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 -