@phdthesis{9022,
abstract = {In the first part of the thesis we consider Hermitian random matrices. Firstly, we consider sample covariance matrices XX∗ with X having independent identically distributed (i.i.d.) centred entries. We prove a Central Limit Theorem for differences of linear statistics of XX∗ and its minor after removing the first column of X. Secondly, we consider Wigner-type matrices and prove that the eigenvalue statistics near cusp singularities of the limiting density of states are universal and that they form a Pearcey process. Since the limiting eigenvalue distribution admits only square root (edge) and cubic root (cusp) singularities, this concludes the third and last remaining case of the Wigner-Dyson-Mehta universality conjecture. The main technical ingredients are an optimal local law at the cusp, and the proof of the fast relaxation to equilibrium of the Dyson Brownian motion in the cusp regime.
In the second part we consider non-Hermitian matrices X with centred i.i.d. entries. We normalise the entries of X to have variance N −1. It is well known that the empirical eigenvalue density converges to the uniform distribution on the unit disk (circular law). In the first project, we prove universality of the local eigenvalue statistics close to the edge of the spectrum. This is the non-Hermitian analogue of the TracyWidom universality at the Hermitian edge. Technically we analyse the evolution of the spectral distribution of X along the Ornstein-Uhlenbeck flow for very long time
(up to t = +∞). In the second project, we consider linear statistics of eigenvalues for macroscopic test functions f in the Sobolev space H2+ϵ and prove their convergence to the projection of the Gaussian Free Field on the unit disk. We prove this result for non-Hermitian matrices with real or complex entries. The main technical ingredients are: (i) local law for products of two resolvents at different spectral parameters, (ii) analysis of correlated Dyson Brownian motions.
In the third and final part we discuss the mathematically rigorous application of supersymmetric techniques (SUSY ) to give a lower tail estimate of the lowest singular value of X − z, with z ∈ C. More precisely, we use superbosonisation formula to give an integral representation of the resolvent of (X − z)(X − z)∗ which reduces to two and three contour integrals in the complex and real case, respectively. The rigorous analysis of these integrals is quite challenging since simple saddle point analysis cannot be applied (the main contribution comes from a non-trivial manifold). Our result
improves classical smoothing inequalities in the regime |z| ≈ 1; this result is essential to prove edge universality for i.i.d. non-Hermitian matrices.},
author = {Cipolloni, Giorgio},
issn = {2663-337X},
pages = {380},
publisher = {IST Austria},
title = {{Fluctuations in the spectrum of random matrices}},
doi = {10.15479/AT:ISTA:9022},
year = {2021},
}
@unpublished{9034,
abstract = {We determine an asymptotic formula for the number of integral points of bounded height on a blow-up of $\mathbb{P}^3$ outside certain planes using universal torsors.},
author = {Wilsch, Florian Alexander},
booktitle = {arXiv},
title = {{Integral points of bounded height on a log Fano threefold}},
year = {2021},
}
@article{9037,
abstract = {We continue our study of ‘no‐dimension’ analogues of basic theorems in combinatorial and convex geometry in Banach spaces. We generalize some results of the paper (Adiprasito, Bárány and Mustafa, ‘Theorems of Carathéodory, Helly, and Tverberg without dimension’, Proceedings of the Thirtieth Annual ACM‐SIAM Symposium on Discrete Algorithms (Society for Industrial and Applied Mathematics, San Diego, California, 2019) 2350–2360) and prove no‐dimension versions of the colored Tverberg theorem, the selection lemma and the weak 𝜀 ‐net theorem in Banach spaces of type 𝑝>1 . To prove these results, we use the original ideas of Adiprasito, Bárány and Mustafa for the Euclidean case, our no‐dimension version of the Radon theorem and slightly modified version of the celebrated Maurey lemma.},
author = {Ivanov, Grigory},
issn = {14692120},
journal = {Bulletin of the London Mathematical Society},
publisher = {London Mathematical Society},
title = {{No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p}},
doi = {10.1112/blms.12449},
year = {2021},
}
@article{9038,
abstract = {Layered materials in which individual atomic layers are bonded by weak van der Waals forces (vdW materials) constitute one of the most prominent platforms for materials research. Particularly, polar vdW crystals, such as hexagonal boron nitride (h-BN), alpha-molybdenum trioxide (α-MoO3) or alpha-vanadium pentoxide (α-V2O5), have received significant attention in nano-optics, since they support phonon polaritons (PhPs)―light coupled to lattice vibrations― with strong electromagnetic confinement and low optical losses. Recently, correlative far- and near-field studies of α-MoO3 have been demonstrated as an effective strategy to accurately extract the permittivity of this material. Here, we use this accurately characterized and low-loss polaritonic material to sense its local dielectric environment, namely silica (SiO2), one of the most widespread substrates in nanotechnology. By studying the propagation of PhPs on α-MoO3 flakes with different thicknesses laying on SiO2 substrates via near-field microscopy (s-SNOM), we extract locally the infrared permittivity of SiO2. Our work reveals PhPs nanoimaging as a versatile method for the quantitative characterization of the local optical properties of dielectric substrates, crucial for understanding and predicting the response of nanomaterials and for the future scalability of integrated nanophotonic devices. },
author = {Aguilar-Merino, Patricia and Álvarez-Pérez, Gonzalo and Taboada-Gutiérrez, Javier and Duan, Jiahua and Prieto Gonzalez, Ivan and Álvarez-Prado, Luis Manuel and Nikitin, Alexey Y. and Martín-Sánchez, Javier and Alonso-González, Pablo},
issn = {20794991},
journal = {Nanomaterials},
number = {1},
publisher = {MDPI},
title = {{Extracting the infrared permittivity of SiO2 substrates locally by near-field imaging of phonon polaritons in a van der Waals crystal}},
doi = {10.3390/nano11010120},
volume = {11},
year = {2021},
}
@article{9046,
author = {Römhild, Roderich and Andersson, Dan I.},
issn = {15537374},
journal = {PLoS Pathogens},
number = {1},
publisher = {Public Library of Science},
title = {{Mechanisms and therapeutic potential of collateral sensitivity to antibiotics}},
doi = {10.1371/journal.ppat.1009172},
volume = {17},
year = {2021},
}
@article{9047,
abstract = {This work analyzes the latency of the simplified successive cancellation (SSC) decoding scheme for polar codes proposed by Alamdar-Yazdi and Kschischang. It is shown that, unlike conventional successive cancellation decoding, where latency is linear in the block length, the latency of SSC decoding is sublinear. More specifically, the latency of SSC decoding is O(N1−1/μ) , where N is the block length and μ is the scaling exponent of the channel, which captures the speed of convergence of the rate to capacity. Numerical results demonstrate the tightness of the bound and show that most of the latency reduction arises from the parallel decoding of subcodes of rate 0 or 1.},
author = {Mondelli, Marco and Hashemi, Seyyed Ali and Cioffi, John M. and Goldsmith, Andrea},
issn = {15582248},
journal = {IEEE Transactions on Wireless Communications},
number = {1},
pages = {18--27},
publisher = {IEEE},
title = {{Sublinear latency for simplified successive cancellation decoding of polar codes}},
doi = {10.1109/TWC.2020.3022922},
volume = {20},
year = {2021},
}
@article{9048,
abstract = {The analogy between an equilibrium partition function and the return probability in many-body unitary dynamics has led to the concept of dynamical quantum phase transition (DQPT). DQPTs are defined by nonanalyticities in the return amplitude and are present in many models. In some cases, DQPTs can be related to equilibrium concepts, such as order parameters, yet their universal description is an open question. In this Letter, we provide first steps toward a classification of DQPTs by using a matrix product state description of unitary dynamics in the thermodynamic limit. This allows us to distinguish the two limiting cases of “precession” and “entanglement” DQPTs, which are illustrated using an analytical description in the quantum Ising model. While precession DQPTs are characterized by a large entanglement gap and are semiclassical in their nature, entanglement DQPTs occur near avoided crossings in the entanglement spectrum and can be distinguished by a complex pattern of nonlocal correlations. We demonstrate the existence of precession and entanglement DQPTs beyond Ising models, discuss observables that can distinguish them, and relate their interplay to complex DQPT phenomenology.},
author = {De Nicola, Stefano and Michailidis, Alexios and Serbyn, Maksym},
issn = {0031-9007},
journal = {Physical Review Letters},
keywords = {General Physics and Astronomy},
number = {4},
publisher = {American Physical Society},
title = {{Entanglement view of dynamical quantum phase transitions}},
doi = {10.1103/physrevlett.126.040602},
volume = {126},
year = {2021},
}
@phdthesis{9056,
abstract = {In this thesis we study persistence of multi-covers of Euclidean balls and the geometric structures underlying their computation, in particular Delaunay mosaics and Voronoi tessellations.
The k-fold cover for some discrete input point set consists of the space where at least k balls of radius r around the input points overlap. Persistence is a notion that captures, in some sense, the topology of the shape underlying the input. While persistence is usually computed for the union of balls, the k-fold cover is of interest as it captures local density,
and thus might approximate the shape of the input better if the input data is noisy. To compute persistence of these k-fold covers, we need a discretization that is provided by higher-order Delaunay mosaics.
We present and implement a simple and efficient algorithm for the computation of higher-order Delaunay mosaics, and use it to give experimental results for their combinatorial properties. The algorithm makes use of a new geometric structure, the rhomboid tiling. It contains the higher-order Delaunay mosaics as slices, and by introducing a filtration
function on the tiling, we also obtain higher-order α-shapes as slices. These allow us to compute persistence of the multi-covers for varying radius r; the computation for varying k is less straight-foward and involves the rhomboid tiling directly. We apply our algorithms to experimental sphere packings to shed light on their structural properties. Finally, inspired by periodic structures in packings and materials, we propose and implement an algorithm for periodic Delaunay triangulations to be integrated into the Computational Geometry Algorithms Library (CGAL), and discuss
the implications on persistence for periodic data sets.},
author = {Osang, Georg F},
issn = {2663-337X},
pages = {134},
publisher = {IST Austria},
title = {{Multi-cover persistence and Delaunay mosaics}},
doi = {10.15479/AT:ISTA:9056},
year = {2021},
}
@unpublished{9082,
abstract = {Acquired mutations are sufficiently frequent such that the genome of a single cell offers a record of its history of cell divisions. Among more common somatic genomic alterations are loss of heterozygosity (LOH). Large LOH events are potentially detectable in single cell RNA sequencing (scRNA-seq) datasets as tracts of monoallelic expression for constitutionally heterozygous single nucleotide variants (SNVs) located among contiguous genes. We identified runs of monoallelic expression, consistent with LOH, uniquely distributed throughout the genome in single cell brain cortex transcriptomes of F1 hybrids involving different inbred mouse strains. We then phylogenetically reconstructed single cell lineages and simultaneously identified cell types by corresponding gene expression patterns. Our results are consistent with progenitor cells giving rise to multiple cortical cell types through stereotyped expansion and distinct waves of neurogenesis. Compared to engineered recording systems, LOH events accumulate throughout the genome and across the lifetime of an organism, affording tremendous capacity for encoding lineage information and increasing resolution for later cell divisions. This approach can conceivably be computationally incorporated into scRNA-seq analysis and may be useful for organisms where genetic engineering is prohibitive, such as humans.},
author = {Anderson, Donovan J. and Pauler, Florian and McKenna, Aaron and Shendure, Jay and Hippenmeyer, Simon and Horwitz, Marshall S.},
booktitle = {bioRxiv},
publisher = {Cold Spring Harbor Laboratory},
title = {{Simultaneous identification of brain cell type and lineage via single cell RNA sequencing}},
doi = {10.1101/2020.12.31.425016},
year = {2021},
}
@article{9093,
abstract = {We employ the Gross-Pitaevskii equation to study acoustic emission generated in a uniform Bose gas by a static impurity. The impurity excites a sound-wave packet, which propagates through the gas. We calculate the shape of this wave packet in the limit of long wave lengths, and argue that it is possible to extract properties of the impurity by observing this shape. We illustrate here this possibility for a Bose gas with a trapped impurity atom -- an example of a relevant experimental setup. Presented results are general for all one-dimensional systems described by the nonlinear Schrödinger equation and can also be used in nonatomic systems, e.g., to analyze light propagation in nonlinear optical media. Finally, we calculate the shape of the sound-wave packet for a three-dimensional Bose gas assuming a spherically symmetric perturbation.},
author = {Marchukov, Oleksandr and Volosniev, Artem},
issn = {2542-4653},
journal = {SciPost Physics},
number = {2},
publisher = {SciPost Foundation},
title = {{Shape of a sound wave in a weakly-perturbed Bose gas}},
doi = {10.21468/scipostphys.10.2.025},
volume = {10},
year = {2021},
}
@article{9097,
abstract = {Psoriasis is a chronic inflammatory skin disease clinically characterized by the appearance of red colored, well-demarcated plaques with thickened skin and with silvery scales. Recent studies have established the involvement of a complex signalling network of interactions between cytokines, immune cells and skin cells called keratinocytes. Keratinocytes form the cells of the outermost layer of the skin (epidermis). Visible plaques in psoriasis are developed due to the fast proliferation and unusual differentiation of keratinocyte cells. Despite that, the exact mechanism of the appearance of these plaques in the cytokine-immune cell network is not clear. A mathematical model embodying interactions between key immune cells believed to be involved in psoriasis, keratinocytes and relevant cytokines has been developed. The complex network formed of these interactions poses several challenges. Here, we choose to study subnetworks of this complex network and initially focus on interactions involving TNFα, IL-23/IL-17, and IL-15. These are chosen based on known evidence of their therapeutic efficacy. In addition, we explore the role of IL-15 in the pathogenesis of psoriasis and its potential as a future drug target for a novel treatment option. We perform steady state analyses for these subnetworks and demonstrate that the interactions between cells, driven by cytokines could cause the emergence of a psoriasis state (hyper-proliferation of keratinocytes) when levels of TNFα, IL-23/IL-17 or IL-15 are increased. The model results explain and support the clinical potentiality of anti-cytokine treatments. Interestingly, our results suggest different dynamic scenarios underpin the pathogenesis of psoriasis, depending upon the dominant cytokines of subnetworks. We observed that the increase in the level of IL-23/IL-17 and IL-15 could lead to psoriasis via a bistable route, whereas an increase in the level of TNFα would lead to a monotonic and gradual disease progression. Further, we demonstrate how this insight, bistability, could be exploited to improve the current therapies and develop novel treatment strategies for psoriasis.},
author = {Pandey, Rakesh and Al-Nuaimi, Yusur and Mishra, Rajiv Kumar and Spurgeon, Sarah K. and Goodfellow, Marc},
issn = {20452322},
journal = {Scientific Reports},
publisher = {Springer Nature},
title = {{Role of subnetworks mediated by TNF α, IL-23/IL-17 and IL-15 in a network involved in the pathogenesis of psoriasis}},
doi = {10.1038/s41598-020-80507-7},
volume = {11},
year = {2021},
}
@article{9098,
abstract = {We study properties of the volume of projections of the n-dimensional
cross-polytope $\crosp^n = \{ x \in \R^n \mid |x_1| + \dots + |x_n| \leqslant 1\}.$ We prove that the projection of $\crosp^n$ onto a k-dimensional coordinate subspace has the maximum possible volume for k=2 and for k=3.
We obtain the exact lower bound on the volume of such a projection onto a two-dimensional plane. Also, we show that there exist local maxima which are not global ones for the volume of a projection of $\crosp^n$ onto a k-dimensional subspace for any n>k⩾2.},
author = {Ivanov, Grigory},
issn = {0012365X},
journal = {Discrete Mathematics},
number = {5},
publisher = {Elsevier},
title = {{On the volume of projections of the cross-polytope}},
doi = {10.1016/j.disc.2021.112312},
volume = {344},
year = {2021},
}
@article{9099,
abstract = {We show that on an Abelian variety over an algebraically closed field of positive characteristic, the obstruction to lifting an automorphism to a field of characteristic zero as a morphism vanishes if and only if it vanishes for lifting it as a derived autoequivalence. We also compare the deformation space of these two types of deformations.},
author = {Srivastava, Tanya K},
issn = {14208938},
journal = {Archiv der Mathematik},
publisher = {Springer Nature},
title = {{Lifting automorphisms on Abelian varieties as derived autoequivalences}},
doi = {10.1007/s00013-020-01564-y},
year = {2021},
}
@article{9100,
abstract = {Marine environments are inhabited by a broad representation of the tree of life, yet our understanding of speciation in marine ecosystems is extremely limited compared with terrestrial and freshwater environments. Developing a more comprehensive picture of speciation in marine environments requires that we 'dive under the surface' by studying a wider range of taxa and ecosystems is necessary for a more comprehensive picture of speciation. Although studying marine evolutionary processes is often challenging, recent technological advances in different fields, from maritime engineering to genomics, are making it increasingly possible to study speciation of marine life forms across diverse ecosystems and taxa. Motivated by recent research in the field, including the 14 contributions in this issue, we highlight and discuss six axes of research that we think will deepen our understanding of speciation in the marine realm: (a) study a broader range of marine environments and organisms; (b) identify the reproductive barriers driving speciation between marine taxa; (c) understand the role of different genomic architectures underlying reproductive isolation; (d) infer the evolutionary history of divergence using model‐based approaches; (e) study patterns of hybridization and introgression between marine taxa; and (f) implement highly interdisciplinary, collaborative research programmes. In outlining these goals, we hope to inspire researchers to continue filling this critical knowledge gap surrounding the origins of marine biodiversity.},
author = {Faria, Rui and Johannesson, Kerstin and Stankowski, Sean},
issn = {14209101},
journal = {Journal of Evolutionary Biology},
number = {1},
pages = {4--15},
publisher = {Wiley},
title = {{Speciation in marine environments: Diving under the surface}},
doi = {10.1111/jeb.13756},
volume = {34},
year = {2021},
}
@article{9101,
abstract = {Behavioral predispositions are innate tendencies of animals to behave in a given way without the input of learning. They increase survival chances and, due to environmental and ecological challenges, may vary substantially even between closely related taxa. These differences are likely to be especially pronounced in long-lived species like crocodilians. This order is particularly relevant for comparative cognition due to its phylogenetic proximity to birds. Here we compared early life behavioral predispositions in two Alligatoridae species. We exposed American alligator and spectacled caiman hatchlings to three different novel situations: a novel object, a novel environment that was open and a novel environment with a shelter. This was then repeated a week later. During exposure to the novel environments, alligators moved around more and explored a larger range of the arena than the caimans. When exposed to the novel object, the alligators reduced the mean distance to the novel object in the second phase, while the caimans further increased it, indicating diametrically opposite ontogenetic development in behavioral predispositions. Although all crocodilian hatchlings face comparable challenges, e.g., high predation pressure, the effectiveness of parental protection might explain the observed pattern. American alligators are apex predators capable of protecting their offspring against most dangers, whereas adult spectacled caimans are frequently predated themselves. Their distancing behavior might be related to increased predator avoidance and also explain the success of invasive spectacled caimans in the natural habitats of other crocodilians.},
author = {Reber, Stephan A. and Oh, Jinook and Janisch, Judith and Stevenson, Colin and Foggett, Shaun and Wilkinson, Anna},
issn = {14359456},
journal = {Animal Cognition},
publisher = {Springer Nature},
title = {{Early life differences in behavioral predispositions in two Alligatoridae species}},
doi = {10.1007/s10071-020-01461-5},
year = {2021},
}
@article{9119,
abstract = {We present DILS, a deployable statistical analysis platform for conducting demographic inferences with linked selection from population genomic data using an Approximate Bayesian Computation framework. DILS takes as input single‐population or two‐population data sets (multilocus fasta sequences) and performs three types of analyses in a hierarchical manner, identifying: (a) the best demographic model to study the importance of gene flow and population size change on the genetic patterns of polymorphism and divergence, (b) the best genomic model to determine whether the effective size Ne and migration rate N, m are heterogeneously distributed along the genome (implying linked selection) and (c) loci in genomic regions most associated with barriers to gene flow. Also available via a Web interface, an objective of DILS is to facilitate collaborative research in speciation genomics. Here, we show the performance and limitations of DILS by using simulations and finally apply the method to published data on a divergence continuum composed by 28 pairs of Mytilus mussel populations/species.},
author = {Fraisse, Christelle and Popovic, Iva and Mazoyer, Clément and Spataro, Bruno and Delmotte, Stéphane and Romiguier, Jonathan and Loire, Étienne and Simon, Alexis and Galtier, Nicolas and Duret, Laurent and Bierne, Nicolas and Vekemans, Xavier and Roux, Camille},
issn = {17550998},
journal = {Molecular Ecology Resources},
publisher = {Wiley},
title = {{DILS: Demographic inferences with linked selection by using ABC}},
doi = {10.1111/1755-0998.13323},
year = {2021},
}
@article{9121,
abstract = {We show that the energy gap for the BCS gap equation is
Ξ=μ(8e−2+o(1))exp(π2μ−−√a)
in the low density limit μ→0. Together with the similar result for the critical temperature by Hainzl and Seiringer (Lett Math Phys 84: 99–107, 2008), this shows that, in the low density limit, the ratio of the energy gap and critical temperature is a universal constant independent of the interaction potential V. The results hold for a class of potentials with negative scattering length a and no bound states.},
author = {Lauritsen, Asbjørn Bækgaard},
issn = {0377-9017},
journal = {Letters in Mathematical Physics},
keywords = {Mathematical Physics, Statistical and Nonlinear Physics},
publisher = {Springer Nature},
title = {{The BCS energy gap at low density}},
doi = {10.1007/s11005-021-01358-5},
volume = {111},
year = {2021},
}
@article{9158,
abstract = {While several tools have been developed to study the ground state of many-body quantum spin systems, the limitations of existing techniques call for the exploration of new approaches. In this manuscript we develop an alternative analytical and numerical framework for many-body quantum spin ground states, based on the disentanglement formalism. In this approach, observables are exactly expressed as Gaussian-weighted functional integrals over scalar fields. We identify the leading contribution to these integrals, given by the saddle point of a suitable effective action. Analytically, we develop a field-theoretical expansion of the functional integrals, performed by means of appropriate Feynman rules. The expansion can be truncated to a desired order to obtain analytical approximations to observables. Numerically, we show that the disentanglement approach can be used to compute ground state expectation values from classical stochastic processes. While the associated fluctuations grow exponentially with imaginary time and the system size, this growth can be mitigated by means of an importance sampling scheme based on knowledge of the saddle point configuration. We illustrate the advantages and limitations of our methods by considering the quantum Ising model in 1, 2 and 3 spatial dimensions. Our analytical and numerical approaches are applicable to a broad class of systems, bridging concepts from quantum lattice models, continuum field theory, and classical stochastic processes.},
author = {De Nicola, Stefano},
issn = {1742-5468},
journal = {Journal of Statistical Mechanics: Theory and Experiment},
keywords = {Statistics, Probability and Uncertainty, Statistics and Probability, Statistical and Nonlinear Physics},
number = {1},
publisher = {IOP Publishing},
title = {{Disentanglement approach to quantum spin ground states: Field theory and stochastic simulation}},
doi = {10.1088/1742-5468/abc7c7},
volume = {2021},
year = {2021},
}
@article{9173,
abstract = {We show that Hilbert schemes of points on supersingular Enriques surface in characteristic 2, Hilbn(X), for n ≥ 2 are simply connected, symplectic varieties but are not irreducible symplectic as the hodge number h2,0 > 1, even though a supersingular Enriques surface is an irreducible symplectic variety. These are the classes of varieties which appear only in characteristic 2 and they show that the hodge number formula for G¨ottsche-Soergel does not hold over haracteristic 2. It also gives examples of varieties with trivial canonical class which are neither irreducible symplectic nor Calabi-Yau, thereby showing that there are strictly more classes of simply connected varieties with trivial canonical class in characteristic 2 than over C as given by Beauville-Bogolomov decomposition theorem.},
author = {Srivastava, Tanya K},
issn = {0007-4497},
journal = {Bulletin des Sciences Mathematiques},
number = {03},
publisher = {Elsevier},
title = {{Pathologies of the Hilbert scheme of points of a supersingular Enriques surface}},
doi = {10.1016/j.bulsci.2021.102957},
volume = {167},
year = {2021},
}
@unpublished{9199,
abstract = {We associate a certain tensor product lattice to any primitive integer lattice and ask about its typical shape. These lattices are related to the tangent bundle of Grassmannians and their study is motivated by Peyre's programme on "freeness" for rational points of bounded height on Fano
varieties.},
author = {Browning, Timothy D and Horesh, Tal and Wilsch, Florian Alexander},
booktitle = {arXiv},
title = {{Equidistribution and freeness on Grassmannians}},
year = {2021},
}