TY - JOUR
AB - We study dynamical optimal transport metrics between density matricesassociated to symmetric Dirichlet forms on finite-dimensional C∗-algebras. Our settingcovers arbitrary skew-derivations and it provides a unified framework that simultaneously generalizes recently constructed transport metrics for Markov chains, Lindblad equations, and the Fermi Ornstein–Uhlenbeck semigroup. We develop a non-nommutative differential calculus that allows us to obtain non-commutative Ricci curvature bounds, logarithmic Sobolev inequalities, transport-entropy inequalities, andspectral gap estimates.
AU - Carlen, Eric A.
AU - Maas, Jan
ID - 6358
IS - 2
JF - Journal of Statistical Physics
SN - 00224715
TI - Non-commutative calculus, optimal transport and functional inequalities in dissipative quantum systems
VL - 178
ER -
TY - JOUR
AB - The strong rate of convergence of the Euler-Maruyama scheme for nondegenerate SDEs with irregular drift coefficients is considered. In the case of α-Hölder drift in the recent literature the rate α/2 was proved in many related situations. By exploiting the regularising effect of the noise more efficiently, we show that the rate is in fact arbitrarily close to 1/2 for all α>0. The result extends to Dini continuous coefficients, while in d=1 also to all bounded measurable coefficients.
AU - Dareiotis, Konstantinos
AU - Gerencser, Mate
ID - 6359
JF - Electronic Journal of Probability
TI - On the regularisation of the noise for the Euler-Maruyama scheme with irregular drift
VL - 25
ER -
TY - JOUR
AB - We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix W˜ and its minor W. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of W˜ and W. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.
AU - Cipolloni, Giorgio
AU - Erdös, László
ID - 6488
IS - 3
JF - Random Matrices: Theory and Application
SN - 20103263
TI - Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices
VL - 9
ER -
TY - JOUR
AB - This paper presents two algorithms. The first decides the existence of a pointed homotopy between given simplicial maps 𝑓,𝑔:𝑋→𝑌, and the second computes the group [𝛴𝑋,𝑌]∗ of pointed homotopy classes of maps from a suspension; in both cases, the target Y is assumed simply connected. More generally, these algorithms work relative to 𝐴⊆𝑋.
AU - Filakovský, Marek
AU - Vokřínek, Lukas
ID - 6563
JF - Foundations of Computational Mathematics
SN - 16153375
TI - Are two given maps homotopic? An algorithmic viewpoint
VL - 20
ER -
TY - JOUR
AB - We consider the monotone variational inequality problem in a Hilbert space and describe a projection-type method with inertial terms under the following properties: (a) The method generates a strongly convergent iteration sequence; (b) The method requires, at each iteration, only one projection onto the feasible set and two evaluations of the operator; (c) The method is designed for variational inequality for which the underline operator is monotone and uniformly continuous; (d) The method includes an inertial term. The latter is also shown to speed up the convergence in our numerical results. A comparison with some related methods is given and indicates that the new method is promising.
AU - Shehu, Yekini
AU - Li, Xiao-Huan
AU - Dong, Qiao-Li
ID - 6593
JF - Numerical Algorithms
SN - 1017-1398
TI - An efficient projection-type method for monotone variational inequalities in Hilbert spaces
VL - 84
ER -
TY - JOUR
AB - While Hartree–Fock theory is well established as a fundamental approximation for interacting fermions, it has been unclear how to describe corrections to it due to many-body correlations. In this paper we start from the Hartree–Fock state given by plane waves and introduce collective particle–hole pair excitations. These pairs can be approximately described by a bosonic quadratic Hamiltonian. We use Bogoliubov theory to construct a trial state yielding a rigorous Gell-Mann–Brueckner–type upper bound to the ground state energy. Our result justifies the random-phase approximation in the mean-field scaling regime, for repulsive, regular interaction potentials.
AU - Benedikter, Niels P
AU - Nam, Phan Thành
AU - Porta, Marcello
AU - Schlein, Benjamin
AU - Seiringer, Robert
ID - 6649
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Optimal upper bound for the correlation energy of a Fermi gas in the mean-field regime
VL - 374
ER -
TY - JOUR
AB - Nearby grid cells have been observed to express a remarkable degree of long-rangeorder, which is often idealized as extending potentially to infinity. Yet their strict peri-odic firing and ensemble coherence are theoretically possible only in flat environments, much unlike the burrows which rodents usually live in. Are the symmetrical, coherent grid maps inferred in the lab relevant to chart their way in their natural habitat? We consider spheres as simple models of curved environments and waiting for the appropriate experiments to be performed, we use our adaptation model to predict what grid maps would emerge in a network with the same type of recurrent connections, which on the plane produce coherence among the units. We find that on the sphere such connections distort the maps that single grid units would express on their own, and aggregate them into clusters. When remapping to a different spherical environment, units in each cluster maintain only partial coherence, similar to what is observed in disordered materials, such as spin glasses.
AU - Stella, Federico
AU - Urdapilleta, Eugenio
AU - Luo, Yifan
AU - Treves, Alessandro
ID - 6796
IS - 4
JF - Hippocampus
SN - 10509631
TI - Partial coherence and frustration in self-organizing spherical grids
VL - 30
ER -
TY - JOUR
AB - Super-resolution fluorescence microscopy has become an important catalyst for discovery in the life sciences. In STimulated Emission Depletion (STED) microscopy, a pattern of light drives fluorophores from a signal-emitting on-state to a non-signalling off-state. Only emitters residing in a sub-diffraction volume around an intensity minimum are allowed to fluoresce, rendering them distinguishable from the nearby, but dark fluorophores. STED routinely achieves resolution in the few tens of nanometers range in biological samples and is suitable for live imaging. Here, we review the working principle of STED and provide general guidelines for successful STED imaging. The strive for ever higher resolution comes at the cost of increased light burden. We discuss techniques to reduce light exposure and mitigate its detrimental effects on the specimen. These include specialized illumination strategies as well as protecting fluorophores from photobleaching mediated by high-intensity STED light. This opens up the prospect of volumetric imaging in living cells and tissues with diffraction-unlimited resolution in all three spatial dimensions.
AU - Jahr, Wiebke
AU - Velicky, Philipp
AU - Danzl, Johann G
ID - 6808
IS - 3
JF - Methods
SN - 1046-2023
TI - Strategies to maximize performance in STimulated Emission Depletion (STED) nanoscopy of biological specimens
VL - 174
ER -
TY - JOUR
AB - In resource allocation games, selfish players share resources that are needed in order to fulfill their objectives. The cost of using a resource depends on the load on it. In the traditional setting, the players make their choices concurrently and in one-shot. That is, a strategy for a player is a subset of the resources. We introduce and study dynamic resource allocation games. In this setting, the game proceeds in phases. In each phase each player chooses one resource. A scheduler dictates the order in which the players proceed in a phase, possibly scheduling several players to proceed concurrently. The game ends when each player has collected a set of resources that fulfills his objective. The cost for each player then depends on this set as well as on the load on the resources in it – we consider both congestion and cost-sharing games. We argue that the dynamic setting is the suitable setting for many applications in practice. We study the stability of dynamic resource allocation games, where the appropriate notion of stability is that of subgame perfect equilibrium, study the inefficiency incurred due to selfish behavior, and also study problems that are particular to the dynamic setting, like constraints on the order in which resources can be chosen or the problem of finding a scheduler that achieves stability.
AU - Avni, Guy
AU - Henzinger, Thomas A
AU - Kupferman, Orna
ID - 6761
JF - Theoretical Computer Science
SN - 03043975
TI - Dynamic resource allocation games
VL - 807
ER -
TY - JOUR
AB - We present a unified framework tackling two problems: class-specific 3D reconstruction from a single image, and generation of new 3D shape samples. These tasks have received considerable attention recently; however, most existing approaches rely on 3D supervision, annotation of 2D images with keypoints or poses, and/or training with multiple views of each object instance. Our framework is very general: it can be trained in similar settings to existing approaches, while also supporting weaker supervision. Importantly, it can be trained purely from 2D images, without pose annotations, and with only a single view per instance. We employ meshes as an output representation, instead of voxels used in most prior work. This allows us to reason over lighting parameters and exploit shading information during training, which previous 2D-supervised methods cannot. Thus, our method can learn to generate and reconstruct concave object classes. We evaluate our approach in various settings, showing that: (i) it learns to disentangle shape from pose and lighting; (ii) using shading in the loss improves performance compared to just silhouettes; (iii) when using a standard single white light, our model outperforms state-of-the-art 2D-supervised methods, both with and without pose supervision, thanks to exploiting shading cues; (iv) performance improves further when using multiple coloured lights, even approaching that of state-of-the-art 3D-supervised methods; (v) shapes produced by our model capture smooth surfaces and fine details better than voxel-based approaches; and (vi) our approach supports concave classes such as bathtubs and sofas, which methods based on silhouettes cannot learn.
AU - Henderson, Paul M
AU - Ferrari, Vittorio
ID - 6952
JF - International Journal of Computer Vision
SN - 0920-5691
TI - Learning single-image 3D reconstruction by generative modelling of shape, pose and shading
VL - 128
ER -
TY - JOUR
AU - Zhang, Yuzhou
AU - Friml, Jiří
ID - 6997
IS - 3
JF - New Phytologist
SN - 0028-646x
TI - Auxin guides roots to avoid obstacles during gravitropic growth
VL - 225
ER -
TY - JOUR
AB - The central object of investigation of this paper is the Hirzebruch class, a deformation of the Todd class, given by Hirzebruch (for smooth varieties). The generalization for singular varieties is due to Brasselet–Schürmann–Yokura. Following the work of Weber, we investigate its equivariant version for (possibly singular) toric varieties. The local decomposition of the Hirzebruch class to the fixed points of the torus action and a formula for the local class in terms of the defining fan are recalled. After this review part, we prove the positivity of local Hirzebruch classes for all toric varieties, thus proving false the alleged counterexample given by Weber.
AU - Rychlewicz, Kamil P
ID - 6965
JF - Bulletin of the London Mathematical Society
SN - 0024-6093
TI - The positivity of local equivariant Hirzebruch class for toric varieties
ER -
TY - JOUR
AB - We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.
AU - Rapcak, Miroslav
AU - Soibelman, Yan
AU - Yang, Yaping
AU - Zhao, Gufang
ID - 7004
JF - Communications in Mathematical Physics
SN - 0010-3616
TI - Cohomological Hall algebras, vertex algebras and instantons
VL - 376
ER -
TY - JOUR
AB - The unusual correlated state that emerges in URu2Si2 below THO = 17.5 K is known as “hidden order” because even basic characteristics of the order parameter, such as its dimensionality (whether it has one component or two), are “hidden.” We use resonant ultrasound spectroscopy to measure the symmetry-resolved elastic anomalies across THO. We observe no anomalies in the shear elastic moduli, providing strong thermodynamic evidence for a one-component order parameter. We develop a machine learning framework that reaches this conclusion directly from the raw data, even in a crystal that is too small for traditional resonant ultrasound. Our result rules out a broad class of theories of hidden order based on two-component order parameters, and constrains the nature of the fluctuations from which unconventional superconductivity emerges at lower temperature. Our machine learning framework is a powerful new tool for classifying the ubiquitous competing orders in correlated electron systems.
AU - Ghosh, Sayak
AU - Matty, Michael
AU - Baumbach, Ryan
AU - Bauer, Eric D.
AU - Modic, Kimberly A
AU - Shekhter, Arkady
AU - Mydosh, J. A.
AU - Kim, Eun-Ah
AU - Ramshaw, B. J.
ID - 7084
IS - 10
JF - Science Advances
TI - One-component order parameter in URu2Si2 uncovered by resonant ultrasound spectroscopy and machine learning
VL - 6
ER -
TY - JOUR
AB - Removal of the Bax gene from mice completely protects the somas of retinal ganglion cells (RGCs) from apoptosis following optic nerve injury. This makes BAX a promising therapeutic target to prevent neurodegeneration. In this study, Bax+/− mice were used to test the hypothesis that lowering the quantity of BAX in RGCs would delay apoptosis following optic nerve injury. RGCs were damaged by performing optic nerve crush (ONC) and then immunostaining for phospho-cJUN, and quantitative PCR were used to monitor the status of the BAX activation mechanism in the months following injury. The apoptotic susceptibility of injured cells was directly tested by virally introducing GFP-BAX into Bax−/− RGCs after injury. The competency of quiescent RGCs to reactivate their BAX activation mechanism was tested by intravitreal injection of the JNK pathway agonist, anisomycin. Twenty-four weeks after ONC, Bax+/− mice had significantly less cell loss in their RGC layer than Bax+/+ mice 3 weeks after ONC. Bax+/− and Bax+/+ RGCs exhibited similar patterns of nuclear phospho-cJUN accumulation immediately after ONC, which persisted in Bax+/− RGCs for up to 7 weeks before abating. The transcriptional activation of BAX-activating genes was similar in Bax+/− and Bax+/+ RGCs following ONC. Intriguingly, cells deactivated their BAX activation mechanism between 7 and 12 weeks after crush. Introduction of GFP-BAX into Bax−/− cells at 4 weeks after ONC showed that these cells had a nearly normal capacity to activate this protein, but this capacity was lost 8 weeks after crush. Collectively, these data suggest that 8–12 weeks after crush, damaged cells no longer displayed increased susceptibility to BAX activation relative to their naïve counterparts. In this same timeframe, retinal glial activation and the signaling of the pro-apoptotic JNK pathway also abated. Quiescent RGCs did not show a timely reactivation of their JNK pathway following intravitreal injection with anisomycin. These findings demonstrate that lowering the quantity of BAX in RGCs is neuroprotective after acute injury. Damaged RGCs enter a quiescent state months after injury and are no longer responsive to an apoptotic stimulus. Quiescent RGCs will require rejuvenation to reacquire functionality.
AU - Donahue, RJ
AU - Maes, Margaret E
AU - Grosser, JA
AU - Nickells, RW
ID - 7033
IS - 2
JF - Molecular Neurobiology
SN - 0893-7648
TI - BAX-depleted retinal ganglion cells survive and become quiescent following optic nerve damage
VL - 57
ER -
TY - JOUR
AB - The phytohormone auxin acts as an amazingly versatile coordinator of plant growth and development. With its morphogen-like properties, auxin controls sites and timing of differentiation and/or growth responses both, in quantitative and qualitative terms. Specificity in the auxin response depends largely on distinct modes of signal transmission, by which individual cells perceive and convert auxin signals into a remarkable diversity of responses. The best understood, or so-called canonical mechanism of auxin perception ultimately results in variable adjustments of the cellular transcriptome, via a short, nuclear signal transduction pathway. Additional findings that accumulated over decades implied that an additional, presumably, cell surface-based auxin perception mechanism mediates very rapid cellular responses and decisively contributes to the cell's overall hormonal response. Recent investigations into both, nuclear and cell surface auxin signalling challenged this assumed partition of roles for different auxin signalling pathways and revealed an unexpected complexity in transcriptional and non-transcriptional cellular responses mediated by auxin.
AU - Gallei, Michelle C
AU - Luschnig, C
AU - Friml, Jiří
ID - 7142
IS - 2
JF - Current Opinion in Plant Biology
SN - 1369-5266
TI - Auxin signalling in growth: Schrödinger's cat out of the bag
VL - 53
ER -
TY - JOUR
AB - In the cerebellum, GluD2 is exclusively expressed in Purkinje cells, where it regulates synapse formation and regeneration, synaptic plasticity, and motor learning. Delayed cognitive development in humans with GluD2 gene mutations suggests extracerebellar functions of GluD2. However, extracerebellar expression of GluD2 and its relationship with that of GluD1 are poorly understood. GluD2 mRNA and protein were widely detected, with relatively high levels observed in the olfactory glomerular layer, medial prefrontal cortex, cingulate cortex, retrosplenial granular cortex, olfactory tubercle, subiculum, striatum, lateral septum, anterodorsal thalamic nucleus, and arcuate hypothalamic nucleus. These regions were also enriched for GluD1, and many individual neurons coexpressed the two GluDs. In the retrosplenial granular cortex, GluD1 and GluD2 were selectively expressed at PSD‐95‐expressing glutamatergic synapses, and their coexpression on the same synapses was shown by SDS‐digested freeze‐fracture replica labeling. Biochemically, GluD1 and GluD2 formed coimmunoprecipitable complex formation in HEK293T cells and in the cerebral cortex and hippocampus. We further estimated the relative protein amount by quantitative immunoblotting using GluA2/GluD2 and GluA2/GluD1 chimeric proteins as standards for titration of GluD1 and GluD2 antibodies. Intriguingly, the relative amount of GluD2 was almost comparable to that of GluD1 in the postsynaptic density fraction prepared from the cerebral cortex and hippocampus. In contrast, GluD2 was overwhelmingly predominant in the cerebellum. Thus, we have determined the relative extracerebellar expression of GluD1 and GluD2 at regional, neuronal, and synaptic levels. These data provide a molecular–anatomical basis for possible competitive and cooperative interactions of GluD family members at synapses in various brain regions.
AU - Nakamoto, Chihiro
AU - Konno, Kohtarou
AU - Miyazaki, Taisuke
AU - Nakatsukasa, Ena
AU - Natsume, Rie
AU - Abe, Manabu
AU - Kawamura, Meiko
AU - Fukazawa, Yugo
AU - Shigemoto, Ryuichi
AU - Yamasaki, Miwako
AU - Sakimura, Kenji
AU - Watanabe, Masahiko
ID - 7148
IS - 6
JF - Journal of Comparative Neurology
SN - 0021-9967
TI - Expression mapping, quantification, and complex formation of GluD1 and GluD2 glutamate receptors in adult mouse brain
VL - 528
ER -
TY - JOUR
AB - In recent years, many genes have been associated with chromatinopathies classified as “Cornelia de Lange Syndrome‐like.” It is known that the phenotype of these patients becomes less recognizable, overlapping to features characteristic of other syndromes caused by genetic variants affecting different regulators of chromatin structure and function. Therefore, Cornelia de Lange syndrome diagnosis might be arduous due to the seldom discordance between unexpected molecular diagnosis and clinical evaluation. Here, we review the molecular features of Cornelia de Lange syndrome, supporting the hypothesis that “CdLS‐like syndromes” are part of a larger “rare disease family” sharing multiple clinical features and common disrupted molecular pathways.
AU - Avagliano, Laura
AU - Parenti, Ilaria
AU - Grazioli, Paolo
AU - Di Fede, Elisabetta
AU - Parodi, Chiara
AU - Mariani, Milena
AU - Kaiser, Frank J.
AU - Selicorni, Angelo
AU - Gervasini, Cristina
AU - Massa, Valentina
ID - 7149
IS - 1
JF - Clinical Genetics
SN - 0009-9163
TI - Chromatinopathies: A focus on Cornelia de Lange syndrome
VL - 97
ER -
TY - JOUR
AB - We consider dynamical transport metrics for probability measures on discretisations of a bounded convex domain in ℝd. These metrics are natural discrete counterparts to the Kantorovich metric 𝕎2, defined using a Benamou-Brenier type formula. Under mild assumptions we prove an asymptotic upper bound for the discrete transport metric Wt in terms of 𝕎2, as the size of the mesh T tends to 0. However, we show that the corresponding lower bound may fail in general, even on certain one-dimensional and symmetric two-dimensional meshes. In addition, we show that the asymptotic lower bound holds under an isotropy assumption on the mesh, which turns out to be essentially necessary. This assumption is satisfied, e.g., for tilings by convex regular polygons, and it implies Gromov-Hausdorff convergence of the transport metric.
AU - Gladbach, Peter
AU - Kopfer, Eva
AU - Maas, Jan
ID - 71
IS - 3
JF - SIAM Journal on Mathematical Analysis
SN - 00361410
TI - Scaling limits of discrete optimal transport
VL - 52
ER -
TY - JOUR
AB - In this paper, we introduce an inertial projection-type method with different updating strategies for solving quasi-variational inequalities with strongly monotone and Lipschitz continuous operators in real Hilbert spaces. Under standard assumptions, we establish different strong convergence results for the proposed algorithm. Primary numerical experiments demonstrate the potential applicability of our scheme compared with some related methods in the literature.
AU - Shehu, Yekini
AU - Gibali, Aviv
AU - Sagratella, Simone
ID - 7161
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
TI - Inertial projection-type methods for solving quasi-variational inequalities in real Hilbert spaces
VL - 184
ER -