. As a consequence, a new performance analysis of an MDS code is proposed

Validation and Clinical Applicability of Whole-Volume Automated Segmentation of Optical Coherence Tomography in Retinal Disease Using Deep Learning.

IMPORTANCE: Quantitative volumetric measures of retinal disease in optical coherence tomography (OCT) scans are infeasible to perform owing to the time required for manual grading. Expert-level deep learning systems for automatic OCT segmentation have recently been developed. However, the potential clinical applicability of these systems is largely unknown. OBJECTIVE: To evaluate a deep learning model for whole-volume segmentation of 4 clinically important pathological features and assess clinical applicability. DESIGN, SETTING, AND PARTICIPANTS: This diagnostic study used OCT data from 173 patients with a total of 15 558 B-scans, treated at Moorfields Eye Hospital. The data set included 2 common OCT devices and 2 macular conditions: wet age-related macular degeneration (107 scans) and diabetic macular edema (66 scans), covering the full range of severity, and from 3 points during treatment. Two expert graders performed pixel-level segmentations of intraretinal fluid, subretinal fluid, subretinal hyperreflective material, and pigment epithelial detachment, including all B-scans in each OCT volume, taking as long as 50 hours per scan. Quantitative evaluation of whole-volume model segmentations was performed. Qualitative evaluation of clinical applicability by 3 retinal experts was also conducted. Data were collected from June 1, 2012, to January 31, 2017, for set 1 and from January 1 to December 31, 2017, for set 2; graded between November 2018 and January 2020; and analyzed from February 2020 to November 2020. MAIN OUTCOMES AND MEASURES: Rating and stack ranking for clinical applicability by retinal specialists, model-grader agreement for voxelwise segmentations, and total volume evaluated using Dice similarity coefficients, Bland-Altman plots, and intraclass correlation coefficients. RESULTS: Among the 173 patients included in the analysis (92 [53%] women), qualitative assessment found that automated whole-volume segmentation ranked better than or comparable to at least 1 expert grader in 127 scans (73%; 95% CI, 66%-79%). A neutral or positive rating was given to 135 model segmentations (78%; 95% CI, 71%-84%) and 309 expert gradings (2 per scan) (89%; 95% CI, 86%-92%). The model was rated neutrally or positively in 86% to 92% of diabetic macular edema scans and 53% to 87% of age-related macular degeneration scans. Intraclass correlations ranged from 0.33 (95% CI, 0.08-0.96) to 0.96 (95% CI, 0.90-0.99). Dice similarity coefficients ranged from 0.43 (95% CI, 0.29-0.66) to 0.78 (95% CI, 0.57-0.85). CONCLUSIONS AND RELEVANCE: This deep learning-based segmentation tool provided clinically useful measures of retinal disease that would otherwise be infeasible to obtain. Qualitative evaluation was additionally important to reveal clinical applicability for both care management and research

Efficient implementation of a CCA2-secure variant of McEliece using generalized Srivastava codes

International audienceIn this paper we present efficient implementations of McEliece variants using quasi-dyadic codes. We provide secure parameters for a classical McEliece encryption scheme based on quasi-dyadic generalized Srivastava codes, and successively convert our scheme to a CCA2-secure protocol in the random oracle model applying the Fujisaki-Okamoto transform. In contrast with all other CCA2-secure code-based cryptosystems that work in the random oracle model, our conversion does not require a constant weight encoding function. We present results for both 128-bit and 80-bit security level, and for the latter we also feature an implementation for an embedded device

Assessment of the centre of pressure pattern and moments about S2 in scoliotic subjects during normal walking

Background Context: Research employing gait measurements indicate asymmetries in ground reaction forces and suggest relationships between these asymmetries, neurological dysfunction and spinal deformity. Although, studies have documented the use of centre of pressure (CoP) and net joint moments in gait assessment and have assessed centre of mass (CoM)-CoP distance relationships in clinical conditions, there is a paucity of information relating to the moments about CoM. It is commonly considered that CoM is situated around S2 vertebra in normal upright posture and hence this study uses S2 vertebral prominence as reference point relative to CoM. Purpose: To assess and establish asymmetry in the CoP pattern and moments about S2 vertebral prominence during level walking and its relationship to spinal deformity in adolescents with scoliosis. Patient sample: Nine Adolescent Idiopathic Scoliosis subjects (8 females and 1 male with varying curve magnitudes and laterality) scheduled for surgery within 2-3 days after data collection, took part in this study. Outcome measures: Kinetic and Kinematic Gait assessment was performed with an aim to estimate the CoP displacement and the moments generated by the ground reaction force about the S2 vertebral prominence during left and right stance during normal walking. Methods: The study employed a strain gauge force platform to estimate the medio-lateral and anterior-posterior displacement of COP and a six camera motion analysis system to track the reflective markers to assess the kinematics. The data were recorded simultaneously. Results: Results indicate wide variations in the medio lateral direction CoP, which could be related to the laterality of both the main and compensation curves. This variation is not evident in the anterior-posterior direction. Similar results were recorded for moments about S2 vertebral prominence. Subjects with higher left compensation curve had greater displacement to the left. Conclusion: Although further longitudinal studies are needed, results indicate that the variables identified in this study are applicable to initial screening and surgical evaluation of scoliosis. © 2008 Chockalingam et al; licensee BioMed Central Ltd