Studiens syfte var att undersöka pedagogers uppfattningar av och kunskaper kring att arbeta med genus och drama samt att belysa vilka eventuella utmaningar de möter i arbetet. Studien präglas av kvalitativ metod och utgår ur ett socialkonstruktionistisk perspektiv. Vår ambition var att samla in pedagogernas erfarenheter och uppfattningar i relation till hur normkritisk pedagogik och genusfrågor synliggörs i barns dramalek därför har vi använt intervjuer som datainsamlingsmetod. Resultatet visade att samtliga intervjuade pedagoger uppfattar och använder drama som en pedagogisk kontext för att undersöka jämställdhet tillsammans med barn på ett lekfullt sätt. Detta, i sin tur, belyser dramas kraft som ett normbrytande pedagogiskt verktyg. Resultatet visade även hur pedagogernas förhållningssätt i relation till normer och stereotyper påverkar och utformar sättet barn upplever normer och stereotyper samt hur dramapedagogik bidrar till barns normkritiskt tänkande. Till sist, tydliggjordes hur viktigt pedagogernas medvetandegörande och närvaro är för att styra lärandet utifrån barns behov, medan olika utmaningar som uppstår bör lösas genom en god kollegial och föräldrasamverkan. / The purpose of the study was to investigate educators' perceptions of and knowledge about working with gender and drama and to shed light on the possible challenges they face in their work. The study is characterized by a qualitative method and is based on a social constructionist perspective. Our ambition was to collect the educators' experiences and perceptions in relation to how norm-critical pedagogy and gender issues are made visible in children's drama play, which is why we have used interviews as a data collection method. The results showed that all interviewed educators perceive and use drama as a pedagogical context to investigate gender equality with children in a playful way. This, in turn, highlights the power of drama as a norm-breaking pedagogical tool. The results also showed how the educators' attitudes in relation to norms and stereotypes affect and shape the way children experience norms and stereotypes and how drama pedagogy contributes to children's norm-critical thinking. Finally, it was clarified how important the educators' awareness and presence is to guide learning based on children's needs, while various challenges that arise should be solved through good collegial and parent collaboration.

In this dissertation, we discuss the problem of robust linear subspace estimation using low-rank optimization and propose three formulations of it. We demonstrate how these formulations can be used to solve fundamental computer vision problems, and provide superior performance in terms of accuracy and running time. Consider a set of observations extracted from images (such as pixel gray values, local features, trajectories . . . etc). If the assumption that these observations are drawn from a liner subspace (or can be linearly approximated) is valid, then the goal is to represent each observation as a linear combination of a compact basis, while maintaining a minimal reconstruction error. One of the earliest, yet most popular, approaches to achieve that is Principal Component Analysis (PCA). However, PCA can only handle Gaussian noise, and thus suffers when the observations are contaminated with gross and sparse outliers. To this end, in this dissertation, we focus on estimating the subspace robustly using low-rank optimization, where the sparse outliers are detected and separated through the `1 norm. The robust estimation has a two-fold advantage: First, the obtained basis better represents the actual subspace because it does not include contributions from the outliers. Second, the detected outliers are often of a specific interest in many applications, as we will show throughout this thesis. We demonstrate four different formulations and applications for low-rank optimization. First, we consider the problem of reconstructing an underwater sequence by removing the iii turbulence caused by the water waves. The main drawback of most previous attempts to tackle this problem is that they heavily depend on modelling the waves, which in fact is ill-posed since the actual behavior of the waves along with the imaging process are complicated and include several noise components; therefore, their results are not satisfactory. In contrast, we propose a novel approach which outperforms the state-of-the-art. The intuition behind our method is that in a sequence where the water is static, the frames would be linearly correlated. Therefore, in the presence of water waves, we may consider the frames as noisy observations drawn from a the subspace of linearly correlated frames. However, the noise introduced by the water waves is not sparse, and thus cannot directly be detected using low-rank optimization. Therefore, we propose a data-driven two-stage approach, where the first stage “sparsifies” the noise, and the second stage detects it. The first stage leverages the temporal mean of the sequence to overcome the structured turbulence of the waves through an iterative registration algorithm. The result of the first stage is a high quality mean and a better structured sequence; however, the sequence still contains unstructured sparse noise. Thus, we employ a second stage at which we extract the sparse errors from the sequence through rank minimization. Our method converges faster, and drastically outperforms state of the art on all testing sequences. Secondly, we consider a closely related situation where an independently moving object is also present in the turbulent video. More precisely, we consider video sequences acquired in a desert battlefields, where atmospheric turbulence is typically present, in addition to independently moving targets. Typical approaches for turbulence mitigation follow averaging or de-warping techniques. Although these methods can reduce the turbulence, they distort the independently moving objects which can often be of great interest. Therefore, we address the iv problem of simultaneous turbulence mitigation and moving object detection. We propose a novel three-term low-rank matrix decomposition approach in which we decompose the turbulence sequence into three components: the background, the turbulence, and the object. We simplify this extremely difficult problem into a minimization of nuclear norm, Frobenius norm, and `1 norm. Our method is based on two observations: First, the turbulence causes dense and Gaussian noise, and therefore can be captured by Frobenius norm, while the moving objects are sparse and thus can be captured by `1 norm. Second, since the object’s motion is linear and intrinsically different than the Gaussian-like turbulence, a Gaussian-based turbulence model can be employed to enforce an additional constraint on the search space of the minimization. We demonstrate the robustness of our approach on challenging sequences which are significantly distorted with atmospheric turbulence and include extremely tiny moving objects. In addition to robustly detecting the subspace of the frames of a sequence, we consider using trajectories as observations in the low-rank optimization framework. In particular, in videos acquired by moving cameras, we track all the pixels in the video and use that to estimate the camera motion subspace. This is particularly useful in activity recognition, which typically requires standard preprocessing steps such as motion compensation, moving object detection, and object tracking. The errors from the motion compensation step propagate to the object detection stage, resulting in miss-detections, which further complicates the tracking stage, resulting in cluttered and incorrect tracks. In contrast, we propose a novel approach which does not follow the standard steps, and accordingly avoids the aforementioned diffi- culties. Our approach is based on Lagrangian particle trajectories which are a set of dense trajectories obtained by advecting optical flow over time, thus capturing the ensemble motions v of a scene. This is done in frames of unaligned video, and no object detection is required. In order to handle the moving camera, we decompose the trajectories into their camera-induced and object-induced components. Having obtained the relevant object motion trajectories, we compute a compact set of chaotic invariant features, which captures the characteristics of the trajectories. Consequently, a SVM is employed to learn and recognize the human actions using the computed motion features. We performed intensive experiments on multiple benchmark datasets, and obtained promising results. Finally, we consider a more challenging problem referred to as complex event recognition, where the activities of interest are complex and unconstrained. This problem typically pose significant challenges because it involves videos of highly variable content, noise, length, frame size . . . etc. In this extremely challenging task, high-level features have recently shown a promising direction as in [53, 129], where core low-level events referred to as concepts are annotated and modelled using a portion of the training data, then each event is described using its content of these concepts. However, because of the complex nature of the videos, both the concept models and the corresponding high-level features are significantly noisy. In order to address this problem, we propose a novel low-rank formulation, which combines the precisely annotated videos used to train the concepts, with the rich high-level features. Our approach finds a new representation for each event, which is not only low-rank, but also constrained to adhere to the concept annotation, thus suppressing the noise, and maintaining a consistent occurrence of the concepts in each event. Extensive experiments on large scale real world dataset TRECVID Multimedia Event Detection 2011 and 2012 demonstrate that our approach consistently improves the discriminativity of the high-level features by a significant margin.

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Syfte: Syftet med denna studie var att undersöka aktuell praxis bland optikeri Sverige vad gäller evidensbaserat arbete för att främja god compliance hoskontaktlinspatienter, samt att belysa de eventuella områden där optiker iSverige kan förbättra sitt arbete i ovan nämnda avseende. Metod: En online-baserad enkät med 28 frågor togs fram och delades medOptikerförbundets medlemmar samt via Facebookgruppen Optikforum. Svaren sammanställdes och analyserades. Utvalda frågor poängsattes därmaxpoäng innebar “godkänt”, alltså att deltagaren alltid gör det somefterfrågas i enkäten, i enlighet med Kvalitetsnorm i synvården. Resultat: Antal svarande var 196, varav 190 inkluderades. 108 av dessaarbetade självständigt, alltså utan delegation till annan personal, vidnytillpassning, återbesök samt årskontroll vid kontaktlinstillpassning, ochpoängsattes därför. 24% av de 108 erhöll full poäng och ansågs arbetaevidensbaserat för att främja god kontaktlinsrelaterad compliance. Områdendär dessa 108 optiker fick lägst poäng, och således skulle kunna förbättra sittarbete för att främja kontaktlinsrelaterad compliance, var informerande av:vikten av egenkontroll av ögonen, vikten av rätt skötselrutin om patientenanvänder smink, hur länge kontaktlinserna bör gnuggas samt vikten avlinsvila. Hos de samtliga 190 inkluderades svar framkom att 4 av 5 optiker isamband med årskontroll aldrig eller sällan ber sina patienter att visa hur derengör sina kontaktlinser, eller ber sina patienter visa hur de sätter i- och tarur sina kontaktlinser. Slutsats: Alla optiker i denna studie arbetade inte helt och hålletevidensbaserat. Denna studie visade att optiker i Sveriges arbete med attfrämja kontaktlinsrelaterad compliance kan förbättras, bland annat vad gällertillhandahållande av patientinformation. Detta kan bidra till ökad compliancehos denna patientgrupp, vilket i sin tur kan minska risken förkontaktlinsrelaterade komplikationer. Ökad tillgång till extra utbildning omkontaktlinser för optikerna skulle också kunna förbättra detta arbete. / Purpose: The purpose of this study was to investigate current practiceamongst optometrists in Sweden regarding evidence-based work toencourage compliance in their contact lens patients. Moreover, to highlightthe potential areas where the optometrists possibly could improve their workwithin the field of encouraging contact lens-related compliance. Method: An online based survey was developed and shared with membersof the Swedish Optometrists’s Association, Optikerförbundet, and theFacebook-group ‘Optikforum’. The responses were compiled and analysed.Selected questions were scored, where the maximum score amounted to a“passing grade”, meaning that the participant always does what is requestedin the questionnaire, in accordance with the Quality Norm of vision care. Result: The number of respondents was 196, of which 190 were included.108 of these worked independently, i.e. without delegation to other staff,during new fitting, return visits and annual control during contact lens fitting,and were therefore scored. 24% of the 108 received full points and wereconsidered to be working evidence-based to encourage contact lens-relatedcompliance. Areas where these 108 opticians scored the lowest, and thuscould improve their work to encourage contact lens-related compliance, wereinformative of: the importance of self-examination of the eyes, theimportance of the correct care routine if the patient wears make-up, how longthe contact lenses should be rubbed and the importance of contact lens rest.In the responses of all 190 included, it emerged that 4 out of 5 opticians inconnection with the annual check-up never or rarely ask their patients toshow how they clean their contact lenses, nor ask their patients to show howthey put in and take out their contact lenses. Conclusion: All optometrists in this study were not always working in anevidence-based manner. This study showed that optometrists in Sweden’swork to encourage contact lens-related compliance can be improved, one ofthem being in terms of providing patient information. This can contribute toincreased compliance in this patient group, which in turn can reduce the riskof contact lens-related complications. Increasing the amount of extraeducation for the optometrists regarding contact lenses, could also improvetheir work in this regard.

Capítulo 1. Después de estudiar algunos preliminares sobre familias adecuadas de conjuntos, formulamos y probamos algunas equivalencias, cada una de ellas son una condición suficiente para que la familia defina un conjunto compacto de Gul'ko. Damos una caracterización de conjunto compacto de Gul'ko en términos de emparejamiento con un conjunto $\mathcal{K}$-analítico. Capítulo 2. Estudiamos propiedades de los espacios de Banach débilmente Lindelöf determinados no-separables. Damos una caracterización por medio de la existencia de un generador proyeccional full sobre él. Estudiamos algunos aspectos sobre sistemas biortogonales en espacios de Banach. Usando técnicas de resoluciones proyeccionales de la identidad, probamos una extensión de un resultado de Argyros y Mercourakis. Capítulo 3. En el espacio $(c_0(\Gamma),\|\cdot\|_\infty)$, con $\Gamma\in\mathbb{R}$, damos una norma equivalente estrictamente convexa. Capítulo 4. Consideramos una caracterización de los subespacios de espacios de Banach débilmente compactamente generados, en términos de una propiedad de cubrimiento de la bola unidad por medio de conjuntos $\epsilon$-débilmente compactos. Reemplazamos este concepto por otro más preciso que llamamos $\epsilon$-débilmente auto-compactos, este concepto permite una mejor descripción. Capítulo 5. Damos condiciones intrínsecas, necesarias y suficientes para que un espacio de Banach sea generado por $c_0(\Gamma)$ o $\ell_p(\Gamma)$ para $p\in(1,+\infty)$. Ofrecemos una nueva demostración de un resultado de Rosenthal, sobre operadores de $c_0(\Gamma)$ en un espacio de Banach. / González Correa, AL. (2008). Compacta in Banach spaces [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8312

Cette thèse contient quatre articles qui étudient les phénomènes de rigidité des transforma- tions hamiltoniennes des variétés symplectiques. Le premier article, rédigé en collaboration avec Egor Shelukhin, examine les obstructions à l’existence de symétries hamiltoniennes d’ordre fini sur une variété symplectique fermée (M,ω); c’est-à-dire de torsion hamiltonienne. En d’autres termes, nous étudions les sous- groupes finis du groupe des difféomorphismes hamiltoniens Ham(M,ω). Nous identifions trois sources principales d’obstructions: Contraintes topologiques. Inspirés par un résultat de Polterovich montrant que les variétés symplectiques asphériques n’admettent pas de torsion hamiltonienne, nous établissons que la présence d’un sous-groupe fini non trivial de Ham(M, ω) implique l’existence d’une sphère A ∈ π2(M) avec ⟨[ω],A⟩ > 0 et ⟨c1(M),A⟩ > 0. En particulier, les variétés symplectiques négativement monotones et les variétés symplectiques Calabi-Yau n’admettent pas de torsion hamiltonienne. Présence de courbes J-holomorphes. De manière générale, il y a de nombreux exemples de torsion hamiltonienne, par exemple toute rotation de la sphère de dimension deux par une fraction irrationnelle de π. Lorsque (M,ω) est positivement monotone, nous montrons que l’existence de torsion hamiltonienne impose une condition géométrique qui implique que les sphères J-holomorphes non constantes sont présentes partout. Ce phénomène était prédit dans une liste de problèmes contenue dans la monographie d’introduction de McDuff et de Salamon. Rigidité métrique spectrale. Notre analyse révèle que, pour les variétés symplectiques posi- tivement monotones, il existe un voisinage de l’identité dans Ham(M,ω) dans la topologie induite par la métrique spectrale qui ne contient aucun sous-groupe fini non trivial. Le principal résultat du deuxième article établit que, pour une large classe de variétés sym- plectiques, le flux d’un lacet de difféomorphismes symplectiques est entièrement déterminé par la classe d’homotopie de ses orbites. Comme application, nous obtenons de nouveaux exemples où l’existence d’un point fixe d’une action symplectique du cercle implique qu’elle est hamiltonienne et de nouvelles conditions assurant que le groupe de flux est trivial. De plus, nous obtenons des obstructions à l’existence d’éléments non triviaux de Symp0(M,ω) ayant un ordre fini. Le troisième article, rédigé en collaboration avec Han Lou, démontre une version de la conjecture de Hofer-Zehnder pour les variétés symplectiques fermées semi-positives dont l’homologie quantique est semi-simple; ce résultat généralise le travail révolutionnaire de Shelukhin sur les variétés symplectiques monotones. Le résultat montre qu’un difféomor- phisme hamiltonien possédant plus de points fixes contractiles, comptés homologiquement, que le nombre total de Betti de la variété doit avoir une infinité de points périodiques. La composante clé de la preuve est une nouvelle étude de l’effet de la réduction modulo p, un nombre premier, sur les bornes de l’homologie de Floer filtrée qui proviennent de la semi- simplicité. Cette étude repose sur la théorie des extensions algébriques des corps équipés d’une norme non-archimédienne. Le quatrième article, écrit en collaboration avec Habib Alizadeh et Dylan Cant, examine la déplaçabilité d’une sous-variété lagrangienne fermée L d’une variété symplectique convexe á l’infini par un difféomorphisme hamiltonien à support compact. Nous concluons qu’un difféomorphisme hamiltonien φ dont la norme spectrale est plus petite qu’un ħ(L) > 0 ne dépendant que de L ⊆ W ne peut pas déplacer L. De plus, nous établissons une estimation du nombre de valeurs d’action en terme de la longueur du cup-produit pour le nombre de valeurs d’action; lorsque L est rationnelle, cela implique une estimation du nombre de points d’intersection L ∩ φ(L) en terme de la longueur du cup-produit. Ainsi, nous montrons que le nombre de points fixes d’un difféomorphisme hamiltonien d’une variété symplectique fermée rationnelle (M, ω) dont la norme spectrale est plus petite que la constante de rationalité est au moins de 1 plus la longueur du cup-produit de M. / This thesis comprises four articles that study rigidity phenomena of Hamiltonian transfor- mations of symplectic manifolds. The first article, co-authored with Egor Shelukhin, examines obstructions to the existence of Hamiltonian symmetries of finite order on a closed symplectic manifold (M,ω); Hamil- tonian torsion. In other words, we study the finite subgroups of the group of Hamiltonian diffeomorphisms Ham(M, ω). We identify three primary sources of obstructions: Topological constraints. Inspired by a result of Polterovich showing that symplectically aspherical symplectic manifolds do not admit Hamiltonian torsion, we establish that the presence of a non-trivial finite subgroup of Ham(M,ω) implies that there exists a sphere A ∈ π2(M) with ⟨[ω],A⟩ > 0 and ⟨c1(M),A⟩ > 0. In particular, symplectically Calabi-Yau, and spherically negative-monotone symplectic manifolds do not admit Hamiltonian torsion. The presence of J-holomorphic curves. For general closed symplectic manifolds, there are plenty of examples of Hamiltonian torsion, for instance, any rotation of the two-sphere by an irrational fraction of π. When (M, ω) is spherically positive-monotone, we show the existence of Hamiltonian torsion imposes geometrical uniruledness, which implies that non-constant J-holomorphic spheres are ubiquitous. This phenomenon was predicted in a list of problems contained in the introductory monograph of McDuff and Salamon. The spectral metric rigidity. Our study reveals that for spherically positive-monotone (M, ω), there exists a neighbourhood of the identity in Ham(M,ω), in the topology induced by the spectral metric, that does not contain any non-trivial finite subgroup. The main result of the second article establishes that for a broad class of symplectic manifolds the flux of a loop of symplectic diffeomorphisms is completely determined by the homotopy class of its orbits. As an application, we obtain a new vanishing result for the flux group and new instances where the existence of a fixed point of a symplectic circle action implies that it is Hamiltonian. Moreover, we obtain obstructions to the existence of non-trivial elements of Symp0(M,ω) that have finite order. The third article, co-authored with Han Lou, proves a version of the Hofer-Zehnder conjec- ture for closed semipositive symplectic manifolds whose quantum homology is semisimple; this result generalizes the groundbreaking work of Shelukhin in the spherically positive- monotone setting. The result shows that a Hamiltonian diffeomorphism possessing more contractible fixed points, counted homologically, than the total Betti number of the mani- fold, must have infinitely many periodic points. The key component of the proof is a new study of the effect of reduction modulo a prime on the bounds on filtered Floer homology that arise from semisimplicity. It relies on the theory of algebraic extensions of non-Archimedean normed fields. The fourth article, co-authored with Habib Alizadeh and Dylan Cant, investigates the dis- placeability of a closed Lagrangian submanifold L of a convex-at-infinity symplectic manifold by a compactly supported Hamiltonian diffeomorphism. We conclude that a Hamiltonian diffeomorphism φ whose spectral norm is smaller than some ħ(L) > 0, depending only on L ⊂ W , cannot displace L. Furthermore, we establish a cup-length estimate for the number of action values; when L is rational, this implies a cup-length estimate on the number of intersection points L ∩ φ(L). As a corollary, we demonstrate that the number of fixed points of a Hamiltonian diffeomorphism of a closed rational symplectic manifold (M,ω), whose spectral norm is smaller than the rationality constant, is bounded below by one plus the cup-length of M.

La dialectique entre contrats d’Etat et développement durable existe, malgré une antinomie apparente. Elle s’appuie sur une interaction particulière qui s’est construite depuis l’origine, à travers les contrats d’Etat, instruments conventionnels singuliers et autour des nécessités politiques et économiques de l’époque, avec en toile de fond l’impératif de développement.Face aux évolutions sociales successives et l’absence d’arsenal juridique adapté, les contratsd’Etat se sont développés de façon spécifique entre dépendance, indépendance,interdépendance, hétéronomie et autonomie. En droit international des affaires, c’estprécisément à partir du contrat conçu comme un instrument normatif singulier et à travers sesinteractions avec le contexte extracontractuel au sein duquel il est amené à opérer quel’existence d’un droit du développement durable en matière de contrats d’Etat doit êtrefondée. Cela nécessite une autre vision du droit, sans cesse renouvelée et davantageappropriée aux réalités de notre siècle. / Common discussion points between sustainable development and State contracts exist, despite many visible contradictions. They are based on a particular interaction, built up from the beginning through State contracts, which are highly specific agreements and around political and economic necessities of the time, with the notion of development merely as a requirement in the background. Confronted with successive social changes and the lack of an appropriate judicial framework, State contracts developed in a particular way between dependence, independence, interdependence, heteronomy and autonomy. In international business law, the existence of a sustainable development law related to State contracts must be based precisely on contracts, seen as instruments able to set norms, and must benefit from contracts’interactions with a non-contractual environment. That requires another vision of law, constantly renewed and more adapted to current realities.

A fin de diseñar e implementar lenguajes de programación que tengan en cuenta el paradigma borroso modificaremos el lambda cálculo clásico, adjuntando a cada término un grado, y redefiniendo la beta-reducción, obteniendo que para que el nuevo cálculo verifique la propiedad de Church-Rosser la transmisión de los grados debe hacerse por medio de una función que sea una t-norma o s-conorma. Utilizando esta nueva herramienta diseñamos un lenguaje no determinista que satisface los requerimientos de la programación con datos borrosos. / With the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b-reduction. Thus, for the new calculus to verify the Church-Rosser property, the degree computed with can be made through a function that is a t-norm or an s-conorm. With this new tool we design a nondeterminist language that satisfies fuzzy dataprogramming requirements, and an example of its behaviour is shown.

科学研究費補助金 研究種目:基盤研究(C)(2) 課題番号:08837010 研究代表者:村上 京子 研究期間:1996-1997年度

We consider multivariate trigonometric polynomials with frequencies supported on a fixed but arbitrary frequency index set I, which is a finite set of integer vectors of length d. Naturally, one is interested in spatial discretizations in the d-dimensional torus such that - the sampling values of the trigonometric polynomial at the nodes of this spatial discretization uniquely determines the trigonometric polynomial, - the corresponding discrete Fourier transform is fast realizable, and - the corresponding fast Fourier transform is stable. An algorithm that computes the discrete Fourier transform and that needs a computational complexity that is bounded from above by terms that are linear in the maximum of the number of input and output data up to some logarithmic factors is called fast Fourier transform. We call the fast Fourier transform stable if the Fourier matrix of the discrete Fourier transform has a condition number near one and the fast algorithm does not corrupt this theoretical stability. We suggest to use rank-1 lattices and a generalization as spatial discretizations in order to sample multivariate trigonometric polynomials and we develop construction methods in order to determine reconstructing sampling sets, i.e., sets of sampling nodes that allow for the unique, fast, and stable reconstruction of trigonometric polynomials. The methods for determining reconstructing rank-1 lattices are component{by{component constructions, similar to the seminal methods that are developed in the field of numerical integration. During this thesis we identify a component{by{component construction of reconstructing rank-1 lattices that allows for an estimate of the number of sampling nodes M |I|\le M\le \max\left(\frac{2}{3}|I|^2,\max\{3\|\mathbf{k}\|_\infty\colon\mathbf{k}\in I\}\right) that is sufficient in order to uniquely reconstruct each multivariate trigonometric polynomial with frequencies supported on the frequency index set I. We observe that the bounds on the number M only depends on the number of frequency indices contained in I and the expansion of I, but not on the spatial dimension d. Hence, rank-1 lattices are suitable spatial discretizations in arbitrarily high dimensional problems. Furthermore, we consider a generalization of the concept of rank-1 lattices, which we call generated sets. We use a quite different approach in order to determine suitable reconstructing generated sets. The corresponding construction method is based on a continuous optimization method. Besides the theoretical considerations, we focus on the practicability of the presented algorithms and illustrate the theoretical findings by means of several examples. In addition, we investigate the approximation properties of the considered sampling schemes. We apply the results to the most important structures of frequency indices in higher dimensions, so-called hyperbolic crosses and demonstrate the approximation properties by the means of several examples that include the solution of Poisson's equation as one representative of partial differential equations.