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The mathematical theory of machine learning not only explains the current algorithms but can also motivate principled approaches for the future. This self-contained textbook introduces students and researchers of AI to the main mathematical techniques used to analyze machine learning algorithms, with motivations and applications. Topics covered include the analysis of supervised learning algorithms in the iid setting, the analysis of neural networks (e.g. neural tangent kernel and mean-field analysis), and the analysis of machine learning algorithms in the sequential decision setting (e.g. online learning, bandit problems, and reinforcement learning). Students will learn the basic mathematical tools used in the theoretical analysis of these machine learning problems and how to apply them to the analysis of various concrete algorithms. This textbook is perfect for readers who have some background knowledge of basic machine learning methods, but want to gain sufficient technical knowledge to understand research papers in theoretical machine learning.
Adolescence is a significant period for the formation of relationship networks and the development of internalizing problems. With a sample of Chinese adolescents (N = 3,834, 52.01% girls, Mage = 16.68 at Wave 1), the present study aimed to identify the configuration of adolescents’ relationship qualities from four important domains (i.e., relationship quality with mother, father, peers, and teachers) and how distinct profiles were associated with the development of internalizing problems (indicated by depressive and anxiety symptoms) across high school years. Latent profile analysis identified a five-profile configuration with four convergent profiles (i.e., relationship qualities with others were generally good or bad) and one “Father estrangement” profile (i.e., the relationship quality with others were relatively good but that with father was particularly poor). Further conditional latent growth curve analysis indicated the “Father estrangement” profile was especially vulnerable to an increase in the internalizing problems as compared with other relationship profiles. This study contributes to understanding the characteristics of interpersonal relationship qualities and their influences on adolescent internalizing problems in a non-Western context. Results were further discussed from a culturally specific perspective.
In this study, we investigate the differences between two transient, three-dimensional, thermomechanically coupled ice-sheet models, namely, a first-order approximation model (FOM) and a ‘full’ Stokes ice-sheet model (FSM) under the same numerical framework. For all numerical experiments, we take the FSM outputs as the reference values and calculate the mean relative errors in the velocity and temperature fields for the FOM over 100 years. Four different boundary conditions (ice slope, geothermal heat flux, basal topography and basal sliding) are tested, and by changing these parameters, we verify the thermomechanical behavior of the FOM and discover that the velocity and temperature biases of the FOM generally increase with increases in the ice slope, geothermal heat flux, undulation amplitude of the ice base, and with the existence of basal sliding. In addition, the model difference between the FOM and FSM may accumulate over time, and the spatial distribution patterns of the relative velocity and temperature errors are in good agreement.
To address the shortcomings of existing methods for rotorcraft searching, positioning, tracking and landing on a ship at sea, a dual-channel LIDAR searching, positioning, tracking and landing system (DCLSPTLS) is proposed in this paper, which utilises the multi-pulse laser echoes accumulation method and the physical phenomenon that the laser reflectivity of the ship deck in the near-infrared band is four orders of magnitude higher than that of the sea surface. The DCLSPTLS searching and positioning model, tracking model and landing model are established, respectively. The searching and positioning model can provide estimates of the azimuth angle, the distance of the ship relative to the rotorcraft and the ship's course. With the above parameters as inputs, the total tracking time and the direction of the rotorcraft tracking speed can be obtained by using the tracking model. The landing model can calculate the pitch and the roll angles of the ship's deck relative to the rotorcraft by using the least squares method and the laser irradiation coordinates. The simulation shows that the DCLSPTLS can realise the functions of rotorcraft searching, positioning, tracking and landing by using the above parameters. To verify the effectiveness of the DCLSPTLS, a functional test is performed using a rotorcraft and a model ship on a lake. The test results are consistent with the results of the simulation.
Let
$f: X \to B$
be a relatively minimal fibration of maximal Albanese dimension from a variety X of dimension
$n \ge 2$
to a curve B defined over an algebraically closed field of characteristic zero. We prove that
$K_{X/B}^n \ge 2n! \chi _f$
. It verifies a conjectural formulation of Barja in [2]. Via the strategy outlined in [4], it also leads to a new proof of the Severi inequality for varieties of maximal Albanese dimension. Moreover, when the equality holds and
$\chi _f> 0$
, we prove that the general fibre F of f has to satisfy the Severi equality that
$K_F^{n-1} = 2(n-1)! \chi (F, \omega _F)$
. We also prove some sharper results of the same type under extra assumptions.
The subduction model of the Neo-Tethys during the Early Cretaceous has always been a controversial topic, and the scarcity of Early Cretaceous magmatic rocks in the southern part of the Gangdese batholith is the main cause of this debate. To address this issue, this article presents new zircon U–Pb chronology, zircon Hf isotope, whole-rock geochemistry and Sr–Nd isotope data for the Early Cretaceous quartz diorite dykes with adakite affinity in Liuqiong, Gongga. Zircon U–Pb dating of three samples yielded ages of c. 141–137 Ma, indicating that the Liuqiong quartz diorite was emplaced in the Early Cretaceous. The whole-rock geochemical analysis shows that the Liuqiong quartz diorite is enriched in large-ion lithophile elements (LILEs) and light rare-earth elements (LREEs) and is depleted in high-field-strength elements (HFSEs), which are related to slab subduction. Additionally, the Liuqiong quartz diorite has high SiO2, Al2O3 and Sr contents, high Sr/Y ratios and low heavy rare-earth element (HREE) and Y contents, which are compatible with typical adakite signatures. The initial 87Sr/86Sr values of the Liuqiong adakite range from 0.705617 to 0.705853, and the whole-rock ϵNd(t) values vary between +5.78 and +6.24. The zircon ϵHf(t) values vary from +11.5 to +16.4. Our results show that the Liuqiong adakite magma was derived from partial melting of the Neo-Tethyan oceanic plate (mid-ocean ridge basalt (MORB) + sediment + fluid), with some degree of subsequent peridotite interaction within the overlying mantle wedge. Combining regional data, we favour the interpretation that the Neo-Tethyan oceanic crust was subducted at a low angle beneath the Gangdese during the Early Cretaceous.
Resistant starch (RS) has received increased attention due to its potential health benefits. This study was aimed to investigate the effects of dietary corn RS on immunological characteristics of broilers. A total of 320 broiler chicks were randomly allocated to five dietary treatments: normal corn–soyabean (NC) diet group, corn starch diet group, 4 %, 8 % and 12 % RS diet groups. This trial lasted for 42 d. The relative weights of spleen, thymus and bursa, the concentrations of nitric oxide (NO) and IL-4 in plasma at 21 d of age, as well as the activities of total nitric oxide synthase (TNOS) and inducible nitric oxide synthase (iNOS) in plasma at 21 and 42 d of age showed positive linear responses (P < 0·05) to the increasing dietary RS level. Meanwhile, compared with the birds from the NC group at 21 d of age, birds fed 4 % RS, 8 % RS and 12 % RS diets exhibited higher (P < 0·05) relative weight of bursa and concentrations of NO and interferon-γ in plasma. Birds fed 4 % RS and 8 % RS diets showed higher (P < 0·05) number of IgA-producing cells in the jejunum. While compared with birds from the NC group at 42 d of age, birds fed 12 % RS diet showed higher (P < 0·05) relative weight of spleen and activities of TNOS and iNOS in plasma. These findings suggested that dietary corn RS supplementation can improve immune function in broilers.
Listeriosis is a rare but serious foodborne disease caused by Listeria monocytogenes. This matched case–control study (1:1 ratio) aimed to identify the risk factors associated with food consumption and food-handling habits for the occurrence of sporadic listeriosis in Beijing, China. Cases were defined as patients from whom Listeria was isolated, in addition to the presence of symptoms, including fever, bacteraemia, sepsis and other clinical manifestations corresponding to listeriosis, which were reported via the Beijing Foodborne Disease Surveillance System. Basic patient information and possible risk factors associated with food consumption and food-handling habits were collected through face-to-face interviews. One hundred and six cases were enrolled from 1 January 2018 to 31 December 2020, including 52 perinatal cases and 54 non-perinatal cases. In the non-perinatal group, the consumption of Chinese cold dishes increased the risk of infection by 3.43-fold (95% confidence interval 1.27–9.25, χ2 = 5.92, P = 0.02). In the perinatal group, the risk of infection reduced by 95.2% when raw and cooked foods were well-separated (χ2 = 5.11, P = 0.02). These findings provide important scientific evidence for preventing infection by L. monocytogenes and improving the dissemination of advice regarding food safety for vulnerable populations.
Although the impacts of income, population growth, and other important determinants of land-use change have been widely studied, there is less understanding of how spatial spillovers matter. Utilizing a spatial econometric approach, we investigate the main determinants of natural landscape conversion, focusing on quantifying local and global spatial spillovers. The empirical investigation applies to the Edmonton Metropolitan Region and the Calgary Regional Partnership in Canada. Key results include: (1) determinants of land conversion have significant spillover effects; (2) income, population density, road density, natural land endowment and land suitability for agriculture are all found to have influences on natural land conversion both in the own and neighboring areas; and (3) local (i.e., within the immediate neighboring areas) and global (in the entire study region) spillovers are different in strength and direction. Our work provides useful information for understanding the spillover issues in land conservation, resource governance, and optimal conservation design.
Celestial navigation is an important means of maritime navigation; it can automatically achieve inertially referenced positioning and orientation after a long period of development. However, the impact of different accuracy of observations and the influence of nonstationary states, such as ship speed change and steering, are not taken into account in existing algorithms. To solve this problem, this paper proposes an adaptively robust maritime celestial navigation algorithm, in which each observation value is given an equivalent weight according to the robust estimation theory, and the dynamic balance between astronomical observation and prediction values of vessel motion is adjusted by applying the adaptive factor. With this system, compared with the frequently used least square method and extended Kalman filter algorithm, not only are the real-time and high-precision navigation parameters, such as position, course, and speed for the vessel, calculated simultaneously, but also the influence of abnormal observation and vessel motion status change could be well suppressed.
Sarcopenia is a core contributor to several health consequences, including falls, fractures, physical limitations and disability. The pathophysiological processes of sarcopenia may be counteracted with the proper diet, delaying sarcopenia onset. Dietary pattern analysis is a whole diet approach used to investigate the relationship between diet and sarcopenia. Here, we aimed to investigate this relationship in an elderly Chinese population. A cross-sectional study with 2423 participants aged more than 60 years was performed. Sarcopenia was defined based on the guidelines of the Asian Working Group for Sarcopenia, composed of low muscle mass plus low grip strength and/or low gait speed. Dietary data were collected using a FFQ that included questions on 100 food items along with their specified serving sizes. Three dietary patterns were derived by factor analysis: sweet pattern, vegetable pattern and animal food pattern. The prevalence of sarcopenia was 16·1 %. The higher vegetable pattern score and animal food pattern score were related to lower prevalence of sarcopenia (Ptrend = 0·006 and < 0·001, respectively); the multivariate-adjusted OR of the prevalence of sarcopenia in the highest v. lowest quartiles were 0·54 (95 % CI 0·34, 0·86) and 0·50 (95 % CI 0·33, 0·74), separately. The sweet pattern score was not significantly related to the prevalence of sarcopenia. The present study showed that vegetable pattern and animal food pattern were related to a lower prevalence of sarcopenia in Chinese older adults. Further studies are required to clarify these findings.
A new enantiornithine bird is described on the basis of a well preserved partial skeleton from the Upper Cretaceous Qiupa Formation of Henan Province (central China). It provides new evidence about the osteology of Late Cretaceous enantiornithines, which are mainly known from isolated bones; in contrast, Early Cretaceous forms are often represented by complete skeletons. While the postcranial skeleton shows the usual distinctive characters of enantiornithines, the skull displays several features, including confluence of the antorbital fenestra and the orbit and loss of the postorbital, evolved convergently with modern birds. Although some enantiornithines retained primitive cranial morphologies into the latest Cretaceous Period, at least one lineage evolved cranial modifications that parallel those in modern birds.
The newly discovered Bibole banded iron formations are located within the Nyong Group at the northwest of the Congo Craton in Cameroon. The Bibole banded iron formations comprise oxide (quartz-magnetite) and mixed oxide-silicate (chlorite-magnetite) facies banded iron formations, which are interbedded with felsic gneiss, phyllite and quartz-chlorite schist. Geochemical studies of the quartz-magnetite banded iron formations and chlorite-magnetite banded iron formations reveal that they are composed of >95 wt % Fe2O3 plus SiO2 and have low concentrations of Al2O3, TiO2 and high field strength elements. This indicates that the Bibole banded iron formations were not significantly contaminated by detrital materials. Post-Archaean Australian Shale–normalized rare earth element and yttrium patterns are characterized by positive La and Y anomalies, a relative depletion of light rare earth elements compared to heavy rare earth elements and positive Eu anomalies (average of 1.86 and 1.15 for the quartz-magnetite banded iron formations and chlorite-magnetite banded iron formations, respectively), suggesting the influence of low-temperature hydrothermal fluids and seawater. The quartz-magnetite banded iron formations display true negative Ce anomalies, while the chlorite-magnetite banded iron formations lack Ce anomalies. Combined with their distinct Eu anomalies consistent with Algoma- and Superior-type banded iron formations, we suggest that the Bibole banded iron formations were deposited under oxic to suboxic conditions in an extensional basin. SIMS U–Pb data indicate that the Bibole banded iron formations were deposited at 2466 Ma and experienced metamorphism and metasomatism at 2078 Ma during the Eburnean/Trans-Amazonian orogeny. Overall, these findings suggest that the studied banded iron formations probably marked the onset of the rise of atmospheric oxygen, also known as the Great Oxidation Event in the Congo Craton.
We focus on the population dynamics driven by two classes of truncated $\alpha$-stable processes with Markovian switching. Almost necessary and sufficient conditions for the ergodicity of the proposed models are provided. Also, these results illustrate the impact on ergodicity and extinct conditions as the parameter $\alpha$ tends to 2.
Brucellosis is one of the most serious and widespread zoonotic diseases, which seriously threatens human health and the national economy. This study was based on the T/B dominant epitopes of Brucella outer membrane protein 22 (Omp22), outer membrane protein 19 (Omp19) and outer membrane protein 28 (Omp28), with bioinformatics methods to design a safe and effective multi-epitope vaccine. The amino acid sequences of the proteins were found in the National Center for Biotechnology Information (NCBI) database, and the signal peptides were predicted by the SignaIP-5.0 server. The surface accessibility and hydrophilic regions of proteins were analysed with the ProtScale software and the tertiary structure model of the proteins predicted by I-TASSER software and labelled with the UCSF Chimera software. The software COBEpro, SVMTriP and BepiPred were used to predict B cell epitopes of the proteins. SYFPEITHI, RANKpep and IEDB were employed to predict T cell epitopes of the proteins. The T/B dominant epitopes of three proteins were combined with HEYGAALEREAG and GGGS linkers, and carriers sequences linked to the N- and C-terminus of the vaccine construct with the help of EAAAK linkers. Finally, the tertiary structure and physical and chemical properties of the multi-epitope vaccine construct were analysed. The allergenicity, antigenicity and solubility of the multi-epitope vaccine construct were 7.37–11.30, 0.788 and 0.866, respectively. The Ramachandran diagram of the mock vaccine construct showed 96.0% residues within the favoured and allowed range. Collectively, our results showed that this multi-epitope vaccine construct has a high-quality structure and suitable characteristics, which may provide a theoretical basis for future laboratory experiments.
To unveil the adaptation of Litopenaeus vannamei to elevated ambient ammonia-N, crustacean hyperglycaemic hormone (CHH) was knocked down to investigate its function in glucose metabolism pathway under ammonia-N exposure. When CHH was silenced, haemolymph glucose increased significantly during 3–6 h, decreased significantly during 12–48 h and recovered to the control groups’ level at 72 h. After CHH knock-down, dopamine (DA) contents reduced significantly during 3–24 h, which recovered after 48 h. Besides, the expressions of guanylyl cyclase (GC) and DA1R in the hepatopancreas decreased significantly, while DA4R increased significantly. Correspondingly, the contents of cyclic AMP (cAMP), cyclic GMP (cGMP) and diacylglycerol (DAG) and the expressions of protein kinase A (PKA), protein kinase G (PKG), AMP active protein kinase α (AMPKα) and AMPKγ were significantly down-regulated, while the levels of protein kinase C (PKC) and AMPKβ were significantly up-regulated. The expressions of cyclic AMP response element-binding protein (CREB) and GLUT2 decreased significantly, while GLUT1 increased significantly. Moreover, glycogen content, glycogen synthase and glycogen phosphorylase activities in hepatopancreas and muscle were significantly increased. Furthermore, the levels of key enzymes hexokinase, pyruvate kinase and phosphofructokinase in glycolysis (GLY), rate-limiting enzymes citrate synthase in tricarboxylic acid and critical enzymes phosphoenolpyruvate carboxykinase, fructose diphosphate and glucose-6-phosphatase in gluconeogenesis (GNG) were significantly decreased in hepatopancreas. These results suggest that CHH affects DA and then they affect their receptors to transmit glucose metabolism signals into the hepatopancreas of L. vannamei under ammonia-N stress. CHH acts on the cGMP-PKG-AMPKα-CREB pathway through GC, and CHH affects DA to influence cAMP-PKA-AMPKγ-CREB and DAG-PKC-AMPKβ-CREB pathways, thereby regulating GLUT, inhibiting glycogen metabolism and promoting GLY and GNG. This study contributes to further understand glucose metabolism mechanism of crustacean in response to environmental stress.
N6-Methyladenosine (m6A) regulates oocyte-to-embryo transition and the reprogramming of somatic cells into induced pluripotent stem cells. However, the role of m6A methylation in porcine early embryonic development and its reprogramming characteristics in somatic cell nuclear transfer (SCNT) embryos are yet to be known. Here, we showed that m6A methylation was essential for normal early embryonic development and its aberrant reprogramming in SCNT embryos. We identified a persistent occurrence of m6A methylation in embryos between 1-cell to blastocyst stages and m6A levels abruptly increased during the morula-to-blastocyst transition. Cycloleucine (methylation inhibitor, 20 mM) treatment efficiently reduced m6A levels, significantly decreased the rates of 4-cell embryos and blastocysts, and disrupted normal lineage allocation. Moreover, cycloleucine treatment also led to higher levels in both apoptosis and autophagy in blastocysts. Furthermore, m6A levels in SCNT embryos at the 4-cell and 8-cell stages were significantly lower than that in parthenogenetic activation (PA) embryos, suggesting an abnormal reprogramming of m6A methylation in SCNT embryos. Correspondingly, expression levels of m6A writers (METTL3 and METTL14) and eraser (FTO) were apparently higher in SCNT 8-cell embryos compared with their PA counterparts. Taken together, these results indicated that aberrant nuclear transfer-mediated reprogramming of m6A methylation was involved in regulating porcine early embryonic development.
Poor utilisation efficiency of carbohydrate always leads to metabolic phenotypes in fish. The intestinal microbiota plays an important role in carbohydrate degradation. Whether the intestinal bacteria could alleviate high-carbohydrate diet (HCD)-induced metabolic phenotypes in fish remains unknown. Here, a strain affiliated to Bacillus amyloliquefaciens was isolated from the intestine of Nile tilapia. A basal diet (CON), HCD or HCD supplemented with B. amy SS1 (HCB) was used to feed fish for 10 weeks. The beneficial effects of B. amy SS1 on weight gain and protein accumulation were observed. Fasting glucose and lipid deposition were decreased in the HCB group compared with the HCD group. High-throughput sequencing showed that the abundance of acetate-producing bacteria was increased in the HCB group relative to the HCD group. Gas chromatographic analysis indicated that the concentration of intestinal acetate was increased dramatically in the HCB group compared with that in the HCD group. Glucagon-like peptide-1 was also increased in the intestine and serum of the HCB group. Thus, fish were fed with HCD, HCD supplemented with sodium acetate at 900 mg/kg (HLA), 1800 mg/kg (HMA) or 3600 mg/kg (HHA) diet for 8 weeks, and the HMA and HHA groups mirrored the effects of B. amy SS1. This study revealed that B. amy SS1 could alleviate the metabolic phenotypes caused by HCD by enriching acetate-producing bacteria in fish intestines. Regulating the intestinal microbiota and their metabolites might represent a powerful strategy for fish nutrition modulation and health maintenance in future.