Natural Embedding Research Articles

Natural Embedding of the Stokes Parameters of Polarimetric Synthetic Aperture Radar Images in a Gate-Based Quantum Computer

Quantum algorithms are designed to process quantum data (quantum bits) in a gate-based quantum computer. They are proven rigorously that they reveal quantum advantages over conventional algorithms when their inputs are certain quantum data or some classical data mapped to quantum data. However, in a practical domain, data are classical in nature, and they are very big in dimension, size, and so on. Hence, there is a challenge to map (embed) classical data to quantum data, and even no quantum advantages of quantum algorithms are demonstrated over conventional ones when one processes the mapped classical data in a gate-based quantum computer. For the practical domain of earth observation (EO), due to the different sensors on remote-sensing platforms, we can map directly some types of EO data to quantum data. In particular, we have polarimetric synthetic aperture radar (PolSAR) images characterized by polarized beams. A polarized state of the polarized beam and a quantum bit are the Doppelganger of a physical state. We map them to each other, and we name this direct mapping a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">natural embedding</i> , otherwise an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">artificial embedding</i> . Furthermore, we process our <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally embedded</i> data in a gate-based quantum computer by using a quantum algorithm regardless of its quantum advantages over conventional techniques; namely, we use the QML network as a quantum algorithm to prove that we <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">naturally embedded</i> our data in input qubits of a gate-based quantum computer. Therefore, we employed and directly processed PolSAR images in a QML network. Furthermore, we designed and provided a QML network with an additional layer of a neural network, namely, a hybrid quantum-classical network, and demonstrate how to program (via optimization and backpropagation) this hybrid quantum-classical network when employing and processing PolSAR images. In this work, we used a gate-based quantum computer offered by an IBM Quantum and a classical simulator for a gate-based quantum computer. Our contribution is that we provided very specific EO data with a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">natural embedding</i> feature, the Doppelganger of quantum bits, and processed them in a hybrid quantum-classical network. More importantly, in the future, these PolSAR data can be processed by future quantum algorithms and future quantum computing platforms to obtain (or demonstrate) some quantum advantages over conventional techniques for EO problems.

Rational cohomology of the moduli space of trigonal curves of genus 5

We compute the rational cohomology of the moduli space of trigonal curves of genus 5. We do this by considering their natural embedding in the first Hirzebruch surface and by using Gorinov-Vassiliev's method.

ON INDEPENDENT SYSTEMS OF DEFINING RELATIONS FOR FREE BURNSIDE GROUPS OF PERIOD 3

We construct systems of independent defining relations for free Burnside groups $B(m,3)$ of ranks $m=2, 3$. The proof for the case $m=2$ is established using the matrix representation of $B(2,3)$. For the case $m=3$ the approach is based on the natural embedding of $B(2,3)$ into $B(3,3)$.

On the Hofer girth of the sphere of great circles

An oriented equator of [Formula: see text] is the image of an oriented embedding [Formula: see text] such that it divides [Formula: see text] into two equal area halves. Following Chekanov, we define the Hofer distance between two oriented equators as the infimal Hofer norm of a Hamiltonian diffeomorphism taking one to another. Consider [Formula: see text] the space of oriented equators. We define the Hofer girth of an embedding [Formula: see text] as the infimum of the Hofer diameter of [Formula: see text], where [Formula: see text] is homotopic to [Formula: see text]. There is a natural embedding [Formula: see text], sending a point on the sphere to the positively oriented great circle perpendicular to it. In this paper, we provide an upper bound on the Hofer girth of [Formula: see text].

Using Language Model to Bootstrap Human Activity Recognition Ambient Sensors Based in Smart Homes

Long Short Term Memory (LSTM)-based structures have demonstrated their efficiency for daily living recognition activities in smart homes by capturing the order of sensor activations and their temporal dependencies. Nevertheless, they still fail in dealing with the semantics and the context of the sensors. More than isolated id and their ordered activation values, sensors also carry meaning. Indeed, their nature and type of activation can translate various activities. Their logs are correlated with each other, creating a global context. We propose to use and compare two Natural Language Processing embedding methods to enhance LSTM-based structures in activity-sequences classification tasks: Word2Vec, a static semantic embedding, and ELMo, a contextualized embedding. Results, on real smart homes datasets, indicate that this approach provides useful information, such as a sensor organization map, and makes less confusion between daily activity classes. It helps to better perform on datasets with competing activities of other residents or pets. Our tests show also that the embeddings can be pretrained on different datasets than the target one, enabling transfer learning. We thus demonstrate that taking into account the context of the sensors and their semantics increases the classification performances and enables transfer learning.

Natural language word embeddings as a glimpse into healthcare language and associated mortality surrounding end of life

ObjectivesTo clarify real-world linguistic nuances around dying in hospital as well as inaccuracy in individual-level prognostication to support advance care planning and personalised discussions on limitation of life sustaining treatment...

Commutative L-algebras and measure theory

Abstract Measure and integration theory for finitely additive measures, including vector-valued measures, is shown to be essentially covered by a class of commutative L-algebras, called measurable algebras. The domain and range of any measure is a commutative L-algebra. Each measurable algebra embeds into its structure group, an abelian group with a compatible lattice order, and each (general) measure extends uniquely to a monotone group homomorphism between the structure groups. On the other hand, any measurable algebra X is shown to be the range of an essentially unique measure on a measurable space, which plays the role of a universal covering. Accordingly, we exhibit a fundamental group of X, with stably closed subgroups corresponding to a special class of measures with X as target. All structure groups of measurable algebras arising in a classical context are archimedean. Therefore, they admit a natural embedding into a group of extended real-valued continuous functions on an extremally disconnected compact space, the Stone space of the measurable algebra. Extending Loomis’ integration theory for finitely additive measures, it is proved that, modulo null functions, each integrable function can be represented by a unique continuous function on the Stone space.

Эстетические представления и понятия индуистской традиции: особенности и аналогии

This article deals with the main ideas and basic concepts of Hindu aesthetics. The problem area reveals itself in the question of European culture’s perception of Hindu aesthetics. In this connection, the following questions are actualized: what can be considered as original aesthetic conceptions of Hinduism? is it possible to find direct analogies in other cultures? how relevant and correct is the conceptual apparatus describing various aesthetic phenomena? what is the role of the religious thought in the proposed aesthetic context? Proceeding from the historical and cultural position of aesthetic knowledge as it is presented in the European tradition, key approaches to the phenomenon of the aesthetic are shown, with the ideas of classical German philosophy – the cradle of aesthetic science (A. Baumgarten, I. Kant) – at the centre. The marked heterogeneity of aesthetic knowledge indicates its problematic status in the European historical-philosophical discourse and at the same time allows one to see, against its background, the harmonious place of aesthetics in Hindu culture. It mainly concerns the peculiarities of religious and worldview systems. Further, the paper studies the similarities and differences between the theoretical and ritual ideas and practices in Christianity and Hinduism. In particular, what they have in common is the importance of “threshold people” – liminal personae – in the spiritual life of society. Among the radical differences is the natural embedding of aesthetics in the religious system of India, while for European aesthetics, the religious world is just one of the spheres of the aesthetic. Using the method of comparative text analysis with reference to leading Russian orientalists and foreign researchers (V. Shokhin, D. Zilberman, E. Torchinov, R. Guénon, N. Gupta), the author takes a number of concepts as an example to demonstrate identity of religious and aesthetic ideas in Hindu and European cultures, as well as a possibility of mutual “cultural translation” of such basic concepts as aesthetics, the aesthetic, rasa and bhava.

Publisher Correction to: Natural alpha embeddings

A correction to this paper has been published: https://doi.org/10.1007/s41884-021-00043-9

Birational geometry of moduli spaces of configurations of points on the line

In this paper we study the geometry of GIT configurations of $n$ ordered points on $\mathbb{P}^1$ both from the the birational and the biregular viewpoint. In particular, we prove that any extremal ray of the Mori cone of effective curves of the quotient $(\mathbb{P}^1)^n//PGL(2)$, taken with the symmetric polarization, is generated by a one dimensional boundary stratum of the moduli space. Furthermore, we develop some technical machinery that we use to compute the canonical divisor and the Hilbert polynomial of $(\mathbb{P}^1)^n//PGL(2)$ in its natural embedding, and its group of automorphisms.

Locks Fit into Keys: A Crystal Analysis of Lock Polynomials

Lock polynomials and lock tableaux are natural analogues to key polynomials and Kohnert tableaux, respectively. In this paper, we compare lock polynomials to the much-studied key polynomials and give an explicit description of a crystal structure on lock tableaux. Furthermore, we construct an injective, weight-preserving map from lock tableaux to Kohnert tableaux that intertwines with their respective crystal operators. As a result, we see that the crystal structure on lock tableaux has a natural embedding into the Demazure crystal. We also examine the conditions for which key and lock polynomials are symmetric or quasisymmetric.

Lipschitz free p-spaces for 0 &lt; p &lt; 1

This paper initiates the study of the structure of a new class of $p$-Banach spaces, $0<p<1$, namely the Lipschitz free $p$-spaces (alternatively called Arens-Eells $p$-spaces) $\mathcal{F}_{p}(\mathcal{M})$ over $p$-metric spaces. We systematically develop the theory and show that some results hold as in the case of $p=1$, while some new interesting phenomena appear in the case $0<p<1$ which have no analogue in the classical setting. For the former, we, e.g., show that the Lipschitz free $p$-space over a separable ultrametric space is isomorphic to $\ell_{p}$ for all $0<p\le 1$, or that $\ell_p$ isomorphically embeds into $\mathcal{F}_p(\mathcal{M})$ for any $p$-metric space $\mathcal{M}$. On the other hand, solving a problem by the first author and N. Kalton, there are metric spaces $\mathcal{N}\subset \mathcal{M}$ such that the natural embedding from $\mathcal{F}_p(\mathcal{N})$ to $\mathcal{F}_p(\mathcal{M})$ is not an isometry.

Contracted Ideals of $p$-adic Integral Group Rings

Let $G$ be a cyclic group of order $p^k$ for a prime $p$. There is a natural embedding of $\mathbb{Z}_p[G]$ into a product of rings of integers of cyclotomic fields. We consider the ideals $I$ of $\mathbb{Z}_p[G]$ for which the following statement holds: if $\alpha\in\mathbb{Z}_p[G]$ and $\chi(\alpha)\in\chi(I)$ for all $p$-adic characters $\chi$ of $G$, then $\alpha\in I$. We show that they are precisely the contracted ideals of the embedding. Powers of the augmentation ideal of $\mathbb{Z}_p[G]$ are not contracted in general, and we calculate the obstruction of contraction in this case.

Encrypted video traffic clustering demystified

Cyber threat intelligence officers and forensics investigators often require the behavioural profiling of groups based on their online video viewing activity. It has been demonstrated that encrypted video traffic can be classified under the assumption of using a known subset of video titles based on temporal video viewing trends of particular groups. Nonetheless, composing such a subset is extremely challenging in real situations. Therefore, this work exhibits a novel profiling scheme for encrypted video traffic with no a priori assumption of a known subset of titles. It introduces a seminal synergy of Natural Language Processing (NLP) and Deep Encoder-based feature embedding algorithms with refined clustering schemes from off-the-shelf solutions, in order to group viewing profiles with unknown video streams. This study is the first to highlight the most computationally effective, accurate combinations of feature embedding and clustering using real datasets, thereby, paving the way to future forensics tools for automated behavioural profiling of malicious actors.

Order polarities

Abstract We define an order polarity to be a polarity $(X,Y,{\operatorname{R}})$ where $X$ and $Y$ are partially ordered, and we define an extension polarity to be a triple $(e_X,e_Y,{\operatorname{R}})$ such that $e_X:P\to X$ and $e_Y:P\to Y$ are poset extensions and $(X,Y,{\operatorname{R}})$ is an order polarity. We define a hierarchy of increasingly strong coherence conditions for extension polarities, each equivalent to the existence of a preorder structure on $X\cup Y$ such that the natural embeddings, $\iota _X$ and $\iota _Y$, of $X$ and $Y$, respectively, into $X\cup Y$ preserve the order structures of $X$ and $Y$ in increasingly strict ways. We define a Galois polarity to be an extension polarity satisfying the strongest of these coherence conditions and where $e_X$ and $e_Y$ are meet- and join-extensions, respectively. We show that for such polarities the corresponding preorder on $X\cup Y$ is unique. We define morphisms for polarities, providing the class of Galois polarities with the structure of a category, and we define an adjunction between this category and the category of $\varDelta _1$-completions and appropriate homomorphisms.

A Multidimensional, Multi-tiered System of Supports Model to Promote School Attendance and Address School Absenteeism.

School attendance and school completion are important benchmarks of successful development. Unfortunately, school absenteeism and school dropout remain debilitating and prevalent conditions among youth. Stakeholders invested in promoting school attendance and reducing school absenteeism generally agree that multifaceted ecological frameworks are needed to account for these heterogeneous problems as well as differences across local education agencies and broader jurisdictions. A multi-tiered system of supports (MTSS) framework emphasizes many aspects that match well with school attendance and its problems, including prevention and a continuum of supports, screening, evidence-based assessment and intervention, problem-solving and data-based decision-making, implementation fidelity, and natural embedding into extant school improvement plans. This article outlines a multidimensional MTSS model for school attendance and absenteeism to account for recent developments regarding service delivery within schools. Such developments include integrated models of multi-tiered service delivery to concurrently address multiple domains of functioning, the development of more nuanced approaches for students with various challenges, and consideration of three-dimensional (pyramidal) perspectives to allow simultaneous and yet nuanced strategies for several domain clusters. Sample domain clusters common to the literature that could populate the multiple dimensions or sides of a MTSS pyramid model for school attendance and absenteeism are presented. These domain clusters include (1) school refusal/truancy/school withdrawal/school exclusion, (2) functional profiles and analysis, (3) preschool/elementary/middle/high school, (4) ecological levels of impact on school attendance and its problems, and (5) low/moderate/high absenteeism severity. Recommendations are made as well regarding broader MTSS integration and implementation science vis-à-vis school attendance and its problems.

On certain subgroups of the McCool group

For a positive integer [Formula: see text], with [Formula: see text], let [Formula: see text] be a free group of rank [Formula: see text] and let [Formula: see text] be the subgroup of the automorphism group of [Formula: see text] consisting of all automorphisms which induce the identity on the abelianization of [Formula: see text]. We write [Formula: see text] and [Formula: see text] for the upper McCool group and the partial inner automorphism group, respectively. We show that [Formula: see text] is isomorphic to the quotient of [Formula: see text] by its center and we prove similar results for their associated graded Lie algebras and their Andreadakis–Johnson Lie algebras. Furthermore, we give a presentation of the associated graded Lie algebra over the integers of [Formula: see text] and we prove that it admits a natural embedding into the Andreadakis–Johnson Lie algebra of [Formula: see text]. Although the latter results are known, we present proofs based on different methods.

Matrix factorizations for self-orthogonal categories of modules

For a commutative ring [Formula: see text] and self-orthogonal subcategory [Formula: see text] of [Formula: see text], we consider matrix factorizations whose modules belong to [Formula: see text]. Let [Formula: see text] be a regular element. If [Formula: see text] is [Formula: see text]-regular for every [Formula: see text], we show there is a natural embedding of the homotopy category of [Formula: see text]-factorizations of [Formula: see text] into a corresponding homotopy category of totally acyclic complexes. Moreover, we prove this is an equivalence if [Formula: see text] is the category of projective or flat-cotorsion [Formula: see text]-modules. Dually, using divisibility in place of regularity, we observe there is a parallel equivalence when [Formula: see text] is the category of injective [Formula: see text]-modules.

Lyapunov exponents and Oseledets decomposition in random dynamical systems generated by systems of delay differential equations

Linear skew-product semidynamical systems generated by random systems of delay differential equations are considered, both on a space of continuous functions as~well as on a space of $p$-summable functions. The main result states that in both cases, the Lyapunov exponents are identical, and that the Oseledets decompositions are related by natural embeddings.

Мечтают ли студенты об электропациентах?

Виртуальное (цифровое) обучение обсуждается с точки зрения теории Маслоу. Определяется возможность естественного встраивания цифрового обучения в пирамиду потребностей современного человека.