Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely u...Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.展开更多
The safety and integrity requirements of aerospace composite structures necessitate real-time health monitoring throughout their service life.To this end,distributed optical fiber sensors utilizing back Rayleigh scatt...The safety and integrity requirements of aerospace composite structures necessitate real-time health monitoring throughout their service life.To this end,distributed optical fiber sensors utilizing back Rayleigh scattering have been extensively deployed in structural health monitoring due to their advantages,such as lightweight and ease of embedding.However,identifying the precise location of damage from the optical fiber signals remains a critical challenge.In this paper,a novel approach which namely Modified Sliding Window Principal Component Analysis(MSWPCA)was proposed to facilitate automatic damage identification and localization via distributed optical fiber sensors.The proposed method is able to extract signal characteristics interfered by measurement noise to improve the accuracy of damage detection.Specifically,we applied the MSWPCA method to monitor and analyze the debonding propagation process in honeycomb sandwich panel structures.Our findings demonstrate that the training model exhibits high precision in detecting the location and size of honeycomb debonding,thereby facilitating reliable and efficient online assessment of the structural health state.展开更多
A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbule...A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbulent signal is decomposed into the small scale vortex that has approximate isotropy and the large scale vortex with the digital filter. Then, the large scale vortex is used to detect coherent structures with this method. The principal time scale and profile of coherent structures for velocity components (u, v, w above rice fields are obtained. In order to testify the validity of this method, the correlation of coherent structures and non-coherent structures are also calculated.展开更多
Based on the cognitive radar concept and the basic connotation of cognitive skywave over-the-horizon radar(SWOTHR), the system structure and information processingmechanism about cognitive SWOTHR are researched. Amo...Based on the cognitive radar concept and the basic connotation of cognitive skywave over-the-horizon radar(SWOTHR), the system structure and information processingmechanism about cognitive SWOTHR are researched. Amongthem, the hybrid network system architecture which is thedistributed configuration combining with the centralized cognition and its soft/hardware framework with the sense-detectionintegration are proposed, and the information processing framebased on the lens principle and its information processing flowwith receive-transmit joint adaption are designed, which buildand parse the work law for cognition and its self feedback adjustment with the lens focus model and five stages informationprocessing sequence. After that, the system simulation andthe performance analysis and comparison are provided, whichinitially proves the rationality and advantages of the proposedideas. Finally, four important development ideas of futureSWOTHR toward "high frequency intelligence information processing system" are discussed, which are scene information fusion, dynamic reconfigurable system, hierarchical and modulardesign, and sustainable development. Then the conclusion thatthe cognitive SWOTHR can cause the performance improvement is gotten.展开更多
This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynami...This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.展开更多
This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads.The primary purpose of this series is to understand the magnitude of the dynami...This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads.The primary purpose of this series is to understand the magnitude of the dynamie response of structures to enable better design of structures and response modification devices/systems.Under idealized design condi- tions,the structural responses are obtained by using single directinn input ground motions in the direction of the intended response modification devices/systems,and by assuming that the responses of the structure is deconpleable in three mutual- ly perpendicular directions.This standard practice has been applied to both new and retrofitted structures using various seis- mic protective systems.Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component)of the dynamic response of structures.In order to quantify such effects,it is necessary to examine the principal axes of structures under both static and dynamic loading.In this twn-part series,the first paper is concerned with static loading,which provides definitions and fundamental formulations,with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However,under dynamic or earthquake loading,a relatively small amount of energy transferred across perpendicular direc- tions is accumulated,which may result in significant enlargement of the structural response.This paper deals with a formu- lation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resuhing from the non-existence of principal axes.展开更多
This paper studied the expert system of genotype discrimination for the STR locus D5S818 based on near-infrared spectroscopy-principal discriminant variate (PDV).Six genotypes,i.e.genotypes 10-10,10-11,11-11,11-12,11-...This paper studied the expert system of genotype discrimination for the STR locus D5S818 based on near-infrared spectroscopy-principal discriminant variate (PDV).Six genotypes,i.e.genotypes 10-10,10-11,11-11,11-12,11-13 and 13-13,were selected as research subjects.Based on the optimum polymerase chain reaction (PCR) conditions,about 54 measuring samples for each genotype were obtained;these samples were tested by near-infrared spectroscopy directly.With differences between homozygote genotypes and heterozygote ones,and differences of the total number of core repeat units between the six genotypes,two types of genotyping-tree structure were constructed and their respective PDV models were studied using the near-infrared spectra of the samples as recognition variables.Finally,based on the classification ability of these two genotyping-tree structures,an optimum expert system of genotype discrimination was built using the PDV models.The result demonstrated that the built expert system had good discriminability and robustness;without any preprocessing for PCR products,the six genotypes studied could be discriminated rapidly and correctly.It provided a methodological support for establishing an expert system of genotype discrimination for all genotypes of locus D5S818 and other STR loci.展开更多
Litsea glaucescens Kunth(Mexican bay leaf,laurel)has a wide distribution in Mexico,growing at both riparian and rupicolous environments in the mountainous region of the Central Highlands of the country.Sierra Frí...Litsea glaucescens Kunth(Mexican bay leaf,laurel)has a wide distribution in Mexico,growing at both riparian and rupicolous environments in the mountainous region of the Central Highlands of the country.Sierra Fría-Sierra Laurel is a protected natural area covered by a dry forest.The Mexican bay leaf is associated with the oak forest,especially on ravines.The species has been considered at risk in recent years.This research is focused on analyzing the elements of the environment of the ravines,which are influencing the distribution and establishment of laurel populations in the region.Two mountainous regions of Aguascalientes were selected,Sierra Fría and Sierra Laurel.Three ravines of the basin were selected to obtain environmental data.Variables registered were topographic,edaphic,and biotic.Principal component analysis was used to identify ecological factors associated with the presence of L.glaucescens.Mexican bay leaf populations were registered in 10 ravines.At the structural level in the community,29 woody species were registered,Mexican bay leaf had an Importance Value Index of 15.8,ranking 10th among all species.Individuals of laurel were classified by size classes(S,individuals with heights ranging from 0 to 20 cm;S,heights ranging from 0.2 to 1.0 m;S,heights between 1 and 2 m with light trace of flowering;S,heights greater than 2 m with flowering greater than 30% of the canopy;and S,individuals with heights greater than 5 m,curved trunk and basal regrowth)to obtain the population structure.The importance index value for all the species in the riparian community was calculated to the community level.Edaphic factors that characterized the presence of Mexican bay leaf were a high percentage of rock coverage(90%),less mulch depth,and sandy loam shallow soils.Sites that showed higher cation exchange capacity had a higher presence of individuals of the S,S,and Ssize classes.Class Sindividuals were found in shady places with 97% of intercepted light.Individuals of classes Sand Sendure less shady places(75%–85% of intercepted light),and individuals class Sand Sare more frequent in open canopies and crag conditions.Regarding the ecological site factors,such as riverside stream,and rocks on mountain slopes,L.glaucescens life form is riparian and rupicolous.Cation exchange capacity,sodium and calcium levels play an important role in the presence of Mexican bay leaf.Distribution on the ravine and recruitment of the Mexican bay leaf populations are associated with shaded sites,mainly for individuals of size classes Sand S,versus sunny places for individuals of size classes Sand S.The overall population structure had a positive kurtosis with all plant size categories well represented;statistically,the population structure of L.glaucescens is very close to the normal distribution.The information obtained allows us to affirm that the laurel populations in the mountainous areas of Sierra Fría and Sierra Laurel from central Mexico are in good demographic condition.展开更多
10 quantum chemical descriptors of 21 aromatic compounds have been calculated by the semi-empirical quantum chemical method AM1. The Quantitative Structure-Biodegradability Relationships (QSBR) studies were performe...10 quantum chemical descriptors of 21 aromatic compounds have been calculated by the semi-empirical quantum chemical method AM1. The Quantitative Structure-Biodegradability Relationships (QSBR) studies were performed by the multiple linear regression (MLR), principal component regression (PCR) and back propagation artificial neural network (BP-ANN), respectively. The root mean square error (RMSE) of the training and validation sets of the BP-ANN model are 0.1363 and 0.0244, the mean absolute percentage errors (MAPE) are 0.1638 and 0.0326, the squared correlation coefficients (R^2) are 0.9853 and 0.9996, respectively. The results show that the BP-ANN model achieved a better prediction result than those of MLR and PCR. In addition, some insights into the structural factors affecting the aerobic biodegradation mechanism were discussed in detail.展开更多
Cognitive optical network is the intermediate to combine artificial intelligence technology with network,and also the important network technology to promote network intelligence level constantly.In the paper,it analy...Cognitive optical network is the intermediate to combine artificial intelligence technology with network,and also the important network technology to promote network intelligence level constantly.In the paper,it analyzes the cognitive optical network structure with the application of artificial intelligence technology by starting from the basic conditions of cognitive network and cognitive optional network on the basis of fully understanding the connotation of cognitive network and cognitive optical network,and explores its self-governance functions,so as to better realize the self-optimization and self-configuration of network.展开更多
This paper approaches two main philosophical questions concerning the biological structures,from unicellular to multicellular organisms:one of them(i),referred to the information-body relation,as an extension of the m...This paper approaches two main philosophical questions concerning the biological structures,from unicellular to multicellular organisms:one of them(i),referred to the information-body relation,as an extension of the mind-body relation at human,and another one(ii),to the consciousness problem,concerning the existence and nature of consciousness(if any),at the inferior organisms on the complexity scale,as this concept is known at humans.As philosophy benefits of the privilege to use data/concepts from other sciences to obtain philosophical conclusions,there were included detailed descriptions of some key biologic mechanisms,analyzed from informational perspective,necessary just to support/demonstrate/reinforce the informational nature/substrate of the mentioned relations.The analysis of the close relation between information and body,related to the structuration and functional properties of the biological organisms,from cells to multicellular structures,shows that all of them are able to“embody/disembody”information during/by structuration/destructuration processes of matter,in particular that of DNA/RNA/proteins,their functions appearing as a result of their informational capabilities to internally manage the inter-connection with environment,primarily due to their permanent dependence on the food resources and adaptation/survival needs.The experimental and theoretical studies,revealing/documenting on one hand the automatic management of maintenance metabolic processes,the reproduction,and growth/development,and on the other hand the adaptive decision-making/sentient processes as a responsive reaction to the environmental cues,show/support the consistency of the informational model of the human body and living structures on the entire biological scale,providing support to the informational solution of the stated problems(i)and(ii).A distinct attention is paid to plants,which are organisms without nervous system,but which show/manifest also informational capabilities to detect/react to information and to modulate their behavior accordingly.The question if the living organisms possess a pseudo/proto-consciousness level as a consequence of the informational activity of their body,distinct from human,but active in any biological structure under certain conditions is furthermore discussed,and a reliable definition of rudimentary pseudo/proto-consciousness level is given/described and compared with other empirical/theoretical concepts.展开更多
Using the method of principal component analysis, the paper conducts a systematic study on the issue of how corporate governance influences capital structure. The study manifests the results that the proportion of cir...Using the method of principal component analysis, the paper conducts a systematic study on the issue of how corporate governance influences capital structure. The study manifests the results that the proportion of circulation shares, the ability that other big shareholders contend with the first biggest shareholder, the proportion of corporation-owned shares, and the frequency of directorate meetings all have a positive relationship with the liability level. Meanwhile, the concentration degree of owners' equity, the proportion of state-owned shares, the phenomenon that one person serves as both chairman of directorate and general manager, and the intensity of competition in product market are all negatively related to the level of debt. Finally, the scale of directorate, the proportion of independent directors as well as the percentage of management-owned shares have no significant relationship with the capital structure. The statistic analysis also shows that the proportion of independent directors of some Chinese listed companies does not meet the regulation of the CSRC. In addition, the paper tests the impacts of corporate operating characteristics on capital structure.展开更多
Translational discourse requires at least three participants, therefore it is suggested to consider the universal model of the picture of the world, according to which it is much easier for a translator to combine the...Translational discourse requires at least three participants, therefore it is suggested to consider the universal model of the picture of the world, according to which it is much easier for a translator to combine the pictures of the world of an addressee and an author. An addressee is a mental image existing in the mind of an addresser during the creative process. Having defined its parameters, a translator has an opportunity to deliver the thought of an addresser to an addressee as accurately as possible and to select the means of expression that are clear to an addressee. The type of an addressee correlates with "the relation to the new".展开更多
Principal component analysis (PCA) is a useful tool in process fault detection, but offers little support on fault isolation. In this article, structured residual with strong isolation property is introduced. Althou...Principal component analysis (PCA) is a useful tool in process fault detection, but offers little support on fault isolation. In this article, structured residual with strong isolation property is introduced. Although it is easy to get the residual by transformation matrix in static process, unfortunately, it becomes hard in dynamic process under control loop. Therefore, partial dynamic PCA(PDPCA) is proposed to obtain structured residual and enhance the isolation ability of dynamic process monitoring, and a compound statistic is introduced to resolve the problem resulting from independent variables in every variable subset. Simulations on continuous stirred tank reactor (CSTR) show the effectiveness of the proposed method.展开更多
When the resultant of applied forces does not pass through the center of an active landmass, the landmass will rotate, giving rise to a rotational tectonic stress field. The motion of a fault along the principal stres...When the resultant of applied forces does not pass through the center of an active landmass, the landmass will rotate, giving rise to a rotational tectonic stress field. The motion of a fault along the principal stress plane is de-termined by the mechanic features of the plane. Tensile fractures occur on the faults in the direction of the principal extensional stress plane, and fault-depression basins will be formed under a long-term action. Thrusting and over-thrusting occur on faults in the direction of the principal compressional stress plane, or folds may be formed as a result. Information on geology shows that the North China landmass, which remained stable and intact for a long time, became disjointed in the Eogene period. In the course of disjunction, anticlockwise rotation took place in the Shanxi-Hebei-Shaanxi (Jin-Ji-Shan) landmass, giving rise to the fault-depression system in its periphery. In the Pliocene epoch the landmass lost stability and its eastern boundary moved westward. As a result, the Shanxi gra-ben system appeared and Ordos landmass was formed. Structural and mechanic features of the main faults around Jin-Ji-Shan landmass can be explained with principal stress plane of a rotational tectonic stress field.展开更多
The stability of the surrounding rocks of large underground powerhouses is always emphasized during the construction process,especially in large-scale underground projects under construction,such as the Baihetan hydro...The stability of the surrounding rocks of large underground powerhouses is always emphasized during the construction process,especially in large-scale underground projects under construction,such as the Baihetan hydropower station in China.According to field investigations,numerical simulations and monitoring data analysis,we present a comparative analysis of the deformation and failure characteristics of the surrounding rocks of underground powerhouses on the left and right banks of the Baihetan hydropower station.The failure characteristics and deformation magnitude of the underground powerhouses on the left and right banks are quite different.Under the disadvantageous condition where the maximum principal stress intersects the axis of the powerhouse at a large angle,the left bank underground powerhouse shows prominent stress-controlled failure characteristics such as spalling,slack collapse and concrete cracking.Although the maximum principal stress is in the favorable condition which intersects the right bank powerhouse at a small angle,the relatively high intermediate principal stress with an angle subvertical to the right bank powerhouse plays an essential role in its deformation and failure,indicating that the influence of high intermediate principal stress cannot be ignored.In addition,structural plane-controlled failure and large deformation are also more evident on the right bank due to the extensive distribution of weak structural planes and complex surrounding rock properties.展开更多
Neurological abnormalities identified via neuroimaging are common in patients with Alzheimer’s disease.However,it is not yet possible to easily detect these abnormalities using head computed tomography in the early s...Neurological abnormalities identified via neuroimaging are common in patients with Alzheimer’s disease.However,it is not yet possible to easily detect these abnormalities using head computed tomography in the early stages of the disease.In this review,we evaluated the ways in which modern imaging techniques such as positron emission computed tomography,single photon emission tomography,magnetic resonance spectrum imaging,structural magnetic resonance imaging,magnetic resonance diffusion tensor imaging,magnetic resonance perfusion weighted imaging,magnetic resonance sensitive weighted imaging,and functional magnetic resonance imaging have revealed specific changes not only in brain structure,but also in brain function in Alzheimer’s disease patients.The reviewed literature indicated that decreased fluorodeoxyglucose metabolism in the temporal and parietal lobes of Alzheimer’s disease patients is frequently observed via positron emission computed tomography.Furthermore,patients with Alzheimer’s disease often show a decreased N-acetylaspartic acid/creatine ratio and an increased myoinositol/creatine ratio revealed via magnetic resonance imaging.Atrophy of the entorhinal cortex,hippocampus,and posterior cingulate gyrus can be detected early using structural magnetic resonance imaging.Magnetic resonance sensitive weighted imaging can show small bleeds and abnormal iron metabolism.Task-related functional magnetic resonance imaging can display brain function activity through cerebral blood oxygenation.Resting functional magnetic resonance imaging can display the functional connection between brain neural networks.These are helpful for the differential diagnosis and experimental study of Alzheimer’s disease,and are valuable for exploring the pathogenesis of Alzheimer’s disease.展开更多
Patients with type 2 diabetes mellitus(T2 DM) often have cognitive impairment and structural brain abnormalities.The magnetic resonance imaging(MRI)-based brain atrophy and lesion index can be used to evaluate common ...Patients with type 2 diabetes mellitus(T2 DM) often have cognitive impairment and structural brain abnormalities.The magnetic resonance imaging(MRI)-based brain atrophy and lesion index can be used to evaluate common brain changes and their correlation with cognitive function,and can therefore also be used to reflect whole-brain structural changes related to T2 DM.A total of 136 participants(64 men and 72 women,aged 55–86 years) were recruited for our study between January 2014 and December 2016.All participants underwent MRI and Mini-Mental State Examination assessment(including 42 healthy control,38 T2 DM without cognitive impairment,26 with cognitive impairment but without T2 DM,and 30 T2 DM with cognitive impairment participants).The total and sub-category brain atrophy and lesion index scores in patients with T2 DM with cognitive impairment were higher than those in healthy controls.Differences in the brain atrophy and lesion index of gray matter lesions and subcortical dilated perivascular spaces were found between non-T2 DM patients with cognitive impairment and patients with T2 DM and cognitive impairment.After adjusting for age,the brain atrophy and lesion index retained its capacity to identify patients with T2 DM with cognitive impairment.These findings suggest that the brain atrophy and lesion index,based on T1-weighted and T2-weighted imaging,is of clinical value for identifying patients with T2 DM and cognitive impairment.Gray matter lesions and subcortical dilated perivascular spaces may be potential diagnostic markers of T2 DM that is complicated by cognitive impairment.This study was approved by the Medical Ethics Committee of University of South China(approval No.USC20131109003) on November 9,2013,and was retrospectively registered with the Chinese Clinical Trial Registry(registration No.Chi CTR1900024150) on June 27,2019.展开更多
In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped i...In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.展开更多
基金supported by the National Natural Science Foundation of China,Nos.81671671(to JL),61971451(to JL),U22A2034(to XK),62177047(to XK)the National Defense Science and Technology Collaborative Innovation Major Project of Central South University,No.2021gfcx05(to JL)+6 种基金Clinical Research Cen terfor Medical Imaging of Hunan Province,No.2020SK4001(to JL)Key Emergency Project of Pneumonia Epidemic of Novel Coronavirus Infection of Hu nan Province,No.2020SK3006(to JL)Innovative Special Construction Foundation of Hunan Province,No.2019SK2131(to JL)the Science and Technology lnnovation Program of Hunan Province,Nos.2021RC4016(to JL),2021SK53503(to ML)Scientific Research Program of Hunan Commission of Health,No.202209044797(to JL)Central South University Research Program of Advanced Interdisciplinary Studies,No.2023Q YJC020(to XK)the Natural Science Foundation of Hunan Province,No.2022JJ30814(to ML)。
文摘Patients with mild traumatic brain injury have a diverse clinical presentation,and the underlying pathophysiology remains poorly understood.Magnetic resonance imaging is a non-invasive technique that has been widely utilized to investigate neuro biological markers after mild traumatic brain injury.This approach has emerged as a promising tool for investigating the pathogenesis of mild traumatic brain injury.G raph theory is a quantitative method of analyzing complex networks that has been widely used to study changes in brain structure and function.However,most previous mild traumatic brain injury studies using graph theory have focused on specific populations,with limited exploration of simultaneous abnormalities in structural and functional connectivity.Given that mild traumatic brain injury is the most common type of traumatic brain injury encounte red in clinical practice,further investigation of the patient characteristics and evolution of structural and functional connectivity is critical.In the present study,we explored whether abnormal structural and functional connectivity in the acute phase could serve as indicators of longitudinal changes in imaging data and cognitive function in patients with mild traumatic brain injury.In this longitudinal study,we enrolled 46 patients with mild traumatic brain injury who were assessed within 2 wee ks of injury,as well as 36 healthy controls.Resting-state functional magnetic resonance imaging and diffusion-weighted imaging data were acquired for graph theoretical network analysis.In the acute phase,patients with mild traumatic brain injury demonstrated reduced structural connectivity in the dorsal attention network.More than 3 months of followup data revealed signs of recovery in structural and functional connectivity,as well as cognitive function,in 22 out of the 46 patients.Furthermore,better cognitive function was associated with more efficient networks.Finally,our data indicated that small-worldness in the acute stage could serve as a predictor of longitudinal changes in connectivity in patients with mild traumatic brain injury.These findings highlight the importance of integrating structural and functional connectivity in unde rstanding the occurrence and evolution of mild traumatic brain injury.Additionally,exploratory analysis based on subnetworks could serve a predictive function in the prognosis of patients with mild traumatic brain injury.
基金supported by the National Key Research and Development Program of China(No.2018YFA0702800)the National Natural Science Foundation of China(No.12072056)supported by National Defense Fundamental Scientific Research Project(XXXX2018204BXXX).
文摘The safety and integrity requirements of aerospace composite structures necessitate real-time health monitoring throughout their service life.To this end,distributed optical fiber sensors utilizing back Rayleigh scattering have been extensively deployed in structural health monitoring due to their advantages,such as lightweight and ease of embedding.However,identifying the precise location of damage from the optical fiber signals remains a critical challenge.In this paper,a novel approach which namely Modified Sliding Window Principal Component Analysis(MSWPCA)was proposed to facilitate automatic damage identification and localization via distributed optical fiber sensors.The proposed method is able to extract signal characteristics interfered by measurement noise to improve the accuracy of damage detection.Specifically,we applied the MSWPCA method to monitor and analyze the debonding propagation process in honeycomb sandwich panel structures.Our findings demonstrate that the training model exhibits high precision in detecting the location and size of honeycomb debonding,thereby facilitating reliable and efficient online assessment of the structural health state.
基金Acknowledgments. This research is supported by the Knowledge Innovative Foundation of Chinese Academy of Science (No. KZCX2-204, No. KZ-CX-SW-01-01B), and the National Natural Science Foundation of China (No. 40035010). The authors thank Professors Huang
文摘A parameter-free method based on orthonormal wavelet transforms is recommended for calculating the principal time scale of coherent structures in atmospheric boundary-layer measurements. First, the atmospheric turbulent signal is decomposed into the small scale vortex that has approximate isotropy and the large scale vortex with the digital filter. Then, the large scale vortex is used to detect coherent structures with this method. The principal time scale and profile of coherent structures for velocity components (u, v, w above rice fields are obtained. In order to testify the validity of this method, the correlation of coherent structures and non-coherent structures are also calculated.
基金supported by the National Natural Science Foundation of China(61471391)the China Postdoctoral Science Foundation(2013M542541)
文摘Based on the cognitive radar concept and the basic connotation of cognitive skywave over-the-horizon radar(SWOTHR), the system structure and information processingmechanism about cognitive SWOTHR are researched. Amongthem, the hybrid network system architecture which is thedistributed configuration combining with the centralized cognition and its soft/hardware framework with the sense-detectionintegration are proposed, and the information processing framebased on the lens principle and its information processing flowwith receive-transmit joint adaption are designed, which buildand parse the work law for cognition and its self feedback adjustment with the lens focus model and five stages informationprocessing sequence. After that, the system simulation andthe performance analysis and comparison are provided, whichinitially proves the rationality and advantages of the proposedideas. Finally, four important development ideas of futureSWOTHR toward "high frequency intelligence information processing system" are discussed, which are scene information fusion, dynamic reconfigurable system, hierarchical and modulardesign, and sustainable development. Then the conclusion thatthe cognitive SWOTHR can cause the performance improvement is gotten.
基金funded through a contract from the Federal Highway Administration (Contract No.ETFH61-98-C-00094)a grant from the Earthquake Education Research Centers Program of the National Science Foundation to the Multidisciplinary Center for Earthquake Engineering Research (Grant No.ECC-9701471).
文摘This paper is the first in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads. The primary purpose of this series is to understand the magnitude of the dynamic response of structures to enable better design of structures and control modification devices/systems. Under idealized design conditions, the structural responses are obtained by using single direction input ground motions in the direction of the intended control devices/systems, and by assuming that the responses of the structure is decoupleable in three mutually perpendicular directions. This standard practice has been applied to both new and retrofitted structures using various seismic protective systems. Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects - of which torsion is a component) of the dynamic response of structures. In order to quantify such effects, it is necessary to examine the principal axes of structures under both static and dynamic loading. This first paper deals with quantitative definitions of principal axes and “cross effects” of three-dimensional structures under static load by using linear algebra. It shows theoretically that, for three-dimensional structures, such principal axes rarely exist. Under static loading conditions, the cross effect is typically small and negligible from the viewpoint of engineering applications. However, it provides the theoretical base for subsequent quantification of the response couplings under dynamic loads, which is reported in part II of this series.
基金a contract from the Federal Highway Adiministration(Contract No.ETFH61-98-C-00094)a Grant from the Earthquake Education Research Centers Program of the National Science Foundation to the Multidisciplinary Center for Earthquake Engineering Research(Grant No.EEC-9701471)
文摘This paper is the second in a two-part series that discusses the principal axes of M-DOF structures subjected to static and dynamic loads.The primary purpose of this series is to understand the magnitude of the dynamie response of structures to enable better design of structures and response modification devices/systems.Under idealized design condi- tions,the structural responses are obtained by using single directinn input ground motions in the direction of the intended response modification devices/systems,and by assuming that the responses of the structure is deconpleable in three mutual- ly perpendicular directions.This standard practice has been applied to both new and retrofitted structures using various seis- mic protective systems.Very limited information is available on the effects of neglecting the impact of directional couplings (cross effects of which torsion is a component)of the dynamic response of structures.In order to quantify such effects,it is necessary to examine the principal axes of structures under both static and dynamic loading.In this twn-part series,the first paper is concerned with static loading,which provides definitions and fundamental formulations,with the conclusion that cross effects of a statically loaded M-DOF structure resulting from the lack of principal axes are of insignificant magnitude. However,under dynamic or earthquake loading,a relatively small amount of energy transferred across perpendicular direc- tions is accumulated,which may result in significant enlargement of the structural response.This paper deals with a formu- lation to define the principal axes of M-DOF structures under dynamic loading and develops quantitative measures to identify cross effects resuhing from the non-existence of principal axes.
基金supported by grants from the National Natural Science Foundation of China (Grant no. 81001686)
文摘This paper studied the expert system of genotype discrimination for the STR locus D5S818 based on near-infrared spectroscopy-principal discriminant variate (PDV).Six genotypes,i.e.genotypes 10-10,10-11,11-11,11-12,11-13 and 13-13,were selected as research subjects.Based on the optimum polymerase chain reaction (PCR) conditions,about 54 measuring samples for each genotype were obtained;these samples were tested by near-infrared spectroscopy directly.With differences between homozygote genotypes and heterozygote ones,and differences of the total number of core repeat units between the six genotypes,two types of genotyping-tree structure were constructed and their respective PDV models were studied using the near-infrared spectra of the samples as recognition variables.Finally,based on the classification ability of these two genotyping-tree structures,an optimum expert system of genotype discrimination was built using the PDV models.The result demonstrated that the built expert system had good discriminability and robustness;without any preprocessing for PCR products,the six genotypes studied could be discriminated rapidly and correctly.It provided a methodological support for establishing an expert system of genotype discrimination for all genotypes of locus D5S818 and other STR loci.
基金the Mexican National Council for Science and Technology(Consejo Nacional de Ciencia y Tecnología,CONACYT)for the scholarship granted to the first authorTo Ofelia Castillo Díaz from the Mexican National Protected Areas Commission in the state of Aguascalientes for offering support and financing part of the field work。
文摘Litsea glaucescens Kunth(Mexican bay leaf,laurel)has a wide distribution in Mexico,growing at both riparian and rupicolous environments in the mountainous region of the Central Highlands of the country.Sierra Fría-Sierra Laurel is a protected natural area covered by a dry forest.The Mexican bay leaf is associated with the oak forest,especially on ravines.The species has been considered at risk in recent years.This research is focused on analyzing the elements of the environment of the ravines,which are influencing the distribution and establishment of laurel populations in the region.Two mountainous regions of Aguascalientes were selected,Sierra Fría and Sierra Laurel.Three ravines of the basin were selected to obtain environmental data.Variables registered were topographic,edaphic,and biotic.Principal component analysis was used to identify ecological factors associated with the presence of L.glaucescens.Mexican bay leaf populations were registered in 10 ravines.At the structural level in the community,29 woody species were registered,Mexican bay leaf had an Importance Value Index of 15.8,ranking 10th among all species.Individuals of laurel were classified by size classes(S,individuals with heights ranging from 0 to 20 cm;S,heights ranging from 0.2 to 1.0 m;S,heights between 1 and 2 m with light trace of flowering;S,heights greater than 2 m with flowering greater than 30% of the canopy;and S,individuals with heights greater than 5 m,curved trunk and basal regrowth)to obtain the population structure.The importance index value for all the species in the riparian community was calculated to the community level.Edaphic factors that characterized the presence of Mexican bay leaf were a high percentage of rock coverage(90%),less mulch depth,and sandy loam shallow soils.Sites that showed higher cation exchange capacity had a higher presence of individuals of the S,S,and Ssize classes.Class Sindividuals were found in shady places with 97% of intercepted light.Individuals of classes Sand Sendure less shady places(75%–85% of intercepted light),and individuals class Sand Sare more frequent in open canopies and crag conditions.Regarding the ecological site factors,such as riverside stream,and rocks on mountain slopes,L.glaucescens life form is riparian and rupicolous.Cation exchange capacity,sodium and calcium levels play an important role in the presence of Mexican bay leaf.Distribution on the ravine and recruitment of the Mexican bay leaf populations are associated with shaded sites,mainly for individuals of size classes Sand S,versus sunny places for individuals of size classes Sand S.The overall population structure had a positive kurtosis with all plant size categories well represented;statistically,the population structure of L.glaucescens is very close to the normal distribution.The information obtained allows us to affirm that the laurel populations in the mountainous areas of Sierra Fría and Sierra Laurel from central Mexico are in good demographic condition.
基金supported by the Natural Science Foundation of Fujian Province (D0710019)the Natural Science Foundation of Overseas Chinese Affairs Office of the State Council (09QZR07)
文摘10 quantum chemical descriptors of 21 aromatic compounds have been calculated by the semi-empirical quantum chemical method AM1. The Quantitative Structure-Biodegradability Relationships (QSBR) studies were performed by the multiple linear regression (MLR), principal component regression (PCR) and back propagation artificial neural network (BP-ANN), respectively. The root mean square error (RMSE) of the training and validation sets of the BP-ANN model are 0.1363 and 0.0244, the mean absolute percentage errors (MAPE) are 0.1638 and 0.0326, the squared correlation coefficients (R^2) are 0.9853 and 0.9996, respectively. The results show that the BP-ANN model achieved a better prediction result than those of MLR and PCR. In addition, some insights into the structural factors affecting the aerobic biodegradation mechanism were discussed in detail.
文摘Cognitive optical network is the intermediate to combine artificial intelligence technology with network,and also the important network technology to promote network intelligence level constantly.In the paper,it analyzes the cognitive optical network structure with the application of artificial intelligence technology by starting from the basic conditions of cognitive network and cognitive optional network on the basis of fully understanding the connotation of cognitive network and cognitive optical network,and explores its self-governance functions,so as to better realize the self-optimization and self-configuration of network.
文摘This paper approaches two main philosophical questions concerning the biological structures,from unicellular to multicellular organisms:one of them(i),referred to the information-body relation,as an extension of the mind-body relation at human,and another one(ii),to the consciousness problem,concerning the existence and nature of consciousness(if any),at the inferior organisms on the complexity scale,as this concept is known at humans.As philosophy benefits of the privilege to use data/concepts from other sciences to obtain philosophical conclusions,there were included detailed descriptions of some key biologic mechanisms,analyzed from informational perspective,necessary just to support/demonstrate/reinforce the informational nature/substrate of the mentioned relations.The analysis of the close relation between information and body,related to the structuration and functional properties of the biological organisms,from cells to multicellular structures,shows that all of them are able to“embody/disembody”information during/by structuration/destructuration processes of matter,in particular that of DNA/RNA/proteins,their functions appearing as a result of their informational capabilities to internally manage the inter-connection with environment,primarily due to their permanent dependence on the food resources and adaptation/survival needs.The experimental and theoretical studies,revealing/documenting on one hand the automatic management of maintenance metabolic processes,the reproduction,and growth/development,and on the other hand the adaptive decision-making/sentient processes as a responsive reaction to the environmental cues,show/support the consistency of the informational model of the human body and living structures on the entire biological scale,providing support to the informational solution of the stated problems(i)and(ii).A distinct attention is paid to plants,which are organisms without nervous system,but which show/manifest also informational capabilities to detect/react to information and to modulate their behavior accordingly.The question if the living organisms possess a pseudo/proto-consciousness level as a consequence of the informational activity of their body,distinct from human,but active in any biological structure under certain conditions is furthermore discussed,and a reliable definition of rudimentary pseudo/proto-consciousness level is given/described and compared with other empirical/theoretical concepts.
文摘Using the method of principal component analysis, the paper conducts a systematic study on the issue of how corporate governance influences capital structure. The study manifests the results that the proportion of circulation shares, the ability that other big shareholders contend with the first biggest shareholder, the proportion of corporation-owned shares, and the frequency of directorate meetings all have a positive relationship with the liability level. Meanwhile, the concentration degree of owners' equity, the proportion of state-owned shares, the phenomenon that one person serves as both chairman of directorate and general manager, and the intensity of competition in product market are all negatively related to the level of debt. Finally, the scale of directorate, the proportion of independent directors as well as the percentage of management-owned shares have no significant relationship with the capital structure. The statistic analysis also shows that the proportion of independent directors of some Chinese listed companies does not meet the regulation of the CSRC. In addition, the paper tests the impacts of corporate operating characteristics on capital structure.
文摘Translational discourse requires at least three participants, therefore it is suggested to consider the universal model of the picture of the world, according to which it is much easier for a translator to combine the pictures of the world of an addressee and an author. An addressee is a mental image existing in the mind of an addresser during the creative process. Having defined its parameters, a translator has an opportunity to deliver the thought of an addresser to an addressee as accurately as possible and to select the means of expression that are clear to an addressee. The type of an addressee correlates with "the relation to the new".
基金the National Natural Science Foundation of China (No.60421002).
文摘Principal component analysis (PCA) is a useful tool in process fault detection, but offers little support on fault isolation. In this article, structured residual with strong isolation property is introduced. Although it is easy to get the residual by transformation matrix in static process, unfortunately, it becomes hard in dynamic process under control loop. Therefore, partial dynamic PCA(PDPCA) is proposed to obtain structured residual and enhance the isolation ability of dynamic process monitoring, and a compound statistic is introduced to resolve the problem resulting from independent variables in every variable subset. Simulations on continuous stirred tank reactor (CSTR) show the effectiveness of the proposed method.
基金Joint Seismological Science Foundation of China (No. 201017).
文摘When the resultant of applied forces does not pass through the center of an active landmass, the landmass will rotate, giving rise to a rotational tectonic stress field. The motion of a fault along the principal stress plane is de-termined by the mechanic features of the plane. Tensile fractures occur on the faults in the direction of the principal extensional stress plane, and fault-depression basins will be formed under a long-term action. Thrusting and over-thrusting occur on faults in the direction of the principal compressional stress plane, or folds may be formed as a result. Information on geology shows that the North China landmass, which remained stable and intact for a long time, became disjointed in the Eogene period. In the course of disjunction, anticlockwise rotation took place in the Shanxi-Hebei-Shaanxi (Jin-Ji-Shan) landmass, giving rise to the fault-depression system in its periphery. In the Pliocene epoch the landmass lost stability and its eastern boundary moved westward. As a result, the Shanxi gra-ben system appeared and Ordos landmass was formed. Structural and mechanic features of the main faults around Jin-Ji-Shan landmass can be explained with principal stress plane of a rotational tectonic stress field.
基金the support of the National Natural Science Foundation of China (Grant No. 11902210)the Graduate Student’s Research Innovation Foundation of Sichuan University (Grant No. 2018YJSY076)
文摘The stability of the surrounding rocks of large underground powerhouses is always emphasized during the construction process,especially in large-scale underground projects under construction,such as the Baihetan hydropower station in China.According to field investigations,numerical simulations and monitoring data analysis,we present a comparative analysis of the deformation and failure characteristics of the surrounding rocks of underground powerhouses on the left and right banks of the Baihetan hydropower station.The failure characteristics and deformation magnitude of the underground powerhouses on the left and right banks are quite different.Under the disadvantageous condition where the maximum principal stress intersects the axis of the powerhouse at a large angle,the left bank underground powerhouse shows prominent stress-controlled failure characteristics such as spalling,slack collapse and concrete cracking.Although the maximum principal stress is in the favorable condition which intersects the right bank powerhouse at a small angle,the relatively high intermediate principal stress with an angle subvertical to the right bank powerhouse plays an essential role in its deformation and failure,indicating that the influence of high intermediate principal stress cannot be ignored.In addition,structural plane-controlled failure and large deformation are also more evident on the right bank due to the extensive distribution of weak structural planes and complex surrounding rock properties.
基金This work was supported by the Science and Technology Support Plan of Guizhou Province of China,No.QianKeHe-Zhicheng[2020]4Y129(to HB)the Scientific Research Foundation of Guizhou Health Committee of China,No.gzwkj2017-1-022(to HB)the Scientific Research Project of Guizhou Traditional Chinese Medicine Bureau of China,No.QZYY-2018-044(to HB).
文摘Neurological abnormalities identified via neuroimaging are common in patients with Alzheimer’s disease.However,it is not yet possible to easily detect these abnormalities using head computed tomography in the early stages of the disease.In this review,we evaluated the ways in which modern imaging techniques such as positron emission computed tomography,single photon emission tomography,magnetic resonance spectrum imaging,structural magnetic resonance imaging,magnetic resonance diffusion tensor imaging,magnetic resonance perfusion weighted imaging,magnetic resonance sensitive weighted imaging,and functional magnetic resonance imaging have revealed specific changes not only in brain structure,but also in brain function in Alzheimer’s disease patients.The reviewed literature indicated that decreased fluorodeoxyglucose metabolism in the temporal and parietal lobes of Alzheimer’s disease patients is frequently observed via positron emission computed tomography.Furthermore,patients with Alzheimer’s disease often show a decreased N-acetylaspartic acid/creatine ratio and an increased myoinositol/creatine ratio revealed via magnetic resonance imaging.Atrophy of the entorhinal cortex,hippocampus,and posterior cingulate gyrus can be detected early using structural magnetic resonance imaging.Magnetic resonance sensitive weighted imaging can show small bleeds and abnormal iron metabolism.Task-related functional magnetic resonance imaging can display brain function activity through cerebral blood oxygenation.Resting functional magnetic resonance imaging can display the functional connection between brain neural networks.These are helpful for the differential diagnosis and experimental study of Alzheimer’s disease,and are valuable for exploring the pathogenesis of Alzheimer’s disease.
基金supported by the National Natural Science Foundation of China,No.81271538 (to SNP)345 Talent Project and the Natural Science Foundation of Liaoning Province of China,No.2019-ZD-0794 (to SNP)+1 种基金the Natural Science Foundation of Hunan Province of China,Nos.2017JJ2225 (to JCL),2018JJ2357 (to GHL)Hunan Provincial Science and Technology Innovation Program of China,No.2017SK50203 (to HZ)。
文摘Patients with type 2 diabetes mellitus(T2 DM) often have cognitive impairment and structural brain abnormalities.The magnetic resonance imaging(MRI)-based brain atrophy and lesion index can be used to evaluate common brain changes and their correlation with cognitive function,and can therefore also be used to reflect whole-brain structural changes related to T2 DM.A total of 136 participants(64 men and 72 women,aged 55–86 years) were recruited for our study between January 2014 and December 2016.All participants underwent MRI and Mini-Mental State Examination assessment(including 42 healthy control,38 T2 DM without cognitive impairment,26 with cognitive impairment but without T2 DM,and 30 T2 DM with cognitive impairment participants).The total and sub-category brain atrophy and lesion index scores in patients with T2 DM with cognitive impairment were higher than those in healthy controls.Differences in the brain atrophy and lesion index of gray matter lesions and subcortical dilated perivascular spaces were found between non-T2 DM patients with cognitive impairment and patients with T2 DM and cognitive impairment.After adjusting for age,the brain atrophy and lesion index retained its capacity to identify patients with T2 DM with cognitive impairment.These findings suggest that the brain atrophy and lesion index,based on T1-weighted and T2-weighted imaging,is of clinical value for identifying patients with T2 DM and cognitive impairment.Gray matter lesions and subcortical dilated perivascular spaces may be potential diagnostic markers of T2 DM that is complicated by cognitive impairment.This study was approved by the Medical Ethics Committee of University of South China(approval No.USC20131109003) on November 9,2013,and was retrospectively registered with the Chinese Clinical Trial Registry(registration No.Chi CTR1900024150) on June 27,2019.
文摘In Advances in Pure Mathematics (www.scirp.org/journal/apm), Vol. 1, No. 4 (July 2011), pp. 136-154, the mathematical structure of the much discussed problem of probability known as the Monty Hall problem was mapped in detail. It is styled here as Monty Hall 1.0. The proposed analysis was then generalized to related cases involving any number of doors (d), cars (c), and opened doors (o) (Monty Hall 2.0) and 1 specific case involving more than 1 picked door (p) (Monty Hall 3.0). In cognitive terms, this analysis was interpreted in function of the presumed digital nature of rational thought and language. In the present paper, Monty Hall 1.0 and 2.0 are briefly reviewed (§§2-3). Additional generalizations of the problem are then presented in §§4-7. They concern expansions of the problem to the following items: (1) to any number of picked doors, with p denoting the number of doors initially picked and q the number of doors picked when switching doors after doors have been opened to reveal goats (Monty Hall 3.0;see §4);(3) to the precise conditions under which one’s chances increase or decrease in instances of Monty Hall 3.0 (Monty Hall 3.2;see §6);and (4) to any number of switches of doors (s) (Monty Hall 4.0;see §7). The afore-mentioned article in APM, Vol. 1, No. 4 may serve as a useful introduction to the analysis of the higher variations of the Monty Hall problem offered in the present article. The body of the article is by Leo Depuydt. An appendix by Richard D. Gill (see §8) provides additional context by building a bridge to modern probability theory in its conventional notation and by pointing to the benefits of certain interesting and relevant tools of computation now available on the Internet. The cognitive component of the earlier investigation is extended in §9 by reflections on the foundations of mathematics. It will be proposed, in the footsteps of George Boole, that the phenomenon of mathematics needs to be defined in empirical terms as something that happens to the brain or something that the brain does. It is generally assumed that mathematics is a property of nature or reality or whatever one may call it. There is not the slightest intention in this paper to falsify this assumption because it cannot be falsified, just as it cannot be empirically or positively proven. But there is no way that this assumption can be a factual observation. It can be no more than an altogether reasonable, yet fully secondary, inference derived mainly from the fact that mathematics appears to work, even if some may deem the fact of this match to constitute proof. On the deepest empirical level, mathematics can only be directly observed and therefore directly analyzed as an activity of the brain. The study of mathematics therefore becomes an essential part of the study of cognition and human intelligence. The reflections on mathematics as a phenomenon offered in the present article will serve as a prelude to planned articles on how to redefine the foundations of probability as one type of mathematics in cognitive fashion and on how exactly Boole’s theory of probability subsumes, supersedes, and completes classical probability theory. §§2-7 combined, on the one hand, and §9, on the other hand, are both self-sufficient units and can be read independently from one another. The ultimate design of the larger project of which this paper is part remains the increase of digitalization of the analysis of rational thought and language, that is, of (rational, not emotional) human intelligence. To reach out to other disciplines, an effort is made to describe the mathematics more explicitly than is usual.