Algebraic Properties of Riemannian Manifolds

Algebraic properties are explored for the curvature tensors of Riemannian manifolds, using the irreducible decomposition of curvature tensors. Our method provides a powerful tool to analyze the irreducible basis as well as an algorithm to determine the linear dependence of arbitrary Riemann polynomials. We completely specify 13 independent basis elements for the quartic scalars and explicitly find 13 linear relations among 26 scalar invariants. Our method provides several completely new results, including some clues to identify 23 independent basis elements from 90 quintic scalars, that are difficult to find otherwise.Comment: A few typos corrected; 40 pages (4 appendices: 16 pages). To appear in General Relativity and Gravitatio

Ample Pairs

We show that the ample degree of a stable theory with trivial forking is preserved when we consider the corresponding theory of belles paires, if it exists. This result also applies to the theory of $H$-structures of a trivial theory of rank $1$.Comment: Research partially supported by the program MTM2014-59178-P. The second author conducted research with support of the programme ANR-13-BS01-0006 Valcomo. The third author would like to thank the European Research Council grant 33882

Optimal Aeration Management Strategy for A Small-Scale Food Waste Composting

Food waste is a significant contributor to greenhouse gas emissions when it ends up in landfills. Composting is a sustainable solution to this problem, but it requires controlled and continuous airflow for optimal performance. The objective of this study is to investigate the effect of aeration rates and airflow directions on food waste composting using a closed system with forced aeration. Air was entered into the composting vessel in three directions, which were upward, downward, and a combination of both directions. Each direction was run at aeration rates of 0.1, 0.4, and 0.7 L/min. The findings show that the compost pile aerated at 0.4 L/min by using two-directional airflow can reach the thermophilic temperature within half of the day. The compost pile achieved temperature of 40.94°C after 10.5 hours. Although the compost experienced slightly high in moisture loss (4.3%), the compost still attained the standard values for maturity. The compost produced from food waste could be applied in soil to improve its fertility

Algorithmic Views of Vectorized Polynomial Multipliers for NTRU and NTRU Prime (Long Paper)

This paper explores the design space of vector-optimized polynomial multiplications in the lattice-based key-encapsulation mechanisms NTRU and NTRU Prime. Since NTRU and NTRU Prime do not support straightforward applications of number– theoretic transforms, the state-of-the-art vector code either resorted to Toom–Cook, or introduced various techniques for coefficient ring extensions. All these techniques lead to a large number of small-degree polynomial multiplications, which is the bottleneck in our experiments. For NTRU Prime, we show how to reduce the number of small-degree polynomial multiplications to nearly 1/4 times compared to the previous vectorized code with the same functionality. Our transformations are based on careful choices of FFTs, including Good–Thomas, Rader’s, Schönhage’s, and Bruun’s FFTs. For NTRU, we show how to deploy Toom-5 with 3-bit losses. Furthermore, we show that the Toeplitz matrix–vector product naturally translates into efficient implementations with vector-by-scalar multiplication instructions which do not appear in all prior vector-optimized implementations. We choose the ARM Cortex-A72 CPU which implements the Armv8-A architecture for experiments, because of its wide uses in smartphones, and also the Neon vector instruction set implementing vector-by-scalar multiplications that do not appear in most other vector instruction sets like Intel’s AVX2. Even for platforms without vector-by-scalar multiplications, we expect significant improvements compared to the state of the art, since our transformations reduce the number of multiplication instructions by a large margin. Compared to the state-of-the-art optimized implementations, we achieve 2.18× and 6.7× faster polynomial multiplications for NTRU and NTRU Prime, respectively. For full schemes, we additionally vectorize the polynomial inversions, sorting network, and encoding/decoding subroutines in NTRU and NTRU Prime. For ntruhps2048677, we achieve 7.67×, 2.48×, and 1.77× faster key generation, encapsulation, and decapsulation, respectively. For ntrulpr761, we achieve 3×, 2.87×, and 3.25× faster key generation, encapsulation, and decapsulation, respectively. For sntrup761, there are no previously optimized implementations and we significantly outperform the reference implementation

Cerebral fat embolism after bilateral total knee replacement arthroplasty -A case report-

Fat embolism syndrome is a rare and potentially lethal complication most commonly seen in long bone fractures and intramedullary manipulation. The clinical triad of fat embolism syndrome consists of mental confusion, respiratory distress, and petechiae. This study reports a case of cerebral fat embolism syndrome following elective bilateral total knee replacement. After an uneventful anesthesia and initial recovery, the patient developed neurologic symptoms nine hours postoperatively

Chronic hepatitis virus infection in patients with multiple myeloma: clinical characteristics and outcomes

OBJECTIVES: Cytotoxic agents and steroids are used to treat lymphoid malignancies, but these compounds may exacerbate chronic viral hepatitis. For patients with multiple myeloma, the impact of preexisting hepatitis virus infection is unclear. The aim of this study is to explore the characteristics and outcomes of myeloma patients with chronic hepatitis virus infection. METHODS: From 2003 to 2008, 155 myeloma patients were examined to determine their chronic hepatitis virus infection statuses using serologic tests for the hepatitis B (HBV) and C viruses (HCV). Clinical parameters and outcome variables were retrieved via a medical chart review. RESULTS: The estimated prevalences of chronic HBV and HCV infections were 11.0% (n = 17) and 9.0% (n = 14), respectively. The characteristics of patients who were hepatitis virus carriers and those who were not were similar. However, carrier patients had a higher prevalence of conventional cytogenetic abnormalities (64.3% vs. 25.0%). The cumulative incidences of grade 3-4 elevation of the level of alanine transaminase, 30.0% vs. 12.0%, and hyperbilirubinemia, 20.0% vs. 1.6%, were higher in carriers as well. In a Kaplan-Meier analysis, carrier patients had worse overall survival (median: 16.0 vs. 42.4 months). The prognostic value of carrier status was not statistically significant in the multivariate analysis, but an age of more than 65 years old, the presence of cytogenetic abnormalities, a beta-2-microglobulin level of more than 3.5 mg/L, and a serum creatinine level of more than 2 mg/ dL were independent factors associated with poor prognosis. CONCLUSION: Myeloma patients with chronic hepatitis virus infections might be a distinct subgroup, and close monitoring of hepatic adverse events should be mandatory

YamSat: the First Picosatellite being Developed in Taiwan

This paper describes the current planning and design of the YamSat, the first picosatellite being developed in Taiwan. The design, analysis, manufacture, integration, test and operation of the YamSat will be performed by the National Space Program Office (NSPO), Taiwan, R.O.C, in cooperation with other domestic organizations and companies. It is a member of the CubeSat [1], 10cm x 10cm x 10cm size and within 1kg mass. The major objective of the YamSat is to qualify in space the components and technology developed in Taiwan, including a micro-spectrometer payload using Micro Electro Mechanical Systems (MEMS) technology. The YamSat will be ready for flight in the middle of 2002

Quantifying sediment mass redistribution from joint time-lapse gravimetry and photogrammetry surveys

The accurate quantification of sediment mass redistribution is central to the study of surface processes, yet it remains a challenging task. Here we test a new combination of terrestrial gravity and drone photogrammetry methods to quantify sediment mass redistribution over a 1 km2 area. Gravity and photogrammetry are complementary methods. Indeed, gravity changes are sensitive to mass changes and to their location. Thus, by using photogrammetry data to constrain this location, the sediment mass can be properly estimated from the gravity data. We carried out three joint gravimetry–photogrammetry surveys, once a year in 2015, 2016 and 2017, over a 1 km^2 area in southern Taiwan, featuring both a wide meander of the Laonong River and a slow landslide. We first removed the gravity changes from non-sediment effects, such as tides, groundwater, surface displacements and air pressure variations. Then, we inverted the density of the sediment with an attempt to distinguish the density of the landslide from the density of the river sediments. We eventually estimate an average loss of 3.7 \ub1 0.4  7 10^9 kg of sediment from 2015 to 2017 mostly due to the slow landslide. Although the gravity devices used in this study are expensive and need week-long surveys, new instrumentation currently being developed will enable dense and continuous measurements at lower cost, making the method that has been developed and tested in this study well-suited for the estimation of erosion, sediment transfer and deposition in landscapes

NTT Multiplication for NTT-unfriendly Rings

In this paper, we show how multiplication for polynomial rings used in the NIST PQC finalists Saber and NTRU can be efficiently implemented using the Number-theoretic transform (NTT). We obtain superior performance compared to the previous state of the art implementations using Toom–Cook multiplication on both NIST’s primary software optimization targets AVX2 and Cortex-M4. Interestingly, these two platforms require different approaches: On the Cortex-M4, we use 32-bit NTT-based polynomial multiplication, while on Intel we use two 16-bit NTT-based polynomial multiplications and combine the products using the Chinese Remainder Theorem (CRT). For Saber, the performance gain is particularly pronounced. On Cortex-M4, the Saber NTT-based matrix-vector multiplication is 61% faster than the Toom-Cook multiplication resulting in 22% fewer cycles for Saber encapsulation. For NTRU, the speed-up is less impressive, but still NTT-based multiplication performs better than Toom–Cook for all parameter sets on Cortex-M4. The NTT-based polynomial multiplication for NTRU-HRSS is 10% faster than Toom–Cook which results in a 6% cost reduction for encapsulation. On AVX2, we obtain speed-ups for three out of four NTRU parameter sets. As a further illustration, we also include code for AVX2 and Cortex-M4 for the Chinese Association for Cryptologic Research competition award winner LAC (also a NIST round 2 candidate) which outperforms existing code