TY - CONF
AB - In runtime verification, a monitor watches a trace of a system and, if possible, decides after observing each finite prefix whether or not the unknown infinite trace satisfies a given specification. We generalize the theory of runtime verification to monitors that attempt to estimate numerical values of quantitative trace properties (instead of attempting to conclude boolean values of trace specifications), such as maximal or average response time along a trace. Quantitative monitors are approximate: with every finite prefix, they can improve their estimate of the infinite trace's unknown property value. Consequently, quantitative monitors can be compared with regard to a precision-cost trade-off: better approximations of the property value require more monitor resources, such as states (in the case of finite-state monitors) or registers, and additional resources yield better approximations. We introduce a formal framework for quantitative and approximate monitoring, show how it conservatively generalizes the classical boolean setting for monitoring, and give several precision-cost trade-offs for monitors. For example, we prove that there are quantitative properties for which every additional register improves monitoring precision.
AU - Henzinger, Thomas A
AU - Sarac, Naci E
ID - 9356
T2 - Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science
TI - Quantitative and approximate monitoring
ER -
TY - JOUR
AB - Spin qubits are considered to be among the most promising candidates for building a quantum processor. Group IV hole spin qubits have moved into the focus of interest due to the ease of operation and compatibility with Si technology. In addition, Ge offers the option for monolithic superconductor-semiconductor integration. Here we demonstrate a hole spin qubit operating at fields below 10 mT, the critical field of Al, by exploiting the large out-of-plane hole g-factors in planar Ge and by encoding the qubit into the singlet-triplet states of a double quantum dot. We observe electrically controlled X and Z-rotations with tunable frequencies exceeding 100 MHz and dephasing times of 1μs which we extend beyond 15μs with echo techniques. These results show that Ge hole singlet triplet qubits outperform their electronic Si and GaAs based counterparts in speed and coherence, respectively. In addition, they are on par with Ge single spin qubits, but can be operated at much lower fields underlining their potential for on chip integration with superconducting technologies.
AU - Jirovec, Daniel
AU - Hofmann, Andrea C
AU - Ballabio, Andrea
AU - Mutter, Philipp M.
AU - Tavani, Giulio
AU - Botifoll, Marc
AU - Crippa, Alessandro
AU - Kukucka, Josip
AU - Sagi, Oliver
AU - Martins, Frederico
AU - Saez Mollejo, Jaime
AU - Prieto Gonzalez, Ivan
AU - Borovkov, Maksim
AU - Arbiol, Jordi
AU - Chrastina, Daniel
AU - Isella, Giovanni
AU - Katsaros, Georgios
ID - 8909
JF - Nature Materials
SN - 1476-1122
TI - A singlet triplet hole spin qubit in planar Ge
ER -
TY - DATA
AB - This .zip File contains the data for figures presented in the main text and supplementary material of "A singlet triplet hole spin qubit in planar Ge" by D. Jirovec, et. al. The measurements were done using Labber Software and the data is stored in the hdf5 file format. The files can be opened using either the Labber Log Browser (https://labber.org/overview/) or Labber Python API (http://labber.org/online-doc/api/LogFile.html). A single file is acquired with QCodes and features the corresponding data type. XRD data are in .dat format and a code to open the data is provided. The code for simulations is as well provided in Python.
AU - Jirovec, Daniel
ID - 9323
TI - Research data for "A singlet-triplet hole spin qubit planar Ge"
ER -
TY - THES
AB - Deep learning is best known for its empirical success across a wide range of applications
spanning computer vision, natural language processing and speech. Of equal significance,
though perhaps less known, are its ramifications for learning theory: deep networks have
been observed to perform surprisingly well in the high-capacity regime, aka the overfitting
or underspecified regime. Classically, this regime on the far right of the bias-variance curve
is associated with poor generalisation; however, recent experiments with deep networks
challenge this view.
This thesis is devoted to investigating various aspects of underspecification in deep learning.
First, we argue that deep learning models are underspecified on two levels: a) any given
training dataset can be fit by many different functions, and b) any given function can be
expressed by many different parameter configurations. We refer to the second kind of
underspecification as parameterisation redundancy and we precisely characterise its extent.
Second, we characterise the implicit criteria (the inductive bias) that guide learning in the
underspecified regime. Specifically, we consider a nonlinear but tractable classification
setting, and show that given the choice, neural networks learn classifiers with a large margin.
Third, we consider learning scenarios where the inductive bias is not by itself sufficient to
deal with underspecification. We then study different ways of ‘tightening the specification’: i)
In the setting of representation learning with variational autoencoders, we propose a hand-
crafted regulariser based on mutual information. ii) In the setting of binary classification, we
consider soft-label (real-valued) supervision. We derive a generalisation bound for linear
networks supervised in this way and verify that soft labels facilitate fast learning. Finally, we
explore an application of soft-label supervision to the training of multi-exit models.
AU - Bui Thi Mai, Phuong
ID - 9418
TI - Underspecification in Deep Learning
ER -
TY - JOUR
AB - Given a locally finite set 𝑋⊆ℝ𝑑 and an integer 𝑘≥0, we consider the function 𝐰𝑘:Del𝑘(𝑋)→ℝ on the dual of the order-k Voronoi tessellation, whose sublevel sets generalize the notion of alpha shapes from order-1 to order-k (Edelsbrunner et al. in IEEE Trans Inf Theory IT-29:551–559, 1983; Krasnoshchekov and Polishchuk in Inf Process Lett 114:76–83, 2014). While this function is not necessarily generalized discrete Morse, in the sense of Forman (Adv Math 134:90–145, 1998) and Freij (Discrete Math 309:3821–3829, 2009), we prove that it satisfies similar properties so that its increments can be meaningfully classified into critical and non-critical steps. This result extends to the case of weighted points and sheds light on k-fold covers with balls in Euclidean space.
AU - Edelsbrunner, Herbert
AU - Nikitenko, Anton
AU - Osang, Georg F
ID - 9465
IS - 1
JF - Journal of Geometry
SN - 00472468
TI - A step in the Delaunay mosaic of order k
VL - 112
ER -
TY - JOUR
AB - A key step in understanding the genetic basis of different evolutionary outcomes (e.g., adaptation) is to determine the roles played by different mutation types (e.g., SNPs, translocations and inversions). To do this we must simultaneously consider different mutation types in an evolutionary framework. Here, we propose a research framework that directly utilizes the most important characteristics of mutations, their population genetic effects, to determine their relative evolutionary significance in a given scenario. We review known population genetic effects of different mutation types and show how these may be connected to different evolutionary outcomes. We provide examples of how to implement this framework and pinpoint areas where more data, theory and synthesis are needed. Linking experimental and theoretical approaches to examine different mutation types simultaneously is a critical step towards understanding their evolutionary significance.
AU - Berdan, Emma L.
AU - Blanckaert, Alexandre
AU - Slotte, Tanja
AU - Suh, Alexander
AU - Westram, Anja M
AU - Fragata, Inês
ID - 9470
IS - 12
JF - Molecular Ecology
SN - 09621083
TI - Unboxing mutations: Connecting mutation types with evolutionary consequences
VL - 30
ER -
TY - JOUR
AB - Turbulence in the flow of fluid through a pipe can be suppressed by buoyancy forces. As the suppression of turbulence leads to severe heat transfer deterioration, this is an important and undesirable phenomenon in both heating and cooling applications. Vertical flow is often considered, as the axial buoyancy force can help drive the flow. With heating measured by the buoyancy parameter 𝐶, our direct numerical simulations show that shear-driven turbulence may either be completely laminarised or it transitions to a relatively quiescent convection-driven state. Buoyancy forces cause a flattening of the base flow profile, which in isothermal pipe flow has recently been linked to complete suppression of turbulence (Kühnen et al., Nat. Phys., vol. 14, 2018, pp. 386–390), and the flattened laminar base profile has enhanced nonlinear stability (Marensi et al., J. Fluid Mech., vol. 863, 2019, pp. 50–875). In agreement with these findings, the nonlinear lower-branch travelling-wave solution analysed here, which is believed to mediate transition to turbulence in isothermal pipe flow, is shown to be suppressed by buoyancy. A linear instability of the laminar base flow is responsible for the appearance of the relatively quiescent convection driven state for 𝐶≳4 across the range of Reynolds numbers considered. In the suppression of turbulence, however, i.e. in the transition from turbulence, we find clearer association with the analysis of He et al. (J. Fluid Mech., vol. 809, 2016, pp. 31–71) than with the above dynamical systems approach, which describes better the transition to turbulence. The laminarisation criterion He et al. propose, based on an apparent Reynolds number of the flow as measured by its driving pressure gradient, is found to capture the critical 𝐶=𝐶𝑐𝑟(𝑅𝑒) above which the flow will be laminarised or switch to the convection-driven type. Our analysis suggests that it is the weakened rolls, rather than the streaks, which appear to be critical for laminarisation.
AU - Marensi, Elena
AU - He, Shuisheng
AU - Willis, Ashley P.
ID - 9467
JF - Journal of Fluid Mechanics
SN - 00221120
TI - Suppression of turbulence and travelling waves in a vertical heated pipe
VL - 919
ER -
TY - JOUR
AB - Motivated by the successful application of geometry to proving the Harary--Hill conjecture for “pseudolinear” drawings of $K_n$, we introduce “pseudospherical” drawings of graphs. A spherical drawing of a graph $G$ is a drawing in the unit sphere $\mathbb{S}^2$ in which the vertices of $G$ are represented as points---no three on a great circle---and the edges of $G$ are shortest-arcs in $\mathbb{S}^2$ connecting pairs of vertices. Such a drawing has three properties: (1) every edge $e$ is contained in a simple closed curve $\gamma_e$ such that the only vertices in $\gamma_e$ are the ends of $e$; (2) if $e\ne f$, then $\gamma_e\cap\gamma_f$ has precisely two crossings; and (3) if $e\ne f$, then $e$ intersects $\gamma_f$ at most once, in either a crossing or an end of $e$. We use properties (1)--(3) to define a pseudospherical drawing of $G$. Our main result is that for the complete graph, properties (1)--(3) are equivalent to the same three properties but with “precisely two crossings” in (2) replaced by “at most two crossings.” The proof requires a result in the geometric transversal theory of arrangements of pseudocircles. This is proved using the surprising result that the absence of special arcs (coherent spirals) in an arrangement of simple closed curves characterizes the fact that any two curves in the arrangement have at most two crossings. Our studies provide the necessary ideas for exhibiting a drawing of $K_{10}$ that has no extension to an arrangement of pseudocircles and a drawing of $K_9$ that does extend to an arrangement of pseudocircles, but no such extension has all pairs of pseudocircles crossing twice.
AU - Arroyo Guevara, Alan M
AU - Richter, R. Bruce
AU - Sunohara, Matthew
ID - 9468
IS - 2
JF - SIAM Journal on Discrete Mathematics
SN - 08954801
TI - Extending drawings of complete graphs into arrangements of pseudocircles
VL - 35
ER -
TY - THES
AB - In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management.
We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.
AU - Goharshady, Amir Kafshdar
ID - 8934
SN - 2663-337X
TI - Parameterized and algebro-geometric advances in static program analysis
ER -
TY - JOUR
AB - When short-range attractions are combined with long-range repulsions in colloidal particle systems, complex microphases can emerge. Here, we study a system of isotropic particles, which can form lamellar structures or a disordered fluid phase when temperature is varied. We show that, at equilibrium, the lamellar structure crystallizes, while out of equilibrium, the system forms a variety of structures at different shear rates and temperatures above melting. The shear-induced ordering is analyzed by means of principal component analysis and artificial neural networks, which are applied to data of reduced dimensionality. Our results reveal the possibility of inducing ordering by shear, potentially providing a feasible route to the fabrication of ordered lamellar structures from isotropic particles.
AU - Pȩkalski, J.
AU - Rzadkowski, Wojciech
AU - Panagiotopoulos, A. Z.
ID - 7956
IS - 20
JF - The Journal of chemical physics
TI - Shear-induced ordering in systems with competing interactions: A machine learning study
VL - 152
ER -
TY - JOUR
AB - Neurodevelopmental disorders (NDDs) are a class of disorders affecting brain development and function and are characterized by wide genetic and clinical variability. In this review, we discuss the multiple factors that influence the clinical presentation of NDDs, with particular attention to gene vulnerability, mutational load, and the two-hit model. Despite the complex architecture of
mutational events associated with NDDs, the various proteins involved appear to converge on common pathways, such as synaptic plasticity/function, chromatin remodelers and the mammalian target of rapamycin (mTOR) pathway. A thorough understanding of the mechanisms behind these pathways will hopefully lead to the identification of candidates that could be targeted for treatment approaches.
AU - Parenti, Ilaria
AU - Garcia Rabaneda, Luis E
AU - Schön, Hanna
AU - Novarino, Gaia
ID - 7957
IS - 8
JF - Trends in Neurosciences
SN - 01662236
TI - Neurodevelopmental disorders: From genetics to functional pathways
VL - 43
ER -
TY - JOUR
AB - Let A={A1,…,An} be a family of sets in the plane. For 0≤i2b be integers. We prove that if each k-wise or (k+1)-wise intersection of sets from A has at most b path-connected components, which all are open, then fk+1=0 implies fk≤cfk−1 for some positive constant c depending only on b and k. These results also extend to two-dimensional compact surfaces.
AU - Kalai, Gil
AU - Patakova, Zuzana
ID - 7960
JF - Discrete and Computational Geometry
SN - 01795376
TI - Intersection patterns of planar sets
VL - 64
ER -
TY - JOUR
AB - A string graph is the intersection graph of a family of continuous arcs in the plane. The intersection graph of a family of plane convex sets is a string graph, but not all string graphs can be obtained in this way. We prove the following structure theorem conjectured by Janson and Uzzell: The vertex set of almost all string graphs on n vertices can be partitioned into five cliques such that some pair of them is not connected by any edge (n→∞). We also show that every graph with the above property is an intersection graph of plane convex sets. As a corollary, we obtain that almost all string graphs on n vertices are intersection graphs of plane convex sets.
AU - Pach, János
AU - Reed, Bruce
AU - Yuditsky, Yelena
ID - 7962
IS - 4
JF - Discrete and Computational Geometry
SN - 01795376
TI - Almost all string graphs are intersection graphs of plane convex sets
VL - 63
ER -
TY - CONF
AB - For 1≤m≤n, we consider a natural m-out-of-n multi-instance scenario for a public-key encryption (PKE) scheme. An adversary, given n independent instances of PKE, wins if he breaks at least m out of the n instances. In this work, we are interested in the scaling factor of PKE schemes, SF, which measures how well the difficulty of breaking m out of the n instances scales in m. That is, a scaling factor SF=ℓ indicates that breaking m out of n instances is at least ℓ times more difficult than breaking one single instance. A PKE scheme with small scaling factor hence provides an ideal target for mass surveillance. In fact, the Logjam attack (CCS 2015) implicitly exploited, among other things, an almost constant scaling factor of ElGamal over finite fields (with shared group parameters).
For Hashed ElGamal over elliptic curves, we use the generic group model to argue that the scaling factor depends on the scheme's granularity. In low granularity, meaning each public key contains its independent group parameter, the scheme has optimal scaling factor SF=m; In medium and high granularity, meaning all public keys share the same group parameter, the scheme still has a reasonable scaling factor SF=√m. Our findings underline that instantiating ElGamal over elliptic curves should be preferred to finite fields in a multi-instance scenario.
As our main technical contribution, we derive new generic-group lower bounds of Ω(√(mp)) on the difficulty of solving both the m-out-of-n Gap Discrete Logarithm and the m-out-of-n Gap Computational Diffie-Hellman problem over groups of prime order p, extending a recent result by Yun (EUROCRYPT 2015). We establish the lower bound by studying the hardness of a related computational problem which we call the search-by-hypersurface problem.
AU - Auerbach, Benedikt
AU - Giacon, Federico
AU - Kiltz, Eike
ID - 7966
SN - 0302-9743
T2 - Advances in Cryptology – EUROCRYPT 2020
TI - Everybody’s a target: Scalability in public-key encryption
VL - 12107
ER -
TY - JOUR
AB - Organic materials are known to feature long spin-diffusion times, originating in a generally small spin–orbit coupling observed in these systems. From that perspective, chiral molecules acting as efficient spin selectors pose a puzzle that attracted a lot of attention in recent years. Here, we revisit the physical origins of chiral-induced spin selectivity (CISS) and propose a simple analytic minimal model to describe it. The model treats a chiral molecule as an anisotropic wire with molecular dipole moments aligned arbitrarily with respect to the wire’s axes and is therefore quite general. Importantly, it shows that the helical structure of the molecule is not necessary to observe CISS and other chiral nonhelical molecules can also be considered as potential candidates for the CISS effect. We also show that the suggested simple model captures the main characteristics of CISS observed in the experiment, without the need for additional constraints employed in the previous studies. The results pave the way for understanding other related physical phenomena where the CISS effect plays an essential role.
AU - Ghazaryan, Areg
AU - Paltiel, Yossi
AU - Lemeshko, Mikhail
ID - 7968
IS - 21
JF - The Journal of Physical Chemistry C
SN - 1932-7447
TI - Analytic model of chiral-induced spin selectivity
VL - 124
ER -
TY - JOUR
AB - Multilayer graphene lattices allow for an additional tunability of the band structure by the strong perpendicular electric field. In particular, the emergence of the new multiple Dirac points in ABA stacked trilayer graphene subject to strong transverse electric fields was proposed theoretically and confirmed experimentally. These new Dirac points dubbed “gullies” emerge from the interplay between strong electric field and trigonal warping. In this work, we first characterize the properties of new emergent Dirac points and show that the electric field can be used to tune the distance between gullies in the momentum space. We demonstrate that the band structure has multiple Lifshitz transitions and higher-order singularity of “monkey saddle” type. Following the characterization of the band structure, we consider the spectrum of Landau levels and structure of their wave functions. In the limit of strong electric fields when gullies are well separated in momentum space, they give rise to triply degenerate Landau levels. In the second part of this work, we investigate how degeneracy between three gully Landau levels is lifted in the presence of interactions. Within the Hartree-Fock approximation we show that the symmetry breaking state interpolates between the fully gully polarized state that breaks C3 symmetry at high displacement field and the gully symmetric state when the electric field is decreased. The discontinuous transition between these two states is driven by enhanced intergully tunneling and exchange. We conclude by outlining specific experimental predictions for the existence of such a symmetry-breaking state.
AU - Rao, Peng
AU - Serbyn, Maksym
ID - 7971
IS - 24
JF - Physical Review B
SN - 2469-9950
TI - Gully quantum Hall ferromagnetism in biased trilayer graphene
VL - 101
ER -
TY - JOUR
AB - The goal of limiting global warming to 1.5 °C requires a drastic reduction in CO2 emissions across many sectors of the world economy. Batteries are vital to this endeavor, whether used in electric vehicles, to store renewable electricity, or in aviation. Present lithium-ion technologies are preparing the public for this inevitable change, but their maximum theoretical specific capacity presents a limitation. Their high cost is another concern for commercial viability. Metal–air batteries have the highest theoretical energy density of all possible secondary battery technologies and could yield step changes in energy storage, if their practical difficulties could be overcome. The scope of this review is to provide an objective, comprehensive, and authoritative assessment of the intensive work invested in nonaqueous rechargeable metal–air batteries over the past few years, which identified the key problems and guides directions to solve them. We focus primarily on the challenges and outlook for Li–O2 cells but include Na–O2, K–O2, and Mg–O2 cells for comparison. Our review highlights the interdisciplinary nature of this field that involves a combination of materials chemistry, electrochemistry, computation, microscopy, spectroscopy, and surface science. The mechanisms of O2 reduction and evolution are considered in the light of recent findings, along with developments in positive and negative electrodes, electrolytes, electrocatalysis on surfaces and in solution, and the degradative effect of singlet oxygen, which is typically formed in Li–O2 cells.
AU - Kwak, WJ
AU - Sharon, D
AU - Xia, C
AU - Kim, H
AU - Johnson, LR
AU - Bruce, PG
AU - Nazar, LF
AU - Sun, YK
AU - Frimer, AA
AU - Noked, M
AU - Freunberger, Stefan Alexander
AU - Aurbach, D
ID - 7985
IS - 14
JF - Chemical Reviews
SN - 0009-2665
TI - Lithium-oxygen batteries and related systems: Potential, status, and future
VL - 120
ER -
TY - CONF
AB - We prove general topological Radon-type theorems for sets in ℝ^d, smooth real manifolds or finite dimensional simplicial complexes. Combined with a recent result of Holmsen and Lee, it gives fractional Helly theorem, and consequently the existence of weak ε-nets as well as a (p,q)-theorem. More precisely: Let X be either ℝ^d, smooth real d-manifold, or a finite d-dimensional simplicial complex. Then if F is a finite, intersection-closed family of sets in X such that the ith reduced Betti number (with ℤ₂ coefficients) of any set in F is at most b for every non-negative integer i less or equal to k, then the Radon number of F is bounded in terms of b and X. Here k is the smallest integer larger or equal to d/2 - 1 if X = ℝ^d; k=d-1 if X is a smooth real d-manifold and not a surface, k=0 if X is a surface and k=d if X is a d-dimensional simplicial complex. Using the recent result of the author and Kalai, we manage to prove the following optimal bound on fractional Helly number for families of open sets in a surface: Let F be a finite family of open sets in a surface S such that the intersection of any subfamily of F is either empty, or path-connected. Then the fractional Helly number of F is at most three. This also settles a conjecture of Holmsen, Kim, and Lee about an existence of a (p,q)-theorem for open subsets of a surface.
AU - Patakova, Zuzana
ID - 7989
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Bounding radon number via Betti numbers
VL - 164
ER -
TY - CONF
AB - Given a finite point set P in general position in the plane, a full triangulation is a maximal straight-line embedded plane graph on P. A partial triangulation on P is a full triangulation of some subset P' of P containing all extreme points in P. A bistellar flip on a partial triangulation either flips an edge, removes a non-extreme point of degree 3, or adds a point in P ⧵ P' as vertex of degree 3. The bistellar flip graph has all partial triangulations as vertices, and a pair of partial triangulations is adjacent if they can be obtained from one another by a bistellar flip. The goal of this paper is to investigate the structure of this graph, with emphasis on its connectivity. For sets P of n points in general position, we show that the bistellar flip graph is (n-3)-connected, thereby answering, for sets in general position, an open questions raised in a book (by De Loera, Rambau, and Santos) and a survey (by Lee and Santos) on triangulations. This matches the situation for the subfamily of regular triangulations (i.e., partial triangulations obtained by lifting the points and projecting the lower convex hull), where (n-3)-connectivity has been known since the late 1980s through the secondary polytope (Gelfand, Kapranov, Zelevinsky) and Balinski’s Theorem. Our methods also yield the following results (see the full version [Wagner and Welzl, 2020]): (i) The bistellar flip graph can be covered by graphs of polytopes of dimension n-3 (products of secondary polytopes). (ii) A partial triangulation is regular, if it has distance n-3 in the Hasse diagram of the partial order of partial subdivisions from the trivial subdivision. (iii) All partial triangulations are regular iff the trivial subdivision has height n-3 in the partial order of partial subdivisions. (iv) There are arbitrarily large sets P with non-regular partial triangulations, while every proper subset has only regular triangulations, i.e., there are no small certificates for the existence of non-regular partial triangulations (answering a question by F. Santos in the unexpected direction).
AU - Wagner, Uli
AU - Welzl, Emo
ID - 7990
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Connectivity of triangulation flip graphs in the plane (Part II: Bistellar flips)
VL - 164
ER -
TY - CONF
AB - We define and study a discrete process that generalizes the convex-layer decomposition of a planar point set. Our process, which we call homotopic curve shortening (HCS), starts with a closed curve (which might self-intersect) in the presence of a set P⊂ ℝ² of point obstacles, and evolves in discrete steps, where each step consists of (1) taking shortcuts around the obstacles, and (2) reducing the curve to its shortest homotopic equivalent. We find experimentally that, if the initial curve is held fixed and P is chosen to be either a very fine regular grid or a uniformly random point set, then HCS behaves at the limit like the affine curve-shortening flow (ACSF). This connection between HCS and ACSF generalizes the link between "grid peeling" and the ACSF observed by Eppstein et al. (2017), which applied only to convex curves, and which was studied only for regular grids. We prove that HCS satisfies some properties analogous to those of ACSF: HCS is invariant under affine transformations, preserves convexity, and does not increase the total absolute curvature. Furthermore, the number of self-intersections of a curve, or intersections between two curves (appropriately defined), does not increase. Finally, if the initial curve is simple, then the number of inflection points (appropriately defined) does not increase.
AU - Avvakumov, Sergey
AU - Nivasch, Gabriel
ID - 7991
SN - 18688969
T2 - 36th International Symposium on Computational Geometry
TI - Homotopic curve shortening and the affine curve-shortening flow
VL - 164
ER -