@inproceedings{17144,
  abstract     = {We prove that the medial axis of closed sets is Hausdorff stable in the following sense: Let 𝒮 ⊆ ℝ^d be a fixed closed set that contains a bounding sphere. That is, the bounding sphere is part of the set 𝒮. Consider the space of C^{1,1} diffeomorphisms of ℝ^d to itself, which keep the bounding sphere invariant. The map from this space of diffeomorphisms (endowed with a Banach norm) to the space of closed subsets of ℝ^d (endowed with the Hausdorff distance), mapping a diffeomorphism F to the closure of the medial axis of F(𝒮), is Lipschitz. This extends a previous stability result of Chazal and Soufflet on the stability of the medial axis of C² manifolds under C² ambient diffeomorphisms.},
  author       = {Kourimska, Hana and Lieutier, André and Wintraecken, Mathijs},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{The medial axis of any closed bounded set Is Lipschitz stable with respect to the Hausdorff distance Under ambient diffeomorphisms}},
  doi          = {10.4230/LIPIcs.SoCG.2024.69},
  volume       = {293},
  year         = {2024},
}

@inproceedings{17145,
  abstract     = {Grid peeling is the process of repeatedly removing the convex hull vertices of the grid points that lie inside a given convex curve. It has been conjectured that, for a more and more refined grid, grid peeling converges to a continuous process, the affine curve-shortening flow, which deforms the curve based on the curvature. We prove this conjecture for one class of curves, parabolas with a vertical axis, and we determine the value of the constant factor in the formula that relates the two processes.},
  author       = {Rote, Günter and Rüber, Moritz and Saghafian, Morteza},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Grid peeling of parabolas}},
  doi          = {10.4230/LIPIcs.SoCG.2024.76},
  volume       = {293},
  year         = {2024},
}

@article{17154,
  abstract     = {We compute the deterministic approximation for mixed fluctuation moments of products of deterministic matrices and general Sobolev functions of Wigner matrices. Restricting to polynomials, our formulas reproduce recent results of Male et al. (Random Matrices Theory Appl. 11(2):2250015, 2022), showing that the underlying combinatorics of non-crossing partitions and annular non-crossing permutations continue to stay valid beyond the setting of second-order free probability theory. The formulas obtained further characterize the variance in the functional central limit theorem given in the recent companion paper (Reker in Preprint, arXiv:2204.03419, 2023). and thus allow identifying the fluctuation around the thermal value in certain thermalization problems.},
  author       = {Reker, Jana},
  issn         = {1572-9656},
  journal      = {Mathematical Physics, Analysis and Geometry},
  number       = {3},
  publisher    = {Springer Nature},
  title        = {{Fluctuation moments for regular functions of Wigner Matrices}},
  doi          = {10.1007/s11040-024-09483-y},
  volume       = {27},
  year         = {2024},
}

@phdthesis{17156,
  abstract     = {This dissertation is the summary of the author’s work, concerning the relations between
cohomology rings of algebraic varieties and rings of functions on zero schemes and fixed
point schemes. For most of the thesis, the focus is on smooth complex varieties with
an action of a principally paired group, e.g. a parabolic subgroup of a reductive group.
The fundamental theorem 5.2.11 from co-authored article [66] says that if the principal
nilpotent has a unique zero, then the zero scheme over the Kostant section is isomorphic
to the spectrum of the equivariant cohomology ring, remembering the grading in terms of
a C^* action. A similar statement is proved also for the G-invariant functions on the total
zero scheme over the whole Lie algebra. Additionally, we are able to prove an analogous
result for the GKM spaces, which poses the question on a joint generalisation.
We also tackle the situation of a singular variety. As long as it is embedded in a smooth
variety with regular action, we are able to study its cohomology as well by means of
the zero scheme. In case of e.g. Schubert varieties this determines the cohomology ring
completely. In largest generality, this allows us to see a significant part of the cohomology
ring.
We also show (Theorem 6.2.1) that the cohomology ring of spherical varieties appears as
the ring of functions on the zero scheme. The computational aspect is not easy, but one
can hope that this can bring some concrete information about such cohomology rings.
Lastly, the K-theory conjecture 6.3.1 is studied, with some results attained for GKM
spaces.
The thesis includes also an introduction to group actions on algebraic varieties. In
particular, the vector fields associated to the actions are extensively studied. We also
provide a version of the Kostant section for arbitrary principally paired group, which
parametrises the regular orbits in the Lie algebra of an algebraic group. Before proving
the main theorem, we also include a historical overview of the field. In particular we bring
together the results of Akyildiz, Carrell and Lieberman on non-equivariant cohomology
rings.},
  author       = {Rychlewicz, Kamil P},
  issn         = {2663-337X},
  keywords     = {equivariant cohomology, zero schemes, algebraic groups, Lie algebras},
  pages        = {117},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Equivariant cohomology and rings of functions}},
  doi          = {10.15479/at:ista:17156},
  year         = {2024},
}

@article{17162,
  abstract     = {Cost analysis, also known as resource usage analysis, is the task of finding bounds on the total cost of a program and is a well-studied problem in static analysis. In this work, we consider two classical quantitative problems in cost analysis for probabilistic programs. The first problem is to find a bound on the expected total cost of the program. This is a natural measure for the resource usage of the program and can also be directly applied to average-case runtime analysis. The second problem asks for a tail bound, i.e. ‍given a threshold t the goal is to find a probability bound p such that ℙ[total cost ≥ t] ≤ p. Intuitively, given a threshold t on the resource, the problem is to find the likelihood that the total cost exceeds this threshold.
First, for expectation bounds, a major obstacle in previous works on cost analysis is that they can handle only non-negative costs or bounded variable updates. In contrast, we provide a new variant of the standard notion of cost martingales, that allows us to find expectation bounds for a class of programs with general positive or negative costs and no restriction on the variable updates. More specifically, our approach is applicable as long as there is a lower bound on the total cost incurred along every path.
Second, for tail bounds, all previous methods are limited to programs in which the expected total cost is finite. In contrast, we present a novel approach, based on a combination of our martingale-based method for expectation bounds with a quantitative safety analysis, to obtain a solution to the tail bound problem that is applicable even to programs with infinite expected cost. Specifically, this allows us to obtain runtime tail bounds for programs that do not terminate almost-surely.
In summary, we provide a novel combination of martingale-based cost analysis and quantitative safety analysis that is able to find expectation and tail cost bounds for probabilistic programs, without the restrictions of non-negative costs, bounded updates, or finiteness of the expected total cost. Finally, we provide experimental results showcasing that our approach can solve instances that were beyond the reach of previous methods.},
  author       = {Chatterjee, Krishnendu and Goharshady, Amir Kafshdar and Meggendorfer, Tobias and Zikelic, Dorde},
  issn         = {2475-1421},
  journal      = {Proceedings of the ACM on Programming Languages},
  number       = {OOPSLA1},
  publisher    = {Association for Computing Machinery},
  title        = {{Quantitative bounds on resource usage of probabilistic programs}},
  doi          = {10.1145/3649824},
  volume       = {8},
  year         = {2024},
}

@phdthesis{17164,
  abstract     = {This thesis is structured into two parts. In the first part, we consider the random
variable X := Tr(f1(W)A1 . . . fk(W)Ak) where W is an N × N Hermitian Wigner matrix, k ∈ N, and we choose (possibly N-dependent) regular functions f1, . . . , fk as well as
bounded deterministic matrices A1, . . . , Ak. In this context, we prove a functional central
limit theorem on macroscopic and mesoscopic scales, showing that the fluctuations of X
around its expectation are Gaussian and that the limiting covariance structure is given
by a deterministic recursion. We further give explicit error bounds in terms of the scaling
of f1, . . . , fk and the number of traceless matrices among A1, . . . , Ak, thus extending
the results of Cipolloni, Erdős and Schröder [40] to products of arbitrary length k ≥ 2.
Analyzing the underlying combinatorics leads to a non-recursive formula for the variance
of X as well as the covariance of X and Y := Tr(fk+1(W)Ak+1 . . . fk+ℓ(W)Ak+ℓ) of similar
build. When restricted to polynomials, these formulas reproduce recent results of Male,
Mingo, Peché, and Speicher [107], showing that the underlying combinatorics of noncrossing partitions and annular non-crossing permutations continue to stay valid beyond
the setting of second-order free probability theory. As an application, we consider the
fluctuation of Tr(eitW A1e
−itW A2)/N around its thermal value Tr(A1) Tr(A2)/N2 when t
is large and give an explicit formula for the variance.
The second part of the thesis collects three smaller projects focusing on different random
matrix models. In the first project, we show that a class of weakly perturbed Hamiltonians
of the form Hλ = H0 + λW, where W is a Wigner matrix, exhibits prethermalization.
That is, the time evolution generated by Hλ relaxes to its ultimate thermal state via an
intermediate prethermal state with a lifetime of order λ
−2
. As the main result, we obtain
a general relaxation formula, expressing the perturbed dynamics via the unperturbed
dynamics and the ultimate thermal state. The proof relies on a two-resolvent global law
for the deformed Wigner matrix Hλ.
The second project focuses on correlated random matrices, more precisely on a correlated N × N Hermitian random matrix with a polynomially decaying metric correlation
structure. A trivial a priori bound shows that the operator norm of this model is stochastically dominated by √
N. However, by calculating the trace of the moments of the matrix
and using the summable decay of the cumulants, the norm estimate can be improved to a
bound of order one.
In the third project, we consider a multiplicative perturbation of the form UA(t) where U
is a unitary random matrix and A = diag(t, 1, ..., 1). This so-called UA model was
first introduced by Fyodorov [73] for its applications in scattering theory. We give a
general description of the eigenvalue trajectories obtained by varying the parameter t and
introduce a flow of deterministic domains that separates the outlier resulting from the
rank-one perturbation from the typical eigenvalues for all sub-critical timescales. The
results are obtained under generic assumptions on U that hold for various unitary random
matrices, including the circular unitary ensemble (CUE) in the original formulation of
the model.},
  author       = {Reker, Jana},
  issn         = {2663-337X},
  keywords     = {Random Matrices, Spectrum, Central Limit Theorem, Resolvent, Free Probability},
  pages        = {206},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{Central limit theorems for random matrices: From resolvents to free probability}},
  doi          = {10.15479/at:ista:17164},
  year         = {2024},
}

@inproceedings{17170,
  abstract     = {In this article we extend and strengthen the seminal work by Niyogi, Smale, and Weinberger on the learning of the homotopy type from a sample of an underlying space. In their work, Niyogi, Smale, and Weinberger studied samples of C² manifolds with positive reach embedded in ℝ^d. We extend their results in the following ways: - As the ambient space we consider both ℝ^d and Riemannian manifolds with lower bounded sectional curvature. - In both types of ambient spaces, we study sets of positive reach - a significantly more general setting than C² manifolds - as well as general manifolds of positive reach. - The sample P of a set (or a manifold) 𝒮 of positive reach may be noisy. We work with two one-sided Hausdorff distances - ε and δ - between P and 𝒮. We provide tight bounds in terms of ε and δ, that guarantee that there exists a parameter r such that the union of balls of radius r centred at the sample P deformation-retracts to 𝒮. We exhibit their tightness by an explicit construction. We carefully distinguish the roles of δ and ε. This is not only essential to achieve tight bounds, but also sensible in practical situations, since it allows one to adapt the bound according to sample density and the amount of noise present in the sample separately.},
  author       = {Attali, Dominique and Kourimska, Hana and Fillmore, Christopher D and Ghosh, Ishika and Lieutier, André and Stephenson, Elizabeth R and Wintraecken, Mathijs},
  booktitle    = {40th International Symposium on Computational Geometry},
  isbn         = {9783959773164},
  issn         = {1868-8969},
  location     = {Athens, Greece},
  pages        = {11:1--11:19},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Tight bounds for the learning of homotopy à la Niyogi, Smale, and Weinberger for subsets of euclidean spaces and of Riemannian manifolds}},
  doi          = {10.4230/LIPIcs.SoCG.2024.11},
  volume       = {293},
  year         = {2024},
}

@article{17187,
  abstract     = {The generation of diverse cell types during development is fundamental to brain
functions. We outline a protocol to quantitatively assess the clonal output of individual neural progenitors using mosaic analysis with double markers (MADM) in
mice. We first describe steps to acquire and reconstruct adult MADM clones in
the superior colliculus. Then we detail analysis pipelines to determine clonal
composition and architecture. This protocol enables the buildup of quantitative
frameworks of lineage progression with precise spatial resolution in the brain.
For complete details on the use and execution of this protocol, please refer to
Cheung et al.1},
  author       = {Cheung, Giselle T and Streicher, Carmen and Hippenmeyer, Simon},
  issn         = {2666-1667},
  journal      = {STAR Protocols},
  number       = {3},
  publisher    = {Elsevier},
  title        = {{Protocol for quantitative reconstruction of cell lineage using mosaic analysis with double markers in mice}},
  doi          = {10.1016/j.xpro.2024.103157},
  volume       = {5},
  year         = {2024},
}

@article{17188,
  abstract     = {In a delegation problem, a principal P with commitment power tries to pick one out of 𝑛 options.
Each option is drawn independently from a known distribution. Instead of inspecting the options
herself, P delegates the information acquisition to a rational and self-interested agent A. After
inspection, A proposes one of the options, and P can accept or reject.
Delegation is a classic setting in economic information design with many prominent applications,
but the computational problems are only poorly understood. In this paper, we study a natural
online variant of delegation, in which the agent searches through the options in an online fashion.
For each option, he has to irrevocably decide if he wants to propose the current option or discard
it, before seeing information on the next option(s). How can we design algorithms for P that
approximate the utility of her best option in hindsight?
We show that in general P can obtain a Θ(1∕𝑛)-approximation and extend this result to ratios
of Θ(𝑘∕𝑛) in case (1) A has a lookahead of 𝑘 rounds, or (2) A can propose up to 𝑘 different
options. We provide fine-grained bounds independent of 𝑛 based on three parameters. If the ratio
of maximum and minimum utility for A is bounded by a factor 𝛼, we obtain an Ω(loglog 𝛼∕ log 𝛼)-
approximation algorithm, and we show that this is best possible. Additionally, if P cannot
distinguish options with the same value for herself, we show that ratios polynomial in 1∕𝛼 cannot
be avoided. If there are at most 𝛽 different utility values for A, we show a Θ(1∕𝛽)-approximation.
If the utilities of P and A for each option are related by a factor 𝛾, we obtain an Ω(1∕ log 𝛾)-
approximation, where 𝑂(log log 𝛾∕ log 𝛾) is best possible.},
  author       = {Braun, Pirmin and Hahn, Niklas and Hoefer, Martin and Schecker, Conrad},
  issn         = {0004-3702},
  journal      = {Artificial Intelligence},
  publisher    = {Elsevier},
  title        = {{Delegated online search}},
  doi          = {10.1016/j.artint.2024.104171},
  volume       = {334},
  year         = {2024},
}

@article{17189,
  abstract     = {Supergranules, which are solar flow features with a lateral scale of 30,000–40,000 km and a lifetime of ~24 h, form a prominent component of the Sun’s convective spectrum. However, their internal flows, which can be probed only by helioseismology, are not well understood. We analyse dopplergrams recorded by the Solar Dynamics Observatory satellite to identify and characterize ~23,000 supergranules. We find that the vertical flows peak at a depth of ~10,000 km, and remain invariant over the full range of lateral supergranular scales, contrary to numerical predictions. We also infer that, within the local seismic resolution (≳5,000 km), downflows are ~40% weaker than upflows, indicating an apparent mass-flux imbalance. This may imply that the descending flows also comprise plumes, which maintain the mass balance but are simply too small to be detected by seismic waves. These results challenge the widely used mixing-length description of solar convection.},
  author       = {Hanson, Chris S. and Das, Srijan B and Mani, Prasad and Hanasoge, Shravan and Sreenivasan, Katepalli R.},
  issn         = {2397-3366},
  journal      = {Nature Astronomy},
  pages        = {1088--1101},
  publisher    = {Springer Nature},
  title        = {{Supergranular-scale solar convection not explained by mixing-length theory}},
  doi          = {10.1038/s41550-024-02304-w},
  volume       = {8},
  year         = {2024},
}

@article{17190,
  abstract     = {For a locally finite set, 𝐴⊆ℝ𝑑
, the 𝑘
th Brillouin zone of 𝑎∈𝐴
 is the region of points 𝑥∈ℝ𝑑
 for which ‖𝑥−𝑎‖
 is the 𝑘
th smallest among the Euclidean distances between 𝑥
 and the points in 𝐴
. If 𝐴
 is a lattice, the 𝑘
th Brillouin zones of the points in 𝐴
 are translates of each other, and together they tile space. Depending on the value of 𝑘
, they express medium- or long-range order in the set. We study fundamental geometric and combinatorial properties of Brillouin zones, focusing on the integer lattice and its perturbations. Our results include the stability of a Brillouin zone under perturbations, a linear upper bound on the number of chambers in a zone for lattices in ℝ2
, and the convergence of the maximum volume of a chamber to zero for the integer lattice.},
  author       = {Edelsbrunner, Herbert and Garber, Alexey and Ghafaris, Mohadese and Heiss, Teresa and Saghafiant, Morteza and Wintraecken, Mathijs},
  issn         = {0895-4801},
  journal      = {SIAM Journal on Discrete Mathematics},
  number       = {2},
  pages        = {1784--1807},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Brillouin zones of integer lattices and their perturbations}},
  doi          = {10.1137/22M1489071},
  volume       = {38},
  year         = {2024},
}

@article{17191,
  abstract     = {Dendritic cells migrate to and from lymph nodes in response to chemokine gradients.Data now show that steady-state migration of these cells can be triggered by a mechanosensitive pathway.},
  author       = {Lembo, Sergio and Sixt, Michael K},
  issn         = {1529-2916},
  journal      = {Nature Immunology},
  pages        = {1131–1132 },
  publisher    = {Springer Nature},
  title        = {{Nuclear squeezing wakes up dendritic cells}},
  doi          = {10.1038/s41590-024-01881-2},
  volume       = {25},
  year         = {2024},
}

@misc{17196,
  abstract     = {This .zip File contains the data for the figures presented in the main text and supplementary material of "A gate tunable transmon qubit in planar Ge" by O.Sagi et al. The measurements were done using Qcodes. The description of the files and the instructions on opening the data can be found in the Readme. An additional Jupyter Notebook is attached that walks through the data analysis.},
  author       = {Sagi, Oliver},
  publisher    = {Institute of Science and Technology Austria},
  title        = {{A gate-tunable transmon in planar Ge}},
  doi          = {10.15479/AT:ISTA:17196},
  year         = {2024},
}

@article{18444,
  abstract     = {Animals rely on compensatory actions to maintain stability and navigate their environment efficiently. These actions depend on global visual motion cues known as optic-flow. While the optomotor response has been the traditional focus for studying optic-flow compensation in insects, its simplicity has been insufficient to determine the role of the intricate optic-flow processing network involved in visual course control. Here, we reveal a series of course control behaviours in Drosophila and link them to specific neural circuits. We show that bilateral electrical coupling of optic-flow-sensitive neurons in the fly’s lobula plate are required for a proper course control. This electrical interaction works alongside chemical synapses within the HS-H2 network to control the dynamics and direction of turning behaviours. Our findings reveal how insects use bilateral motion cues for navigation, assigning a new functional significance to the HS-H2 network and suggesting a previously unknown role for gap junctions in non-linear operations.},
  author       = {Pokusaeva, Victoria and Satapathy, Roshan K and Symonova, Olga and Jösch, Maximilian A},
  issn         = {2041-1723},
  journal      = {Nature Communications},
  publisher    = {Springer Nature},
  title        = {{Bilateral interactions of optic-flow sensitive neurons coordinate course control in flies}},
  doi          = {10.1038/s41467-024-53173-w},
  volume       = {15},
  year         = {2024},
}

@article{18446,
  abstract     = {How living systems achieve precision in form and function despite their intrinsic stochasticity is a fundamental yet ongoing question in biology. We generated morphomaps of preimplantation embryogenesis in mouse, rabbit, and monkey embryos, and these morphomaps revealed that although blastomere divisions desynchronized passively, 8-cell embryos converged toward robust three-dimensional shapes. Using topological analysis and genetic perturbations, we found that embryos progressively changed their cellular connectivity to a preferred topology, which could be predicted by a physical model in which actomyosin contractility and noise facilitate topological transitions, lowering surface energy. This mechanism favored regular embryo packing and promoted a higher number of inner cells in the 16-cell embryo. Synchronized division reduced embryo packing and generated substantially more misallocated cells and fewer inner-cell–mass cells. These findings suggest that stochasticity in division timing contributes to robust patterning.},
  author       = {Fabrèges, Dimitri and Corominas-Murtra, Bernat and Moghe, Prachiti and Kickuth, Alison and Ichikawa, Takafumi and Iwatani, Chizuru and Tsukiyama, Tomoyuki and Daniel, Nathalie and Gering, Julie and Stokkermans, Anniek and Wolny, Adrian and Kreshuk, Anna and Duranthon, Véronique and Uhlman, Virginie and Hannezo, Edouard B and Hiiragi, Takashi},
  issn         = {1095-9203},
  journal      = {Science},
  number       = {6718},
  publisher    = {AAAS},
  title        = {{Temporal variability and cell mechanics control robustness in mammalian embryogenesis}},
  doi          = {10.1126/science.adh1145},
  volume       = {386},
  year         = {2024},
}

@article{18451,
  abstract     = {Inorganic nanoparticles can be assembled into superlattices with unique optical and magnetic properties arising from collective behavior. Protein cages can be utilized to guide this assembly by encapsulating nanoparticles and promoting their assembly into ordered structures. However, creating ordered multi-component structures with different protein cage types and sizes remains a challenge. Here, the co-crystallization of two different protein cages (cowpea chlorotic mottle virus and ferritin) characterized by opposing surface charges and unequal diameter is shown. Precise tuning of the electrostatic attraction between the cages enabled the preparation of binary crystals with dimensions up to several tens of micrometers. Additionally, binary metal nanoparticle superlattices are achieved by loading gold and iron oxide nanoparticles inside the cavities of the protein cages. The resulting structure adopts an AB2FCC configuration that also impacts the dipolar coupling between the particles and hence the optical properties of the crystals, providing key insight for the future preparation of plasmonic and magnetic nanoparticle metamaterials.},
  author       = {Zhou, Yu and Shaukat, Ahmed and Seitsonen, Jani and Rigoni, Carlo and Timonen, Jaakko V.I. and Kostiainen, Mauri A.},
  issn         = {2198-3844},
  journal      = {Advanced Science},
  number       = {45},
  publisher    = {Wiley},
  title        = {{Protein cage directed assembly of binary nanoparticle superlattices}},
  doi          = {10.1002/advs.202408416},
  volume       = {11},
  year         = {2024},
}

@article{18465,
  abstract     = {The phytohormone auxin is polarly transported in plants by PIN-FORMED (PIN) transporters and controls virtually all growth and developmental processes. Canonical PINs possess a long, largely disordered cytosolic loop. Auxin transport by canonical PINs is activated by loop phosphorylation by certain kinases. The structure of the PIN transmembrane domains was recently determined, their transport properties remained poorly characterized, and the role of the loop in the transport process was unclear. Here, we determined the quantitative kinetic parameters of auxin transport mediated by Arabidopsis PINs to mathematically model auxin distribution in roots and to test these predictions in vivo. Using chimeras between transmembrane and loop domains of different PINs, we demonstrate a strong correlation between transport parameters and physiological output, indicating that the loop domain is not only required to activate PIN-mediated auxin transport, but it has an additional role in the transport process by a currently unknown mechanism.},
  author       = {Janacek, DP and Kolb, M and Schulz, L and Mergner, J and Kuster, B and Glanc, Matous and Friml, Jiří and Ten Tusscher, K and Schwechheimer, C and Hammes, UZ},
  issn         = {1878-1551},
  journal      = {Developmental Cell},
  number       = {14},
  pages        = {S1534--5807(24)00569--0},
  publisher    = {Elsevier},
  title        = {{Transport properties of canonical PIN-FORMED proteins from Arabidopsis and the role of the loop domain in auxin transport}},
  doi          = {10.1016/j.devcel.2024.09.020},
  volume       = {59},
  year         = {2024},
}

@article{18482,
  abstract     = {This paper is dedicated to an optimization problem. Let A, B ⊂ Rn be compact convex sets. Consider the minimal number t0 > 0 such that t0B covers A after a shift to a vector x0 ∈ 
Rn. The goal is to find t0 and x0. In the special case of B being a unit ball centered at zero, x0 and t0 are known as the Chebyshev center and the Chebyshev radius of A. This paper focuses on the case in which A and B are defined with their black-box support functions. An algorithm for solving such problems efficiently is suggested. The algorithm has a superlinear convergence rate, and it can solve hundred-dimensional test problems in a reasonable time, but some additional conditions on A and B are required to guarantee the presence of convergence. Additionally, the behavior of the algorithm for a simple special case is investigated, which leads to a number of theoretical results. Perturbations of this special case are also studied.},
  author       = {Arkhipov, Pavel},
  issn         = {1608-3032},
  journal      = {Automation and Remote Control},
  number       = {6},
  pages        = {522--532},
  publisher    = {Springer Nature},
  title        = {{An algorithm for finding the generalized Chebyshev center of sets defined via their support functions}},
  doi          = {10.1134/S0005117924060031},
  volume       = {85},
  year         = {2024},
}

@article{18483,
  abstract     = {In this paper we prove a perturbative version of a remarkable Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) result. They prove non perturbative Birkhoff conjecture for centrally-symmetric convex domains, namely, a centrally-symmetric convex domain with integrable billiard is ellipse. We combine techniques from Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) with a local result by Kaloshin–Sorrentino (Ann. Math. 188(1):315–380, 2018) and show that a domain close enough to a centrally symmetric one with integrable billiard is ellipse. To combine these results we derive a slight extension of Bialy–Mironov (Ann. Math. 196(1):389–413, 2022) by proving that a notion of rational integrability is equivalent to the C0-integrability condition used in their paper.},
  author       = {Kaloshin, Vadim and Koudjinan, Edmond and Zhang, Ke},
  issn         = {1420-8970},
  journal      = {Geometric and Functional Analysis},
  pages        = {1973--2007},
  publisher    = {Springer Nature},
  title        = {{Birkhoff conjecture for nearly centrally symmetric domains}},
  doi          = {10.1007/s00039-024-00695-6},
  volume       = {34},
  year         = {2024},
}

@article{18488,
  abstract     = {The advancement of quantum simulators motivates the development of a theoretical framework to assist with efficient state preparation in quantum many-body systems. Generally, preparing a target entangled state via unitary evolution with time-dependent couplings is a challenging task and very little is known about the existence of solutions and their properties. In this work we develop a constructive approach for preparing matrix product states (MPS) via continuous unitary evolution. We provide an explicit construction of the operator that exactly implements the evolution of a given MPS along a specified direction in its tangent space. This operator can be written as a sum of local terms of finite range, yet it is in general non-Hermitian. Relying on the explicit construction of the non-Hermitian generator of the dynamics, we demonstrate the existence of a Hermitian sequence of operators that implements the desired MPS evolution with an error that decreases exponentially with the operator range. The construction is benchmarked on an explicit periodic trajectory in a translationally invariant MPS manifold. We demonstrate that the Floquet unitary generating the dynamics over one period of the trajectory features an approximate MPS-like eigenstate embedded among a sea of thermalizing eigenstates. These results show that our construction is not only useful for state preparation and control of many-body systems, but also provides a generic route towards Floquet scars—periodically driven models with quasilocal generators of dynamics that have exact MPS eigenstates in their spectrum.},
  author       = {Ljubotina, Marko and Petrova, Elena and Schuch, Norbert and Serbyn, Maksym},
  issn         = {2691-3399},
  journal      = {PRX Quantum},
  number       = {4},
  publisher    = {American Physical Society},
  title        = {{Tangent space generators of matrix product states and exact floquet quantum scars}},
  doi          = {10.1103/prxquantum.5.040311},
  volume       = {5},
  year         = {2024},
}