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Institute
The 𝒮-cone provides a common framework for cones of polynomials or exponen- tial sums which establish non-negativity upon the arithmetic-geometric inequality, in particular for sums of non-negative circuit polynomials (SONC) or sums of arithmetic- geometric exponentials (SAGE). In this paper, we study the S-cone and its dual from the viewpoint of second-order representability. Extending results of Averkov and of Wang and Magron on the primal SONC cone, we provide explicit generalized second- order descriptions for rational S-cones and their duals.
In the human brain, the incoming light to the retina is transformed into meaningful representations that allow us to interact with the world. In a similar vein, the RGB pixel values are transformed by a deep neural network (DNN) into meaningful representations relevant to solving a computer vision task it was trained for. Therefore, in my research, I aim to reveal insights into the visual representations in the human visual cortex and DNNs solving vision tasks.
In the previous decade, DNNs have emerged as the state-of-the-art models for predicting neural responses in the human and monkey visual cortex. Research has shown that training on a task related to a brain region’s function leads to better predictivity than a randomly initialized network. Based on this observation, we proposed that we can use DNNs trained on different computer vision tasks to identify functional mapping of the human visual cortex.
To validate our proposed idea, we first investigate a brain region occipital place area (OPA) using DNNs trained on scene parsing task and scene classification task. From the previous investigations about OPA’s functions, we knew that it encodes navigational affordances that require spatial information about the scene. Therefore, we hypothesized that OPA’s representation should be closer to a scene parsing model than a scene classification model as the scene parsing task explicitly requires spatial information about the scene. Our results showed that scene parsing models had representation closer to OPA than scene classification models thus validating our approach.
We then selected multiple DNNs performing a wide range of computer vision tasks ranging from low-level tasks such as edge detection, 3D tasks such as surface normals, and semantic tasks such as semantic segmentation. We compared the representations of these DNNs with all the regions in the visual cortex, thus revealing the functional representations of different regions of the visual cortex. Our results highly converged with previous investigations of these brain regions validating the feasibility of the proposed approach in finding functional representations of the human brain. Our results also provided new insights into underinvestigated brain regions that can serve as starting hypotheses and promote further investigation into those brain regions.
We applied the same approach to find representational insights about the DNNs. A DNN usually consists of multiple layers with each layer performing a computation leading to the final layer that performs prediction for a given task. Training on different tasks could lead to very different representations. Therefore, we first investigate at which stage does the representation in DNNs trained on different tasks starts to differ. We further investigate if the DNNs trained on similar tasks lead to similar representations and on dissimilar tasks lead to more dissimilar representations. We selected the same set of DNNs used in the previous work that were trained on the Taskonomy dataset on a diverse range of 2D, 3D and semantic tasks. Then, given a DNN trained on a particular task, we compared the representation of multiple layers to corresponding layers in other DNNs. From this analysis, we aimed to reveal where in the network architecture task-specific representation is prominent. We found that task specificity increases as we go deeper into the DNN architecture and similar tasks start to cluster in groups. We found that the grouping we found using representational similarity was highly correlated with grouping based on transfer learning thus creating an interesting application of the approach to model selection in transfer learning.
During previous works, several new measures were introduced to compare DNN representations. So, we identified the commonalities in different measures and unified different measures into a single framework referred to as duality diagram similarity. This work opens up new possibilities for similarity measures to understand DNN representations. While demonstrating a much higher correlation with transfer learning than previous state-of-the-art measures we extend it to understanding layer-wise representations of models trained on the Imagenet and Places dataset using different tasks and demonstrate its applicability to layer selection for transfer learning.
In all the previous works, we used the task-specific DNN representations to understand the representations in the human visual cortex and other DNNs. We were able to interpret our findings in terms of computer vision tasks such as edge detection, semantic segmentation, depth estimation, etc. however we were not able to map the representations to human interpretable concepts. Therefore in our most recent work, we developed a new method that associates individual artificial neurons with human interpretable concepts.
Overall, the works in this thesis revealed new insights into the representation of the visual cortex and DNNs...
Polarization of Λ and ¯Λ hyperons along the beam direction in Pb-Pb collisions at √sNN=5.02 TeV
(2022)
The polarization of the Λ and ¯Λ hyperons along the beam (z) direction, Pz, has been measured in Pb-Pb collisions at √sNN=5.02 TeV recorded with ALICE at the Large Hadron Collider (LHC). The main contribution to Pz comes from elliptic flow-induced vorticity and can be characterized by the second Fourier sine coefficient Pz,s2=⟨Pzsin(2φ−2Ψ2)⟩, where φ is thhyperon azimuthal emission angle and Ψ2 is the elliptic flow plane angle. We report the measurement of Pz,s2 for different collision centralities and in the 30%–50% centrality interval as a function of the hyperon transverse momentum and rapidity. The Pz,s2 is positive similarly as measured by the STAR Collaboration in Au-Au collisions at √sNN=200 GeV, with somewhat smaller amplitude in the semicentral collisions. This is the first experimental evidence of a nonzero hyperon Pz in Pb-Pb collisions at the LHC. The comparison of the measured Pz,s2 with the hydrodynamic model calculations shows sensitivity to the competing contributions from thermal and the recently found shear-induced vorticity, as well as to whether the polarization is acquired at the quark-gluon plasma or the hadronic phase.
In this thesis, we cover two intimately related objects in combinatorics, namely random constraint satisfaction problems and random matrices. First we solve a classic constraint satisfaction problem, 2-SAT using the graph structure and a message passing algorithm called Belief Propagation. We also explore another message passing algorithm called Warning Propagation and prove a useful result that can be employed to analyze various type of random graphs. In particular, we use this Warning Propagation to study a Bernoulli sparse parity matrix and reveal a unique phase transition regarding replica symmetry. Lastly, we use variational methods and a version of local limit theorem to prove a sufficient condition for a general random matrix to be of full rank.
Ausgangspunkt der Forschungsarbeit ist der Gebrauch von Gesten in mathematischen Interaktionen von Lernenden. Es wird untersucht, inwiefern Gesten Teil des mathematischen Aushandlungsprozesses sind. Damit ist die Rekonstruktion einer potentiell fachlichen Bedeutung des Gestengebrauchs beim Mathematiklernen das zentrale Forschungsanliegen.
Theoretisch gerahmt wird die Arbeit von Erkenntnissen aus der psychologisch-linguistischen Gestenforschung zur systematischen Beschreibung von Gestik im Zusammenspiel mit der gleichzeitig geäußerten Lautsprache (McNeill, 1992; Kendon, 2004). Es werden ebenso ausgewählte Forschungen zur Gestik beim Mathematiklernen beleuchtet (Arzarello, 2006; Wille, 2020; Kiesow, 2016). Die mathematikdidaktische Interaktionstheorie begründet den sozial-konstruktivistischen Lernbegriff (Krummheuer, 1992). Ausgewählte Aspekte der Semiotik nach C. S. Peirce bieten eine theoretische Fundierung des Zeichenbegriffs und des Kerns mathematischen Agierens, verstanden als diagrammatisches Arbeiten (Peirce, 1931, CP 1.54 u. 1932, CP 2.228).
Von besonderer Bedeutung für die vorliegende Forschungsarbeit ist der linguistische Ansatz der Code-Integration und -Manifestation von redebegleitenden Gesten im Sprachsystem nach Fricke (2007, 2012) in Verbindung mit dem Peirce’schen Diagrammbegriff. Diese Perspektive ermöglicht eine theoretische Fundierung der zunächst empirisch beobachtbaren Multimodalität der Ausdrucksweisen von Lernenden beim gemeinsamen Mathematiktreiben. Der Peirce’sche Diagrammbegriff dient hierbei zur Rekonstruktion einer systemischen Relevanz von Gesten für das Betreiben von Mathematik: Bestimmte Gesten sind semiotisch als mathematische Zeichen beschreibbar und haben potentiell konstituierende Funktion für das diagrammatische Arbeiten der Lernenden. Der übergeordnete Forschungsfokus lautet: Wie nutzen Grundschüler*innen Gestik und Lautsprache, insbesondere in deren Zusammenspiel, um ihre mathematischen Ideen in den interaktiven Aushandlungsprozess einzubringen und über den Verlauf der Interaktion aufzugreifen, möglicherweise weiterzuentwickeln oder auch zu verwerfen? In der Ausdifferenzierung wird die Funktion der verwendeten Gesten und die Rekonstruktion von potentiell gemeinsam gebrauchten Gesten der Interagierenden in den Blick genommen.
Methodisch lässt sich die Forschungsarbeit der qualitativen Sozialforschung (Bohnsack, 2008) bzw. der interpretativen mathematikdidaktischen Unterrichtsforschung zuordnen (Krummheuer & Naujok, 1999). Es werden Beispiele aus mathematischen Interaktionssituationen ausgewertet, in denen sich Paare von Zweitklässler*innen mit einem mathematischen Problem aus der Kombinatorik und der Geometrie beschäftigen. Eine eigens theoriekonform entwickelte Transkriptpartitur dient zur Aufarbeitung der Videodaten. Mit der textbasierten Interaktionsanalyse (Krummheuer, 1992) und der grafisch angelegten Semiotischen Analyse (Schreiber, 2010) in einer Weiterentwicklung der Semiotischen Prozess-Karten (Huth, 2014) werden zwei hierarchisch aufeinander aufbauende Analyseverfahren verwendet.
Zentrale Forschungsergebnisse sind 1) die funktionale und gestalterische Flexibilität des Gestengebrauchs beim diagrammatischen Arbeiten der Lernenden, 2) die Rekonstruktion von Modusschnittstellen der Gesten mit anderen Ausdrucksmodi in Funktion, interaktionaler Bedeutungszuschreibung und Chronologie, und 3) die häufige Verwendung der Gesten als Modus der Wahl der Lernenden in mathematischen Interaktionen. Gesten weisen eine unmittelbare und voraussetzungslose Verfügbarkeit auf, eine funktionale und gestalterische Flexibilität in der mathematischen Auseinandersetzung und die Möglichkeit, Funktionen anderer Modi (vorübergehen) zu übernehmen. Es zeigt sich eine konstitutive und fachliche Bedeutung der Gestik für das mathematisch-diagrammatische Agieren der Lernenden. In der Arbeit wird daraus schließlich das doppelte Kontinuum der Gesten für das Mathematiklernen entwickelt. Es zeigt in der Dimension der Funktion des Gestengebrauchs und der Dimension des Objektbezugs der Gestengestalt die Vielfältigkeit der Gestenfunktionen im gemeinsamen diagrammatischen Arbeiten der Lernenden und gibt Einblick in die verwendeten Gestengestalten.
Die Forschungsarbeit offenbart den Bedarf einer Beachtung von Gesten in der fachdidaktischen Planung und Gestaltung von Mathematikunterricht und in der Erforschung und Diagnostik der mathematischen Entwicklung von Lernenden. Es handelt sich bei Gesten in mathematischen Interaktionen nicht um ein reines Beiwerk der Äußerung, sondern um einen fachlich bedeutsamen Modus in Bezug auf das Mathematiklernen. Der Gebrauch von Gestik ermöglicht die Erzeugung von Diagrammen im Handumdrehen und eröffnet perspektivisch eine Erforschung ihrer Bedeutung für mathematische Lehr-Lern-Prozesse.
Die in dieser Zusammenfassung angegebene Literatur findet sich im Literaturverzeichnis der vorgelegten Forschungsarbeit.
AI-based computer vision systems play a crucial role in the environment perception for autonomous driving. Although the development of self-driving systems has been pursued for multiple decades, it is only recently that breakthroughs in Deep Neural Networks (DNNs) have led to their widespread application in perception pipelines, which are getting more and more sophisticated. However, with this rising trend comes the need for a systematic safety analysis to evaluate the DNN's behavior in difficult scenarios as well as to identify the various factors that cause misbehavior in such systems. This work aims to deliver a crucial contribution to the lacking literature on the systematic analysis of Performance Limiting Factors (PLFs) for DNNs by investigating the task of pedestrian detection in urban traffic from a monocular camera mounted on an autonomous vehicle. To investigate the common factors that lead to DNN misbehavior, six commonly used state-of-the-art object detection architectures and three detection tasks are studied using a new large-scale synthetic dataset and a smaller real-world dataset for pedestrian detection. The systematic analysis includes 17 factors from the literature and four novel factors that are introduced as part of this work. Each of the 21 factors is assessed based on its influence on the detection performance and whether it can be considered a Performance Limiting Factor (PLF). In order to support the evaluation of the detection performance, a novel and task-oriented Pedestrian Detection Safety Metric (PDSM) is introduced, which is specifically designed to aid in the identification of individual factors that contribute to DNN failure. This work further introduces a training approach for F1-Score maximization whose purpose is to ensure that the DNNs are assessed at their highest performance. Moreover, a new occlusion estimation model is introduced to replace the missing pedestrian occlusion annotations in the real-world dataset. Based on a qualitative analysis of the correlation graphs that visualize the correlation between the PLFs and the detection performance, this study identified 16 of the initial 21 factors as being PLFs for DNNs out of which the entropy, the occlusion ratio, the boundary edge strength, and the bounding box aspect ratio turned out to be most severely affecting the detection performance. The findings of this study highlight some of the most serious shortcomings of current DNNs and pave the way for future research to address these issues.
Non-Fungible Token und die Blockchain Technologie haben in dem vergangenen Jahr immer mehr an Popularität gewonnen. Wie bei jeder neuartigen Technologie stellt sich jedoch die Frage, in welchen Bereichen diese eine Anwendung finden können.
Das Ziel in der vorliegenden Arbeit ist es zu beantworten, ob Non-Fungible Token und die Blockchain Technologie eine sinnvolle Anwendung im Bereich von akademischen Zertifikaten hat.
Um diese Frage zu beantworten, sind Gründe für die Anwendung von Non-Fungible Token gegen Nachteile abgewogen und Lösungsansätze für potentielle Risiken erhoben worden. Außerdem wurde selbstständig ein ERC-721 Token Contract für akademische Zertifikate mittels Solidity entwickelt.
Die Arbeit zeigt, dass Blockchain basierte akademische Zertifikate vor allem die Mobilität von Studenten unterstützen, den administrativen Aufwand der Ausstellung und Verifizierung von Abschlusszeugnissen verringern und entgegen der Fälschung von Abschlüssen arbeiten. Außerdem können erwägte Risiken und Nachteile durch Zusammenschluss von Institutionen zu einer Konsortialen Blockchain umgangen werden.
Die erfolgreiche Entwicklung des ERC-721 Token Contracts “MetaDip” zeigt eine potentielle Umsetzung für die Digitalisierung von Abschlusszeugnissen und demonstriert, dass Non-Fungible Token basierte akademische Zertifikate aktuell bereits technisch realisierbar sind.
Die Arbeit legt dar, dass Non-Fungible Token und die Blockchain Technologie eine vielversprechende Zukunft für akademische Zertifikate bietet und bereits von vereinzelten Institutionen realisiert wird. Jedoch müssen noch einige Vorkehrungen getroffen werden, bevor eine breite Umsetzung von Blockchain basierten akademischen Zertifikaten möglich ist.
In this paper, we introduce an approach for future frames prediction based on a single input image. Our method is able to generate an entire video sequence based on the information contained in the input frame. We adopt an autoregressive approach in our generation process, i.e., the output from each time step is fed as the input to the next step. Unlike other video prediction methods that use “one shot” generation, our method is able to preserve much more details from the input image, while also capturing the critical pixel-level changes between the frames. We overcome the problem of generation quality degradation by introducing a “complementary mask” module in our architecture, and we show that this allows the model to only focus on the generation of the pixels that need to be changed, and to reuse those that should remain static from its previous frame. We empirically validate our methods against various video prediction models on the UT Dallas Dataset, and show that our approach is able to generate high quality realistic video sequences from one static input image. In addition, we also validate the robustness of our method by testing a pre-trained model on the unseen ADFES facial expression dataset. We also provide qualitative results of our model tested on a human action dataset: The Weizmann Action database.
Tasks are a key resource in the process of teaching and learning mathematics, which is why task design continues to be one of the main research issues in mathematics education. Different settings can influence the principles underlying the formulation of tasks, and so does the outdoor context. Specifically, a math trail can be a privileged context, known to promote positive attitudes and additional engagement for the learning of mathematics, confronting students with a sequence of real-life tasks, related to a particular mathematical theme. Recently, mobile devices and apps, i.e., MathCityMap, have been recognized as an important resource to facilitate the extension of the classroom to the outdoors. The study reported in this paper intends to identify the principles of design for mobile theme-based math trails (TBT) that result in rich learning experiences in early algebraic thinking. A designed-based research is used, through a qualitative approach, to develop and refine design principles for TBT about Sequences and Patterns. The iterative approach is described by cycles with the intervention of the researchers, pre-service and in-service teachers and students of the targeted school levels. The results are discussed taking into account previous research and data collected along the cycles, conducing to the development of general design principles for TBT tasks.
Existence of nonradial domains for overdetermined and isoperimetric problems in nonconvex cones
(2022)
In this work we address the question of the existence of nonradial domains inside a nonconvex cone for which a mixed boundary overdetermined problem admits a solution. Our approach is variational, and consists in proving the existence of nonradial minimizers, under a volume constraint, of the associated torsional energy functional. In particular we give a condition on the domain D on the sphere spanning the cone which ensures that the spherical sector is not a minimizer. Similar results are obtained for the relative isoperimetric problem in nonconvex cones.