Canonical Space Research Articles

Linear discriminant analysis for multiple functional data analysis

In multivariate data analysis, Fisher linear discriminant analysis is useful to optimally separate two classes of observations by finding a linear combination of p variables. Functional data analysis deals with the analysis of continuous functions and thus can be seen as a generalisation of multivariate analysis where the dimension of the analysis space p strives to infinity. Several authors propose methods to perform discriminant analysis in this infinite dimensional space. Here, the methodology is introduced to perform discriminant analysis, not on single infinite dimensional functions, but to find a linear combination of p infinite dimensional continuous functions, providing a set of continuous canonical functions which are optimally separated in the canonical space.

Impact of infusion therapy programs on homeostasis indicators in patients suffering from shockogenic trauma from the point of view of statistical reliability

From the point of view of statistical reliability, the influence of various infusion therapy programs on homeostasis indicators of patients suffering from shockogenic trauma is considered. It has been revealed that when entering the intensive care and intensive care department in patients suffering from severe traumatic shock, against the background of algorithms of anti-shock measures at the pre-emergency and hospital stages there are significant individual intervals of examined homeostasis parameters, which indicates expressed personalized disorders of indicators of reflecting function of organs and systems of patients. The variation in the canonical space of the investigated parameters in patients increased after 12 hours, after admission to the intensive care and resuscitation department. Anti-shock therapy contributed to the fact that the distribution of patients of all three groups in the canonical space after the first 24 hours was dynamically compacted, indicating a decrease in differences between patients of each group during the treatment process. Cluster analysis and multi-dimensional scaling revealed the multilateral dynamics of the relationship between independent variables in various infusion therapy programmes. When patients were admitted to the intensive care and intensive care unit, almost the same orientation of the features of connections between independent variables was noted, however, their polarity was recorded during the treatment process. This shows that the infusion therapy program in patients suffering from severe traumatic shock should be carried out taking into account the dynamics of individual disorders of the investigated homeostasis parameters. It has been statistically proven that different infusion therapy programs have very different effects on homeostasis rates. The use of sterofundin isotonic and 4% modified gelatin in this category of patients has been proven to be the most effective and safe volemic recovery scheme.

Robust utility maximization of terminal wealth with drift and volatility uncertainty

ABSTRACT We give explicit solutions for utility maximization of terminal wealth problem in the presence of Knightian uncertainty in continuous time . We assume there is uncertainty on both drift and volatility of the underlying stocks, which induce nonequivalent measures on canonical space of continuous paths Ω. We take that the uncertainty set resides in compact sets that are time dependent. In this framework, we solve the robust optimization problem with logarithmic, power and exponential utility functions, explicitly. Numerical simulations revealing the effects of uncertainty on the dynamics are also presented.

Hyperalignment: Modeling shared information encoded in idiosyncratic cortical topographies.

Information that is shared across brains is encoded in idiosyncratic fine-scale functional topographies. Hyperalignment captures shared information by projecting pattern vectors for neural responses and connectivities into a common, high-dimensional information space, rather than by aligning topographies in a canonical anatomical space. Individual transformation matrices project information from individual anatomical spaces into the common model information space, preserving the geometry of pairwise dissimilarities between pattern vectors, and model cortical topography as mixtures of overlapping, individual-specific topographic basis functions, rather than as contiguous functional areas. The fundamental property of brain function that is preserved across brains is information content, rather than the functional properties of local features that support that content. In this Perspective, we present the conceptual framework that motivates hyperalignment, its computational underpinnings for joint modeling of a common information space and idiosyncratic cortical topographies, and discuss implications for understanding the structure of cortical functional architecture.

On Dynamic Programming Principle for Stochastic Control Under Expectation Constraints

This paper studies the dynamic programming principle using the measurable selection method for stochastic control of continuous processes. The novelty of this work is to incorporate intermediate expectation constraints on the canonical space at each time t. Motivated by some financial applications, we show that several types of dynamic trading constraints can be reformulated into expectation constraints on paths of controlled state processes. Our results can therefore be employed to recover the dynamic programming principle for these optimal investment problems under dynamic constraints, possibly path-dependent, in a non-Markovian framework.

Existence of limiting distribution for affine processes

In this paper, sufficient conditions are given for the existence of limiting distribution of a conservative affine process on the canonical state space R⩾0m×Rn, where m,n∈Z⩾0 with m+n>0. Our main theorem extends and unifies some known results for OU-type processes on Rn and one-dimensional CBI processes (with state space R⩾0). To prove our result, we combine analytical and probabilistic techniques; in particular, the stability theory for ODEs plays an important role.

Elementary operators on Hilbert modules over prime C⁎-algebras

Let X be a right Hilbert module over a C⁎-algebra A equipped with the canonical operator space structure. We define an elementary operator on X as a map ϕ:X→X for which there exists a finite number of elements ui in the C⁎-algebra B(X) of adjointable operators on X and vi in the multiplier algebra M(A) of A such that ϕ(x)=∑iuixvi for x∈X. If X=A this notion agrees with the standard notion of an elementary operator on A. In this paper we extend Mathieu's theorem for elementary operators on prime C⁎-algebras by showing that the completely bounded norm of each elementary operator on a non-zero Hilbert A-module X agrees with the Haagerup norm of its corresponding tensor in B(X)⊗M(A) if and only if A is a prime C⁎-algebra.

Dependence Analysis Between Childhood Social Indicators and Human Development Index Through Canonical Correlation Analysis

This paper presents a dependence analysis between childhood social indicators (selected from the UNICEF and World Development Indicators) and the Human Development Index (HDI). This analysis, made through a canonical correlation, aimed to measure the relationship between child well-being and the modern standards of sustainable social development. First we have selected variables related to basic needs for children until primary school from the UNICEF database, and to mitigate missing values problem, for each country we have taken the average value per year, and, if missing values problem persists, a proper statistical imputation technique was applied. Then, with all variables having complete cases, the canonical correlation analysis generated a canonical space divided into four quadrants in order to verify the relations between variables and countries. We have found two significant characteristic roots with canonical correlation values of 0.91 and 0.56, each characteristic root was, respectively, labeled as “Health & Primary Schooling” (showing an inverse correlation between neonatal mortality rate and health and primary schooling) and “Primary Education” showing a positive correlation between primary education enrollments and primary education completion. Our approach indicates that the selected child well-being indicators not only are correlated to the HDI, but they also complement this development measure considering child well-being indicators, because considering the health and education variables it could be identified countries from a superior HDI class that are more similar with countries from an inferior HDI class and countries from an inferior HDI class that are more similar with countries from a superior class. Although the selected variables represent the underlying conditions for a child to grow up with dignity, according to United Nations’ Sustainable Development Goals, the data availability for variables with low occurrences of missing cases was scarce, preventing the use of all available variables from the UNICEF database. We have divided the canonical space into four quadrants, each one with dominant characteristics from a specific HDI class. Then, the presented 182 countries were plotted against this space in order to relate the childhood well-being indicator with the HDI classes.

Statistical mechanics of gravitational systems with regular orbits: rigid body model of vector resonant relaxation

I consider a self-gravitating, N-body system assuming that the N constituents follow regular orbits about the center of mass of the cluster, where a central massive object may be present. I calculate the average over a characteristic timescale of the full, N-body Hamiltonian including all kinetic and potential energy terms. The resulting effective system allows for the identification of the orbital planes with N rigid, disk-shaped tops, that can rotate about their fixed common centre and are subject to mutual gravitational torques. The time-averaging imposes boundaries on the canonical generalized momenta of the resulting canonical phase space. I investigate the statistical mechanics induced by the effective Hamiltonian on this bounded phase space and calculate the thermal equilibrium states. These are a result of the relaxation of spins’ directions, identified with orbital planes’ orientations, which is called vector resonant relaxation. I calculate the dependence of spins’ angular velocity dispersion on temperature and calculate the velocity distribution functions. I argue that the range of validity of the gravitational phase transitions, identified in the special case of zero kinetic term by Roupas, Kocsis and Tremaine, is expanded to non-zero values of the ratio of masses between the cluster of N-bodies and the central massive object. The relevance with astrophysics is discussed focusing on stellar clusters. The same analysis performed on an unbounded phase space accounts for continuous rigid tops.

Faster Dynamic Graph CNN: Faster Deep Learning on 3D Point Cloud Data

Geometric data are commonly expressed using point clouds, with most 3D data collection devices outputting data in this form. Research on processing point cloud data for deep learning is ongoing. However, it has been difficult to apply such data as input to a convolutional neural network (CNN) or recurrent neural network (RNN) because of their unstructured and unordered features. In this study, this problem was resolved by arranging point cloud data in a canonical space through a graph CNN. The proposed graph CNN works dynamically at each layer of the network and learns the global geometric features by capturing the neighbor information of the points. In addition, by using a squeeze-and-excitation module that recalibrates the information for each layer, we achieved a good trade-off between the performance and the computation cost, and a residual-type skip connection network was designed to train the deep models efficiently. Using the proposed model, we achieved a state-of-the-art performance in terms of classification and segmentation on benchmark datasets, namely ModelNet40 and ShapeNet, while being able to train our model 2 to 2.5 times faster than other similar models.

Properties of Elementary Fermions of the Standard Model Deduced from Linear Canonical Transformations Representation

This paper is a continuation of our works concerning Linear Canonical Transformations (LCT) and Phase Space Representation of Quantum Theory. The purpose is to study the spinorial representation of some particular LCT called Isodispersion LCT (ILCT) and to deduce a relation between them and some properties of the elementary fermions of the Standard Model of Particle Physics. After giving the definition of ILCT for the case of a general pseudo-Euclidean space and constructing their spinorial representation, we consider the particular case of a pentadimensional space with signature (1, 4). We then deduce a classification of quarks, leptons and their antiparticles according to the values of electric charge, weak hypercharge, weak isospin and colors after the introduction of appropriate operators defined from the generators of the Clifford Algebra corresponding to the ILCT spinorial representation. It is established that the electric charge is composed of four terms, the weak hypercharge of five terms and the weak isospin of two terms. Existence of sterile neutrinos and the possibility of describing a fermions generation with a single field are suggested.

Espaço urbano e subversão queer

Neste artigo, pretendo discutir as relações estabelecidas entre gênero, sexualidade e espaço urbano, a partir da prática discursiva intersemiótica de Linn da Quebrada. Pretendo, também, refletir sobre os lugares de resistência que corpos considerados desviantes ocupam subvertendo o valor inicial do espaço urbano, ou seja, ressignificando um status arquitetônico/urbanístico. Assim, fugindo dos padrões naturalizados de gênero e sexualidade passam a viver uma experiência diferente nas cidades, entre centro e periferia, entre lugares e não-lugares, reinventando a cidade com características que ela nunca teve ou jamais imaginou ter. Para esta análise, utilizo um recorte do corpus de minha pesquisa: a canção “Bomba pra Caralho” – como exemplar de produção discursiva do espaço canônico musical (cf. MAINGUENEAU, 2006). Na análise, utilizo o arcabouço teórico e metodológico da Análise do Discurso de linha francesa; reflexões sobre a relação entre o corpo e a cidade vindas da filosofia, sociologia e da arquitetura; além de pressupostos das teorias Queer, para pensar gênero e sexualidade para além da perspectiva dos binarismos, historicamente e discursivamente construídos, que orientam (performam) as práticas dos sujeitos, inclusive no campo da arquitetura e urbanismo.

Categorified canonical bases and framed BPS states

We consider a cluster variety associated to a triangulated surface without punctures. The algebra of regular functions on this cluster variety possesses a canonical vector space basis parametrized by certain measured laminations on the surface. To each lamination, we associate a graded vector space, and we prove that the graded dimension of this vector space gives the expansion in cluster coordinates of the corresponding basis element. We discuss the relation to framed BPS states in $\mathcal{N}=2$ field theories of class $\mathcal{S}$.

The moduli space of Fano manifolds with Kähler–Ricci solitons

We construct a canonical Hausdorff complex analytic moduli space of Fano manifolds with Kähler–Ricci solitons. This enlarges the moduli space of Fano manifolds with Kähler–Einstein metrics. We discover a moment map picture for Kähler–Ricci solitons, and give complex analytic charts on the topological space consisting of Kähler–Ricci solitons, by studying differential geometric aspects of this moment map. Some stacky words and arguments on Gromov–Hausdorff convergence help to glue them together in the holomorphic manner.

Conformal and Killing vector fields on real submanifolds of the canonical complex space form $\mathbb{C}^{m}$

In this paper, we find a conformal vector field as well as a Killing vector field on a compact real submanifold of the canonical complex space form (Cm, J, h , i). In particular, using immersion ψ : M → Cm of a compact real submanifold M and the complex structure J of the canonical complex space form (Cm, J, h , i), we find conditions under which the tangential component of Jψ is a conformal vector field as well as conditions under which it is a Killing vector field. Finally, we obtain a characterization of n-spheres in the canonical complex space form (Cm, J, h , i).

Effective quantum extended spacetime of polymer Schwarzschild black hole

The physical interpretation and eventual fate of gravitational singularities in a theory surpassing classical general relativity are puzzling questions that have generated a great deal of interest among various quantum gravity approaches. In the context of loop quantum gravity (LQG), one of the major candidates for a non-perturbative background-independent quantisation of general relativity, considerable effort has been devoted to construct effective models in which these questions can be studied. In these models, classical singularities are replaced by a ‘bounce’ induced by quantum geometry corrections. Undesirable features may arise however depending on the details of the model. In this paper, we focus on Schwarzschild black holes and propose a new effective quantum theory based on polymerisation of new canonical phase space variables inspired by those successful in loop quantum cosmology. The quantum corrected spacetime resulting from the solutions of the effective dynamics is characterised by infinitely many pairs of trapped and anti-trapped regions connected via a space-like transition surface replacing the central singularity. Quantum effects become relevant at a unique mass independent curvature scale, while they become negligible in the low curvature region near the horizon. The effective quantum metric describes also the exterior regions and asymptotically classical Schwarzschild geometry is recovered. We however find that physically acceptable solutions require us to select a certain subset of initial conditions, corresponding to a specific mass (de-)amplification after the bounce. We also sketch the corresponding quantum theory and explicitly compute the kernel of the Hamiltonian constraint operator.

Top-Push Constrained Modality-Adaptive Dictionary Learning for Cross-Modality Person Re-Identification

Person re-identification aims to match person captured by multiple non-overlapping cameras that mainly mean standard RGB cameras. In contemporary surveillance, cameras of different modalities such as infrared cameras and depth cameras are introduced because of their unique advantages in poor illumination scenarios. However, re-identifying the persons across such cameras of different modalities is extremely difficult and, unfortunately, seldom discussed. It is mainly caused by extremely different appearances of the person shown under such different camera modalities. In this paper, we tackle this challenging cross-modality people re-identification through a top-push constrained modality-adaptive dictionary learning. The proposed model asymmetrically projects the heterogeneous features from dissimilar modalities onto a common space. In this way, the modality-specific bias is mitigated. Thus, the heterogeneous data can be simultaneously enforced by a shared dictionary in a canonical space. Moreover, a top-push ranking graph regularization is embedded in the proposed model to improve the discriminability, which efficiently further boosts the matching accuracy. In order to implement the proposed model, an iterative process is developed in this paper to optimize these two processes jointly. Extensive experiments on the benchmark SYSU-MM01 and BIWI RGBD-ID person re-identification datasets show promising results which outperform state-of-the-art methods.

Natural Hamiltonian formulation of composite higher derivative theories

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which differs from the usual Ostrogradsky approach to higher derivative theories, are elaborated for mechanical systems and illustrated for simple examples. Both a canonical space and a set of constraints emerge naturally from the transformation rule for the variables. In other words, the setting for quantization and the procedure for eliminating instabilities arise naturally.

Reclaiming an Irish National Hero: Seamus De Búrca’s Biography of Peadar Kearney, The Soldier’s Song (1957)

ABSTRACTAnalyses of musical biography have, understandably, largely focused on well-known composers with an established place in the national myth. To explain why particular events or individuals become incorporated into national narratives, historical research on memory has increasingly turned to the analysis of both forgetting and remembering. Likewise, biographical studies must look beyond great composers to those not deemed worthy of the national myth. Irish playwright Seamus de Búrca attempted to create a canonical space in the national myth for his uncle, Peadar Kearney (O Cearnaigh), in a biography he titled The Soldier’s Song: The Story of Peadar O Cearnaigh. From an Irish nationalist family, de Búrca revered Kearney, a nationalist revolutionary and lyricist of the national anthem, “The Soldier’s Song.” The biography was, however, strikingly unsuccessful, and Kearney remains largely forgotten. A reception history of de Búrca’s biography and an analysis of why Ireland’s national narrative excluded Kearney facilitates an understanding of its ideological underpinnings. A study of de Búrca’s work indicates the value of looking beyond biography itself, not only to reception but to commemoration and processes of social and institutional forgetting.

Deep Cross-Modal Correlation Learning for Audio and Lyrics in Music Retrieval

Deep cross-modal learning has successfully demonstrated excellent performance in cross-modal multimedia retrieval, with the aim of learning joint representations between different data modalities. Unfortunately, little research focuses on cross-modal correlation learning where temporal structures of different data modalities, such as audio and lyrics, should be taken into account. Stemming from the characteristic of temporal structures of music in nature, we are motivated to learn the deep sequential correlation between audio and lyrics. In this work, we propose a deep cross-modal correlation learning architecture involving two-branch deep neural networks for audio modality and text modality (lyrics). Data in different modalities are converted to the same canonical space where intermodal canonical correlation analysis is utilized as an objective function to calculate the similarity of temporal structures. This is the first study that uses deep architectures for learning the temporal correlation between audio and lyrics. A pretrained Doc2Vec model followed by fully connected layers is used to represent lyrics. Two significant contributions are made in the audio branch, as follows: (i) We propose an end-to-end network to learn cross-modal correlation between audio and lyrics, where feature extraction and correlation learning are simultaneously performed and joint representation is learned by considering temporal structures. (ii) And, as for feature extraction, we further represent an audio signal by a short sequence of local summaries (VGG16 features) and apply a recurrent neural network to compute a compact feature that better learns the temporal structures of music audio. Experimental results, using audio to retrieve lyrics or using lyrics to retrieve audio, verify the effectiveness of the proposed deep correlation learning architectures in cross-modal music retrieval.