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ISTA Thesis
No full textRotations constitute one of the fundamental symmetries in physics, characterized by their intricate group structure and infinite dimensional representations. In contrast to classical rotations, quantum mechanics unveils the SO(3) symmetry group structure, manifesting in phenomena without classical counterparts, from angular momentum quantization to non-trivial addition of angular momenta.
While most studies of topological physics have focused on two-band systems, the SO(3) symmetry group of quantum rotors offers an inherently more complex platform with unprecedented possibilities for exploring topological phenomena. Despite their ubiquity in nature– from molecules to nanorotors– their potential for hosting topological phases has remained largely unexamined.
In this thesis, we mainly focus on periodically driven linear molecules as a prototype for studying topological phenomena in quantum rotors. Recent technological advances in coherent control of molecules, particularly through precisely shaped laser pulses, have made it possible to investigate linear rotors in the context of topology. While planar rotors have received some attention in recent years, threedimensional rotors–particularly linear molecules–harbor substantially richer topological phenomena due to their non-abelian nature and their additional angular degrees of freedom. We demonstrate that these systems can host novel edge states and topological features fundamentally impossible in planar systems.
We begin by establishing a theoretical bridge between periodically kicked rotors and "crystalline" lattices in angular momentum space. Using non-interacting linear molecules as our primary example, we show how quantum interference and revival patterns lead to the possibility to simulate band models with arbitrary number of bands N. While our framework applies to various quantum rotors, including nanorotors and kicked Bose-Einstein condensates, linear
molecules provide an ideal experimental platform due to their abovementioned precise controllability.
The core of this work examines adiabatic dynamics of 3D quantum rotors, establishing a geometric framework based on the Euler class to characterize its non-abelian topology. The non-Hermitian nature of the system enables novel braiding behaviors and topological transitions impossible in static systems, leading to an anomalous Dirac string phase with edge states in each gap, even though the Berry phases are all zero. These features can be directly observed through
molecular alignment and rotational level populations.
These findings establish quantum rotors as an alternative platform for studying multi-band topological physics, while suggesting practical implementations for quantum computation where topological protection could offer natural resilience against decoherence. The rich structure of three-dimensional rotation groups, combined with the tunability of topological features through driving parameters, makes this platform particularly valuable for exploring fundamental
physics and developing quantum technologies
TIR1-produced cAMP as a second messenger in transcriptional auxin signalling
No full textThe phytohormone auxin (Aux) is a principal endogenous developmental signal in plants. It mediates transcriptional reprogramming by a well-established canonical signalling mechanism. TIR1/AFB auxin receptors are F-box subunits of an ubiquitin ligase complex; after auxin perception, they associate with Aux/IAA transcriptional repressors and ubiquitinate them for degradation, thus enabling the activation of auxin response factor (ARF) transcription factors1,2,3. Here we revise this paradigm by showing that without TIR1 adenylate cyclase (AC) activity4, auxin-induced degradation of Aux/IAAs is not sufficient to mediate the transcriptional auxin response. Abolishing the TIR1 AC activity does not affect auxin-induced degradation of Aux/IAAs but renders TIR1 non-functional in mediating transcriptional reprogramming and auxin-regulated development, including shoot, root, root hair growth and lateral root formation. Transgenic plants show that local cAMP production in the vicinity of the Aux/IAA–ARF complex by unrelated AC enzymes bypasses the need for auxin perception and is sufficient to induce ARF-mediated transcription. These discoveries revise the canonical model of auxin signalling and establish TIR1/AFB-produced cAMP as a second messenger essential for transcriptional reprograming
Aharonov–Casher theorems for Dirac operators on manifolds with boundary and APS boundary condition
No full textThe Aharonov–Casher theorem is a result on the number of the so-called zero modes of a system described by the magnetic Pauli operator in R2. In this paper we address the same question for the Dirac operator on a flat two-dimensional manifold with boundary and Atiyah–Patodi–Singer boundary condition. More concretely we are interested in the plane and a disc with a finite number of circular holes cut out. We consider a smooth compactly supported magnetic field on the manifold and an arbitrary magnetic field inside the holes
Influence of surface engineering on the transport properties of lead sulfide nanomaterials
No full textLead Sulfide (PbS) has garnered attention as a promising thermoelectric (TE) material due to its natural abundance and cost-effectiveness. However, its practical application is hindered by inherently high lattice thermal conductivity and low electrical conductivity. In this study, we address these challenges by surface functionalization of PbS nanocrystals using Cu2S molecular complexes-based ligand displacement. The molecular complexes facilitate the incorporation of Cu into the PbS matrix and leads to the formation of nanoscale defects, dislocations, and strain fields while optimizing the charge carrier transport. The structural modulations enhance the phonon scattering and lead to a significant reduction in lattice thermal conductivity of 0.60 W m−1K−1 at 867 K in the PbS-Cu2S system. Simultaneously, the Cu incorporation improves electrical conductivity by increasing both carrier concentration and mobility with carefully optimized the content of Cu2S molecular complexes. These synergistic modifications yield a peak figure-of-merit (zT) of 1.05 at 867 K for the PbS-1.0 %Cu2S sample, representing an almost twofold enhancement in TE performance compared to pristine PbS. This work highlights the effectiveness of surface treatment in overcoming the intrinsic limitations of PbS-based materials and presents a promising strategy for the development of high-efficiency TE systems
Parameter estimation for Gibbs distributions
No full textA central problem in computational statistics is to convert a procedure for sampling combinatorial objects into a procedure for counting those objects, and vice versa. We consider sampling problems which come from Gibbs distributions, which are families of probability distributions over a discrete space Ω with probability mass function of the form μ^Ω_β(ω) ∝ e^{β H(ω)} for β in an interval [β_min, β_max] and H(ω) ∈ {0} ∪ [1, n]. Two important parameters are the partition function, which is the normalization factor Z(β) = ∑_{ω ∈ Ω} e^{β H(ω)}, and the vector of pre-image counts c_x=|H^-1(x)|.
We develop black-box sampling algorithms to estimate the counts roughly Õ(n²/ε²) samples for integer-valued distributions and Õ(q/ε²) samples for general distributions, where q = (log Z(β_max))/Z(β_min) (ignoring some second-order terms and parameters). We show this is optimal up to logarithmic factors. We illustrate with improved algorithms for counting connected subgraphs, independent sets, and perfect matchings. As a key subroutine, we estimate all values of the partition function using Õ(n²/ε²) samples for integer-valued distributions and Õ(q/ε²) samples for general distributions. This improves over a prior algorithm of Huber (2015) which computes a single point estimate Z(β_max) and which uses a slightly larger amount of samples. We show matching lower bounds, demonstrating this complexity is optimal as a function of n and q up to logarithmic terms
Super-resolution expansion microscopy in plant roots
No full textSuper-resolution methods provide far better spatial resolution than the optical diffraction limit of about half the wavelength of light (∼200-300 nm). Nevertheless, they have yet to attain widespread use in plants, largely due to plants’ challenging optical properties. Expansion microscopy improves effective resolution by isotropically increasing the physical distances between sample structures while preserving relative spatial arrangements and clearing the sample. However, its application to plants has been hindered by the rigid, mechanically cohesive structure of plant tissues. Here, we report on whole-mount expansion microscopy of thale cress (Arabidopsis thaliana) root tissues (PlantEx), achieving a four-fold resolution increase over conventional microscopy. Our results highlight the microtubule cytoskeleton organization and interaction between molecularly defined cellular constituents. Combining PlantEx with stimulated emission depletion (STED) microscopy, we increase nanoscale resolution and visualize the complex organization of subcellular organelles from intact tissues by example of the densely packed COPI-coated vesicles associated with the Golgi apparatus and put these into a cellular structural context. Our results show that expansion microscopy can be applied to increase effective imaging resolution in Arabidopsis root specimens
ISTA Thesis
No full textTopological Data Analysis (TDA) is a discipline utilizing the mathematical field of topology to study data, most prominently collections of point sets. This thesis summarizes three projects related to computations in TDA.
The first one establishes a variant of TDA for chromatic point sets, where each point is given a color. For example, we are given positions of cells within a tumor microenvironment, and color the cancerous cells red, and the immune cells blue.
The aim is then to give a quantitative description of how the two or more sets of points spatially interact. Building on image, kernel and cokernel variants of persistent homology, we suggest six-packs of persistent diagrams as such a descriptor.
We describe a construction of a chromatic alpha complex, which enables efficient computation of several variants of the six-packs. We give topological descriptions of natural subcomplexes of the chromatic alpha complex, and show that the radii of the simplices form a discrete Morse function. Finally, we provide an implementation of the presented chromatic TDA pipeline.
The second part aims to translate a powerful tool of sheaf theory to elementary terms using labeled matrices. The goal is to enable their use in computational settings. We show that derived categories of sheaves over finite posets have, up to isomorphism, unique objects---minimal injective resolutions---and give a concrete algorithm to compute them. We further describe simple algorithms to compute derived pushforwards and pullbacks for monotonic maps, and their proper variants for inclusions, and demonstrate their tractability by providing an implementation. Finally, we suggest a discrete definition of microsupport and show desirable properties inspired by discrete Morse theory.
In the last part, we present a collection of observations about collapses. We give a characterization of collapsibility in terms of unitriangular submatrices of the boundary matrix, a cotree-tree decomposition, and the optimal solution to a variant of the Procrustes problem. We establish relation between dual collapses and relative Morse theory and pose several open questions. Finally, focusing on complexes embedded in the three-dimensional Euclidean space, we describe a relation between the collapsibility and the triviality of a polygonal knot
Stirring the false vacuum via interacting quantized bubbles on a 5,564-qubit quantum annealer
No full textFalse vacuum decay—the transition from a metastable quantum state to a true vacuum state—plays an important role in quantum field theory and non-equilibrium phenomena such as phase transitions and dynamical metastability. The non-perturbative nature of false vacuum decay and the limited experimental access to this process make it challenging to study, leaving several open questions regarding how true vacuum bubbles form, move and interact. Here we observe quantized bubble formation in real time, a key feature of false vacuum decay dynamics, using a quantum annealer with 5,564 superconducting flux qubits. We develop an effective model that captures both initial bubble creation and subsequent interactions, and remains accurate under dissipation. The annealer reveals coherent scaling laws in the driven many-body dynamics for more than 1,000 intrinsic qubit time units. This work provides a method for investigating false vacuum dynamics of large quantum systems in quantum annealers
Mesoscopic eigenvalue statistics for Wigner-type matrices
No full textWe prove a universal mesoscopic central limit theorem for linear eigenvalue statistics of a Wigner-type matrix inside the bulk of the spectrum with compactly supported twice continuously differentiable test functions. The main novel ingredient is an optimal local law for the two-point function and a general class of related quantities involving two resolvents at nearby spectral parameters.On établit un théorème limite central universel pour les statistiques linéaires mésoscopiques des valeurs propres d’une matrice de type Wigner au milieu du spectre, avec des fonctions de classe
et à support compact. La principale nouveauté de cette approche est qu’elle repose sur une loi locale optimale pour la fonction à deux points , ainsi que pour une classe plus générale d’observables impliquant deux résolvantes évaluées en des paramètres proches
Generalization in multi-objective machine learning
No full textModern machine learning tasks often require considering not just one but multiple objectives. For example, besides the prediction quality, this could be the efficiency, robustness or fairness of the learned models, or any of their combinations. Multi-objective learning offers a natural framework for handling such problems without having to commit to early trade-offs. Surprisingly, statistical learning theory so far offers almost no insight into the generalization properties of multi-objective learning. In this work, we make first steps to fill this gap: We establish foundational generalization bounds for the multi-objective setting as well as generalization and excess bounds for learning with scalarizations. We also provide the first theoretical analysis of the relation between the Pareto-optimal sets of the true objectives and the Pareto-optimal sets of their empirical approximations from training data. In particular, we show a surprising asymmetry: All Pareto-optimal solutions can be approximated by empirically Pareto-optimal ones, but not vice versa