Stopping Sets of Algebraic Geometry Codes

Abstract — Stopping sets and stopping set distribution of a linear code play an important role in the performance analysis of iterative decoding for this linear code. Let C be an [n, k] linear code over Fq with parity-check matrix H, wheretherowsof H may be dependent. Let [n] ={1, 2,...,n} denote the set of column indices of H. Astopping set S of C with parity-check matrix H is a subset of [n] such that the restriction of H to S does not contain a row of weight 1. The stopping set distribution {Ti (H)} n i=0 enumerates the number of stopping sets with size i of C with parity-check matrix H. Denote H ∗ , the paritycheck matrix, consisting of all the nonzero codewords in the dual code C ⊥. In this paper, we study stopping sets and stopping set distributions of some residue algebraic geometry (AG) codes with parity-check matrix H ∗. First, we give two descriptions of stopping sets of residue AG codes. For the simplest AG codes, i.e., the generalized Reed–Solomon codes, it is easy to determine all the stopping sets. Then, we consider the AG codes from elliptic curves. We use the group structure of rational points of elliptic curves to present a complete characterization of stopping sets. Then, the stopping sets, the stopping set distribution, and the stopping distance of the AG code from an elliptic curve are reduced to the search, counting, and decision versions of the subset sum problem in the group of rational points of the elliptic curve, respectively. Finally, for some special cases, we determine the stopping set distributions of the AG codes from elliptic curves. Index Terms — Algebraic geometry codes, elliptic curves, stopping distance, stopping sets, stopping set distribution, subset sum problem. I

Anti-osteoporosis activity of Astragalus membranaceus Bunge extract in experimental rats

Purpose: To investigate the anti-osteoporosis effect of Astragalus membranaceus (Fisch.) Bunge. extract (AMBE) in experimental rats.Method: Female Sprague-Dawley rats were randomly divided into six groups: control group, ovariectomy (OVX) with vehicle group, OVX with 17β-estradiol (E2, 25 μg/kg/day) group, and OVX with AMBE doses (60, 120 and 240 mg/kg/day) groups. Daily oral administration of AMBE or E2 was started 4 weeks after OVX and lasted for 16 weeks. The bone mineral density (BMD) of L4 vertebrae and right femurs was evaluated. The length of each femur was measured with a micrometer, and the center of diaphysis was determined. Three representative L4 vertebrae were selected to evaluate trabecular microarchitecture. Serum alkaline phosphatase (ALP), urinary calcium (U-Ca), urinary phosphorus (UP), urinary creatinine (Cr) and osteocalcin (OC) levels were measured.Results: AMBE dose-dependently inhibited the bone mineral density (BMD) reduction of L4 vertebrae (0.27 ± 0.03 g/cm2, p < 0.05) and femurs (0.23 ± 0.03 g/cm2, p < 0.05) caused by OVX and prevented the deterioration of trabecular microarchitecture (p < 0.05), which were accompanied by a significant decrease in skeletal remodeling (p < 0.05) as evidenced by the lower levels of bone turnover markers. A higher dosage of AMBE treatment (240 mg/kg/day) increased U-Ca/Cr (0.27 ± 0.03 mmol/mmol), ALP (137.23 ± 16.72 U/L), U-P/Cr (4.18 ± 0.27 mmol/mmol) and OC (8.47 ± 0.26 mmol/L) levels (both p < 0.05).Conclusion: The findings of this study indicate that AMBE prevents OVX-induced osteoporosis in rats.Keywords: Astragalus membranaceus (Fisch.) Bunge, Osteoporosis, Ovariectomy, Bone mineral densit

Acoustic Emission from Porous Collapse and Moving Dislocations in Granular Mg-Ho Alloys under Compression and Tension.

We identified heterogeneous Mg-Ho alloys as an ideal material to measure the most extensive acoustic emission spectra available. Mg-Ho alloys are porous and show a high density of dislocations, which slide under external tension and compression. These dislocations nucleate near numerous heterogeneities. Two mechanisms compete under external forcing in the structural collapse, namely collapsing holes and the movements of dislocations. Their respective fingerprints in acoustic emission (AE) measurements are very different and relate to their individual signal strengths. Porous collapse generates very strong AE signals while dislocation movements create more but weaker AE signals. This allows the separation of the two processes even though they almost always coincide temporarily. The porous collapse follows approximately mean-field behavior (ε = 1.4, τ' = 1.82, α = 2.56, x = 1.93, χ = 1.95) with mean field scaling fulfilled. The exponents for dislocation movement are greater (ε = 1.92, τ' = 2.44, α = 3.0, x = 1.7, χ = 1.42) and follows approximately the force integrated mean-field predictions. The Omori scaling is similar for both mechanisms. The Bath's law is well fulfilled for the porous collapse but not for the dislocation movements. We suggest that such 'complex' mixing behavior is dominant in many other complex materials such as (multi-) ferroics, entropic alloys and porous ferroelastics, and, potentially, homogeneous materials with the simultaneous appearance of different collapse mechanisms.We appreciate the support of the Natural Science Foundation of China (51320105014, 51621063) and 111 project 2.0 (BP2018008). EKHS is grateful to EPSRC (EP/P024904/1) and the Leverhulme trust (RPG-2012-564)

LungTrack: towards contactless and zero dead-zone respiration monitoring with commodity RFIDs

International audienceRespiration rate sensing plays a critical role in elderly care and patient monitoring. The latest research has explored the possibility of employing Wi-Fi signals for respiration sensing without attaching a device to the target. A critical issue with these solutions includes that good monitoring performance could only be achieved at certain locations within the sensing range, while the performance could be quite poor at other "dead zones." In addition, due to the contactless nature, it is challenging to monitor multiple targets simultaneously as the reflected signals are often mixed together. In this work, we present our system, named LungTrack, hosted on commodity RFID devices for respiration monitoring. Our system retrieves subtle signal fluctuations at the receiver caused by chest displacement during respiration without need for attaching any devices to the target. It addresses the dead-zone issue and enables simultaneous monitoring of two human targets by employing one RFID reader and carefully positioned multiple RFID tags, using an optimization technique. Comprehensive experiments demonstrate that LungTrack can achieve a respiration monitoring accuracy of greater than 98% for a single target at all sensing locations (within 1 st − 5 th Fresnel zones) using just one RFID reader and five tags, when the target's orientation is known a priori. For the challenging scenario involve two human targets, LungTrack is able to achieve greater than 93% accuracy when the targets are separated by at least 10 cm

Acoustic Emission from Porous Collapse and Moving Dislocations in Granular Mg-Ho Alloys under Compression and Tension

We identified heterogeneous Mg-Ho alloys as an ideal material to measure the most extensive acoustic emission spectra available. Mg-Ho alloys are porous and show a high density of dislocations, which slide under external tension and compression. These dislocations nucleate near numerous heterogeneities. Two mechanisms compete under external forcing in the structural collapse, namely collapsing holes and the movements of dislocations. Their respective fingerprints in acoustic emission (AE) measurements are very different and relate to their individual signal strengths. Porous collapse generates very strong AE signals while dislocation movements create more but weaker AE signals. This allows the separation of the two processes even though they almost always coincide temporarily. The porous collapse follows approximately mean-field behavior (ε = 1.4, τ’ = 1.82, α = 2.56, x = 1.93, χ = 1.95) with mean field scaling fulfilled. The exponents for dislocation movement are greater (ε = 1.92, τ’ = 2.44, α = 3.0, x = 1.7, χ = 1.42) and follows approximately the force integrated mean-field predictions. The Omori scaling is similar for both mechanisms. The Bath’s law is well fulfilled for the porous collapse but not for the dislocation movements. We suggest that such ‘complex’ mixing behavior is dominant in many other complex materials such as (multi-) ferroics, entropic alloys and porous ferroelastics, and, potentially, homogeneous materials with the simultaneous appearance of different collapse mechanisms