TY - JOUR
AB - 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.
AU - Srivastava, Tanya K
ID - 9173
IS - 03
JF - Bulletin des Sciences Mathematiques
SN - 0007-4497
TI - Pathologies of the Hilbert scheme of points of a supersingular Enriques surface
VL - 167
ER -
TY - GEN
AB - Formal design of embedded and cyber-physical systems relies on mathematical
modeling. In this paper, we consider the model class of hybrid automata whose
dynamics are defined by affine differential equations. Given a set of
time-series data, we present an algorithmic approach to synthesize a hybrid
automaton exhibiting behavior that is close to the data, up to a specified
precision, and changes in synchrony with the data. A fundamental problem in our
synthesis algorithm is to check membership of a time series in a hybrid
automaton. Our solution integrates reachability and optimization techniques for
affine dynamical systems to obtain both a sufficient and a necessary condition
for membership, combined in a refinement framework. The algorithm processes one
time series at a time and hence can be interrupted, provide an intermediate
result, and be resumed. We report experimental results demonstrating the
applicability of our synthesis approach.
AU - Garcia Soto, Miriam
AU - Henzinger, Thomas A
AU - Schilling, Christian
ID - 9200
KW - hybrid automaton
KW - membership
KW - system identification
T2 - arXiv
TI - Synthesis of hybrid automata with affine dynamics from time-series data
ER -
TY - GEN
AB - 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.
AU - Browning, Timothy D
AU - Horesh, Tal
AU - Wilsch, Florian Alexander
ID - 9199
T2 - arXiv
TI - Equidistribution and freeness on Grassmannians
ER -
TY - JOUR
AB - Cryo-EM grid preparation is an important bottleneck in protein structure determination, especially for membrane proteins, typically requiring screening of a large number of conditions. We systematically investigated the effects of buffer components, blotting conditions and grid types on the outcome of grid preparation of five different membrane protein samples. Aggregation was the most common type of problem which was addressed by changing detergents, salt concentration or reconstitution of proteins into nanodiscs or amphipols. We show that the optimal concentration of detergent is between 0.05 and 0.4% and that the presence of a low concentration of detergent with a high critical micellar concentration protects the proteins from denaturation at the air-water interface. Furthermore, we discuss the strategies for achieving an adequate ice thickness, particle coverage and orientation distribution on free ice and on support films. Our findings provide a clear roadmap for comprehensive screening of conditions for cryo-EM grid preparation of membrane proteins.
AU - Kampjut, Domen
AU - Steiner, Julia
AU - Sazanov, Leonid A
ID - 9205
IS - 3
JF - iScience
TI - Cryo-EM grid optimization for membrane proteins
VL - 24
ER -
TY - JOUR
AB - The precise engineering of thermoelectric materials using nanocrystals as their building blocks has proven to be an excellent strategy to increase energy conversion efficiency. Here we present a synthetic route to produce Sb-doped PbS colloidal nanoparticles. These nanoparticles are then consolidated into nanocrystalline PbS:Sb using spark plasma sintering. We demonstrate that the introduction of Sb significantly influences the size, geometry, crystal lattice and especially the carrier concentration of PbS. The increase of charge carrier concentration achieved with the introduction of Sb translates into an increase of the electrical and thermal conductivities and a decrease of the Seebeck coefficient. Overall, PbS:Sb nanomaterial were characterized by two-fold higher thermoelectric figures of merit than undoped PbS.
AU - Cadavid, Doris
AU - Wei, Kaya
AU - Liu, Yu
AU - Zhang, Yu
AU - Li, Mengyao
AU - Genç, Aziz
AU - Berestok, Taisiia
AU - Ibáñez, Maria
AU - Shavel, Alexey
AU - Nolas, George S.
AU - Cabot, Andreu
ID - 9206
IS - 4
JF - Materials
TI - Synthesis, bottom up assembly and thermoelectric properties of Sb-doped PbS nanocrystal building blocks
VL - 14
ER -
TY - CONF
AB - We propose a novel hybridization method for stability analysis that over-approximates nonlinear dynamical systems by switched systems with linear inclusion dynamics. We observe that existing hybridization techniques for safety analysis that over-approximate nonlinear dynamical systems by switched affine inclusion dynamics and provide fixed approximation error, do not suffice for stability analysis. Hence, we propose a hybridization method that provides a state-dependent error which converges to zero as the state tends to the equilibrium point. The crux of our hybridization computation is an elegant recursive algorithm that uses partial derivatives of a given function to obtain upper and lower bound matrices for the over-approximating linear inclusion. We illustrate our method on some examples to demonstrate the application of the theory for stability analysis. In particular, our method is able to establish stability of a nonlinear system which does not admit a polynomial Lyapunov function.
AU - Garcia Soto, Miriam
AU - Prabhakar, Pavithra
ID - 9202
T2 - 2020 IEEE Real-Time Systems Symposium
TI - Hybridization for stability verification of nonlinear switched systems
ER -
TY - JOUR
AB - The Landau–Pekar equations describe the dynamics of a strongly coupled polaron.
Here, we provide a class of initial data for which the associated effective Hamiltonian
has a uniform spectral gap for all times. For such initial data, this allows us to extend the
results on the adiabatic theorem for the Landau–Pekar equations and their derivation
from the Fröhlich model obtained in previous works to larger times.
AU - Feliciangeli, Dario
AU - Rademacher, Simone Anna Elvira
AU - Seiringer, Robert
ID - 9225
JF - Letters in Mathematical Physics
SN - 03779017
TI - Persistence of the spectral gap for the Landau–Pekar equations
VL - 111
ER -
TY - JOUR
AB - We re-examine attempts to study the many-body localization transition using measures that are physically natural on the ergodic/quantum chaotic regime of the phase diagram. Using simple scaling arguments and an analysis of various models for which rigorous results are available, we find that these measures can be particularly adversely affected by the strong finite-size effects observed in nearly all numerical studies of many-body localization. This severely impacts their utility in probing the transition and the localized phase. In light of this analysis, we discuss a recent study (Šuntajs et al., 2020) of the behaviour of the Thouless energy and level repulsion in disordered spin chains, and its implications for the question of whether MBL is a true phase of matter.
AU - Abanin, D. A.
AU - Bardarson, J. H.
AU - De Tomasi, G.
AU - Gopalakrishnan, S.
AU - Khemani, V.
AU - Parameswaran, S. A.
AU - Pollmann, F.
AU - Potter, A. C.
AU - Serbyn, Maksym
AU - Vasseur, R.
ID - 9224
JF - Annals of Physics
SN - 00034916
TI - Distinguishing localization from chaos: Challenges in finite-size systems
VL - 427
ER -
TY - GEN
AB - We consider a model of the Riemann zeta function on the critical axis and study its maximum over intervals of length (log T)θ, where θ is either fixed or tends to zero at a suitable rate.
It is shown that the deterministic level of the maximum interpolates smoothly between the ones
of log-correlated variables and of i.i.d. random variables, exhibiting a smooth transition ‘from
3/4 to 1/4’ in the second order. This provides a natural context where extreme value statistics of
log-correlated variables with time-dependent variance and rate occur. A key ingredient of the
proof is a precise upper tail tightness estimate for the maximum of the model on intervals of
size one, that includes a Gaussian correction. This correction is expected to be present for the
Riemann zeta function and pertains to the question of the correct order of the maximum of
the zeta function in large intervals.
AU - Arguin, Louis-Pierre
AU - Dubach, Guillaume
AU - Hartung, Lisa
ID - 9230
T2 - arXiv
TI - Maxima of a random model of the Riemann zeta function over intervals of varying length
ER -
TY - JOUR
AB - Genomic imprinting is an epigenetic mechanism that results in parental allele-specific expression of ~1% of all genes in mouse and human. Imprinted genes are key developmental regulators and play pivotal roles in many biological processes such as nutrient transfer from the mother to offspring and neuronal development. Imprinted genes are also involved in human disease, including neurodevelopmental disorders, and often occur in clusters that are regulated by a common imprint control region (ICR). In extra-embryonic tissues ICRs can act over large distances, with the largest surrounding Igf2r spanning over 10 million base-pairs. Besides classical imprinted expression that shows near exclusive maternal or paternal expression, widespread biased imprinted expression has been identified mainly in brain. In this review we discuss recent developments mapping cell type specific imprinted expression in extra-embryonic tissues and neocortex in the mouse. We highlight the advantages of using an inducible uniparental chromosome disomy (UPD) system to generate cells carrying either two maternal or two paternal copies of a specific chromosome to analyze the functional consequences of genomic imprinting. Mosaic Analysis with Double Markers (MADM) allows fluorescent labeling and concomitant induction of UPD sparsely in specific cell types, and thus to over-express or suppress all imprinted genes on that chromosome. To illustrate the utility of this technique, we explain how MADM-induced UPD revealed new insights about the function of the well-studied Cdkn1c imprinted gene, and how MADM-induced UPDs led to identification of highly cell type specific phenotypes related to perturbed imprinted expression in the mouse neocortex. Finally, we give an outlook on how MADM could be used to probe cell type specific imprinted expression in other tissues in mouse, particularly in extra-embryonic tissues.
AU - Pauler, Florian
AU - Hudson, Quanah
AU - Laukoter, Susanne
AU - Hippenmeyer, Simon
ID - 9188
IS - 5
JF - Neurochemistry International
KW - Cell Biology
KW - Cellular and Molecular Neuroscience
SN - 0197-0186
TI - Inducible uniparental chromosome disomy to probe genomic imprinting at single-cell level in brain and beyond
VL - 145
ER -