TY - JOUR
AB - In many basic shear flows, such as pipe, Couette, and channel flow, turbulence does not
arise from an instability of the laminar state, and both dynamical states co-exist. With decreasing flow speed (i.e., decreasing Reynolds number) the fraction of fluid in laminar motion increases while turbulence recedes and eventually the entire flow relaminarizes. The first step towards understanding the nature of this transition is to determine if the phase change is of either first or second order. In the former case, the turbulent fraction would drop discontinuously to zero as the Reynolds number decreases while in the latter the process would be continuous. For Couette flow, the flow between two parallel plates, earlier studies suggest a discontinuous scenario. In the present study we realize a Couette flow between two concentric cylinders which allows studies to be carried out in large aspect ratios and for extensive observation times. The presented measurements show that the transition in this circular Couette geometry is continuous suggesting that former studies were limited by finite size effects. A further characterization of this transition, in particular its relation to the directed percolation universality class, requires even larger system sizes than presently available.
AU - Avila, Kerstin
AU - Hof, Björn
ID - 8999
IS - 1
JF - Entropy
TI - Second-order phase transition in counter-rotating taylor-couette flow experiment
VL - 23
ER -
TY - JOUR
AB - Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane. We show that such a model arises naturally in the context of quantum impurity problems. In particular, we demonstrate a setup in which the lowest-energy spectrum of two linear bosonic or fermionic molecules immersed in a quantum many-particle environment can coincide with the anyonic spectrum on the sphere. This paves the way toward the experimental realization of anyons on the sphere using molecular impurities. Furthermore, since a change in the alignment of the molecules corresponds to the exchange of the particles on the sphere, such a realization reveals a novel type of exclusion principle for molecular impurities, which could also be of use as a powerful technique to measure the statistics parameter. Finally, our approach opens up a simple numerical route to investigate the spectra of many anyons on the sphere. Accordingly, we present the spectrum of two anyons on the sphere in the presence of a Dirac monopole field.
AU - Brooks, Morris
AU - Lemeshko, Mikhail
AU - Lundholm, D.
AU - Yakaboylu, Enderalp
ID - 9005
IS - 1
JF - Physical Review Letters
SN - 00319007
TI - Molecular impurities as a realization of anyons on the two-sphere
VL - 126
ER -
TY - JOUR
AB - Availability of the essential macronutrient nitrogen in soil plays a critical role in plant growth, development, and impacts agricultural productivity. Plants have evolved different strategies for sensing and responding to heterogeneous nitrogen distribution. Modulation of root system architecture, including primary root growth and branching, is among the most essential plant adaptions to ensure adequate nitrogen acquisition. However, the immediate molecular pathways coordinating the adjustment of root growth in response to distinct nitrogen sources, such as nitrate or ammonium, are poorly understood. Here, we show that growth as manifested by cell division and elongation is synchronized by coordinated auxin flux between two adjacent outer tissue layers of the root. This coordination is achieved by nitrate‐dependent dephosphorylation of the PIN2 auxin efflux carrier at a previously uncharacterized phosphorylation site, leading to subsequent PIN2 lateralization and thereby regulating auxin flow between adjacent tissues. A dynamic computer model based on our experimental data successfully recapitulates experimental observations. Our study provides mechanistic insights broadening our understanding of root growth mechanisms in dynamic environments.
AU - Ötvös, Krisztina
AU - Marconi, Marco
AU - Vega, Andrea
AU - O’Brien, Jose
AU - Johnson, Alexander J
AU - Abualia, Rashed
AU - Antonielli, Livio
AU - Montesinos López, Juan C
AU - Zhang, Yuzhou
AU - Tan, Shutang
AU - Cuesta, Candela
AU - Artner, Christina
AU - Bouguyon, Eleonore
AU - Gojon, Alain
AU - Friml, Jiří
AU - Gutiérrez, Rodrigo A.
AU - Wabnik, Krzysztof T
AU - Benková, Eva
ID - 9010
IS - 3
JF - EMBO Journal
SN - 02614189
TI - Modulation of plant root growth by nitrogen source-defined regulation of polar auxin transport
VL - 40
ER -
TY - JOUR
AB - We study dynamics and thermodynamics of ion transport in narrow, water-filled channels, considered as effective 1D Coulomb systems. The long range nature of the inter-ion interactions comes about due to the dielectric constants mismatch between the water and the surrounding medium, confining the electric filed to stay mostly within the water-filled channel. Statistical mechanics of such Coulomb systems is dominated by entropic effects which may be accurately accounted for by mapping onto an effective quantum mechanics. In presence of multivalent ions the corresponding quantum mechanics appears to be non-Hermitian. In this review we discuss a framework for semiclassical calculations for the effective non-Hermitian Hamiltonians. Non-Hermiticity elevates WKB action integrals from the real line to closed cycles on a complex Riemann surfaces where direct calculations are not attainable. We circumvent this issue by applying tools from algebraic topology, such as the Picard-Fuchs equation. We discuss how its solutions relate to the thermodynamics and correlation functions of multivalent solutions within narrow, water-filled channels.
AU - Gulden, Tobias
AU - Kamenev, Alex
ID - 9020
IS - 1
JF - Entropy
TI - Dynamics of ion channels via non-hermitian quantum mechanics
VL - 23
ER -
TY - THES
AB - 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.
AU - Cipolloni, Giorgio
ID - 9022
TI - Fluctuations in the spectrum of random matrices
ER -
TY - GEN
AB - 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.
AU - Wilsch, Florian Alexander
ID - 9034
T2 - arXiv
TI - Integral points of bounded height on a log Fano threefold
ER -
TY - JOUR
AB - In this short note, we prove that the square root of the quantum Jensen-Shannon divergence is a true metric on the cone of positive matrices, and hence in particular on the quantum state space.
AU - Virosztek, Daniel
ID - 9036
IS - 3
JF - Advances in Mathematics
KW - General Mathematics
SN - 0001-8708
TI - The metric property of the quantum Jensen-Shannon divergence
VL - 380
ER -
TY - JOUR
AB - 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.
AU - Ivanov, Grigory
ID - 9037
JF - Bulletin of the London Mathematical Society
SN - 00246093
TI - No-dimension Tverberg's theorem and its corollaries in Banach spaces of type p
ER -
TY - JOUR
AB - 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.
AU - Aguilar-Merino, Patricia
AU - Álvarez-Pérez, Gonzalo
AU - Taboada-Gutiérrez, Javier
AU - Duan, Jiahua
AU - Prieto Gonzalez, Ivan
AU - Álvarez-Prado, Luis Manuel
AU - Nikitin, Alexey Y.
AU - Martín-Sánchez, Javier
AU - Alonso-González, Pablo
ID - 9038
IS - 1
JF - Nanomaterials
TI - Extracting the infrared permittivity of SiO2 substrates locally by near-field imaging of phonon polaritons in a van der Waals crystal
VL - 11
ER -
TY - JOUR
AU - Römhild, Roderich
AU - Andersson, Dan I.
ID - 9046
IS - 1
JF - PLoS Pathogens
SN - 15537366
TI - Mechanisms and therapeutic potential of collateral sensitivity to antibiotics
VL - 17
ER -
TY - JOUR
AB - 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.
AU - Mondelli, Marco
AU - Hashemi, Seyyed Ali
AU - Cioffi, John M.
AU - Goldsmith, Andrea
ID - 9047
IS - 1
JF - IEEE Transactions on Wireless Communications
SN - 15361276
TI - Sublinear latency for simplified successive cancellation decoding of polar codes
VL - 20
ER -
TY - JOUR
AB - 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.
AU - De Nicola, Stefano
AU - Michailidis, Alexios
AU - Serbyn, Maksym
ID - 9048
IS - 4
JF - Physical Review Letters
KW - General Physics and Astronomy
SN - 0031-9007
TI - Entanglement view of dynamical quantum phase transitions
VL - 126
ER -
TY - THES
AB - 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.
AU - Osang, Georg F
ID - 9056
SN - 2663-337X
TI - Multi-cover persistence and Delaunay mosaics
ER -
TY - JOUR
AB - The sensory and cognitive abilities of the mammalian neocortex are underpinned by intricate columnar and laminar circuits formed from an array of diverse neuronal populations. One approach to determining how interactions between these circuit components give rise to complex behavior is to investigate the rules by which cortical circuits are formed and acquire functionality during development. This review summarizes recent research on the development of the neocortex, from genetic determination in neural stem cells through to the dynamic role that specific neuronal populations play in the earliest circuits of neocortex, and how they contribute to emergent function and cognition. While many of these endeavors take advantage of model systems, consideration will also be given to advances in our understanding of activity in nascent human circuits. Such cross-species perspective is imperative when investigating the mechanisms underlying the dysfunction of early neocortical circuits in neurodevelopmental disorders, so that one can identify targets amenable to therapeutic intervention.
AU - Hanganu-Opatz, Ileana L.
AU - Butt, Simon J. B.
AU - Hippenmeyer, Simon
AU - De Marco García, Natalia V.
AU - Cardin, Jessica A.
AU - Voytek, Bradley
AU - Muotri, Alysson R.
ID - 9073
IS - 5
JF - The Journal of Neuroscience
KW - General Neuroscience
SN - 0270-6474
TI - The logic of developing neocortical circuits in health and disease
VL - 41
ER -
TY - GEN
AB - 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.
AU - Anderson, Donovan J.
AU - Pauler, Florian
AU - McKenna, Aaron
AU - Shendure, Jay
AU - Hippenmeyer, Simon
AU - Horwitz, Marshall S.
ID - 9082
T2 - bioRxiv
TI - Simultaneous identification of brain cell type and lineage via single cell RNA sequencing
ER -
TY - JOUR
AB - 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.
AU - Marchukov, Oleksandr
AU - Volosniev, Artem
ID - 9093
IS - 2
JF - SciPost Physics
SN - 2542-4653
TI - Shape of a sound wave in a weakly-perturbed Bose gas
VL - 10
ER -
TY - JOUR
AB - Dendritic cells (DCs) are crucial for the priming of naive T cells and the initiation of adaptive immunity. Priming is initiated at a heterologous cell–cell contact, the immunological synapse (IS). While it is established that F-actin dynamics regulates signaling at the T cell side of the contact, little is known about the cytoskeletal contribution on the DC side. Here, we show that the DC actin cytoskeleton is decisive for the formation of a multifocal synaptic structure, which correlates with T cell priming efficiency. DC actin at the IS appears in transient foci that are dynamized by the WAVE regulatory complex (WRC). The absence of the WRC in DCs leads to stabilized contacts with T cells, caused by an increase in ICAM1-integrin–mediated cell–cell adhesion. This results in lower numbers of activated and proliferating T cells, demonstrating an important role for DC actin in the regulation of immune synapse functionality.
AU - Leithner, Alexander F
AU - Altenburger, LM
AU - Hauschild, R
AU - Assen, Frank P
AU - Rottner, K
AU - TEB, Stradal
AU - Diz-Muñoz, A
AU - Stein, JV
AU - Sixt, Michael K
ID - 9094
IS - 4
JF - Journal of Cell Biology
SN - 0021-9525
TI - Dendritic cell actin dynamics control contact duration and priming efficiency at the immunological synapse
VL - 220
ER -
TY - JOUR
AB - 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.
AU - Pandey, Rakesh
AU - Al-Nuaimi, Yusur
AU - Mishra, Rajiv Kumar
AU - Spurgeon, Sarah K.
AU - Goodfellow, Marc
ID - 9097
JF - Scientific Reports
TI - Role of subnetworks mediated by TNF α, IL-23/IL-17 and IL-15 in a network involved in the pathogenesis of psoriasis
VL - 11
ER -
TY - JOUR
AB - 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.
AU - Ivanov, Grigory
ID - 9098
IS - 5
JF - Discrete Mathematics
SN - 0012365X
TI - On the volume of projections of the cross-polytope
VL - 344
ER -
TY - JOUR
AB - 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.
AU - Srivastava, Tanya K
ID - 9099
JF - Archiv der Mathematik
SN - 0003889X
TI - Lifting automorphisms on Abelian varieties as derived autoequivalences
ER -