@misc{5436,
abstract = {Recently there has been a significant effort to handle quantitative properties in formal verification and synthesis. While weighted automata over finite and infinite words provide a natural and flexible framework to express quantitative properties, perhaps surprisingly, some basic system properties such as average response time cannot be expressed using weighted automata, nor in any other know decidable formalism. In this work, we introduce nested weighted automata as a natural extension of weighted automata which makes it possible to express important quantitative properties such as average response time.
In nested weighted automata, a master automaton spins off and collects results from weighted slave automata, each of which computes a quantity along a finite portion of an infinite word. Nested weighted automata can be viewed as the quantitative analogue of monitor automata, which are used in run-time verification. We establish an almost complete decidability picture for the basic decision problems about nested weighted automata, and illustrate their applicability in several domains. In particular, nested weighted automata can be used to decide average response time properties.},
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {29},
publisher = {IST Austria},
title = {{Nested weighted automata}},
doi = {10.15479/AT:IST-2015-170-v2-2},
year = {2015},
}
@misc{5437,
abstract = {We consider the core algorithmic problems related to verification of systems with respect to three classical quantitative properties, namely, the mean-payoff property, the ratio property, and the minimum initial credit for energy property.
The algorithmic problem given a graph and a quantitative property asks to compute the optimal value (the infimum value over all traces) from every node of the graph. We consider graphs with constant treewidth, and it is well-known that the control-flow graphs of most programs have constant treewidth. Let $n$ denote the number of nodes of a graph, $m$ the number of edges (for constant treewidth graphs $m=O(n)$) and $W$ the largest absolute value of the weights.
Our main theoretical results are as follows.
First, for constant treewidth graphs we present an algorithm that approximates the mean-payoff value within a multiplicative factor of $\epsilon$ in time $O(n \cdot \log (n/\epsilon))$ and linear space, as compared to the classical algorithms that require quadratic time. Second, for the ratio property we present an algorithm that for constant treewidth graphs works in time $O(n \cdot \log (|a\cdot b|))=O(n\cdot\log (n\cdot W))$, when the output is $\frac{a}{b}$, as compared to the previously best known algorithm with running time $O(n^2 \cdot \log (n\cdot W))$. Third, for the minimum initial credit problem we show that (i)~for general graphs the problem can be solved in $O(n^2\cdot m)$ time and the associated decision problem can be solved in $O(n\cdot m)$ time, improving the previous known $O(n^3\cdot m\cdot \log (n\cdot W))$ and $O(n^2 \cdot m)$ bounds, respectively; and (ii)~for constant treewidth graphs we present an algorithm that requires $O(n\cdot \log n)$ time, improving the previous known $O(n^4 \cdot \log (n \cdot W))$ bound.
We have implemented some of our algorithms and show that they present a significant speedup on standard benchmarks. },
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {27},
publisher = {IST Austria},
title = {{Faster algorithms for quantitative verification in constant treewidth graphs}},
doi = {10.15479/AT:IST-2015-330-v2-1},
year = {2015},
}
@misc{5438,
abstract = {The edit distance between two words w1, w2 is the minimal number of word operations (letter insertions, deletions, and substitutions) necessary to transform w1 to w2. The edit distance generalizes to languages L1, L2, where the edit distance is the minimal number k such that for every word from L1 there exists a word in L2 with edit distance at most k. We study the edit distance computation problem between pushdown automata and their subclasses.
The problem of computing edit distance to a pushdown automaton is undecidable, and in practice, the interesting question is to compute the edit distance from a pushdown automaton (the implementation, a standard model for programs with recursion) to a regular language (the specification). In this work, we present a complete picture of decidability and complexity for deciding whether, for a given threshold k, the edit distance from a pushdown automaton to a finite automaton is at most k. },
author = {Chatterjee, Krishnendu and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Otop, Jan},
issn = {2664-1690},
pages = {15},
publisher = {IST Austria},
title = {{Edit distance for pushdown automata}},
doi = {10.15479/AT:IST-2015-334-v1-1},
year = {2015},
}
@misc{5439,
abstract = {The target discounted-sum problem is the following: Given a rational discount factor 0 < λ < 1 and three rational values a, b, and t, does there exist a finite or an infinite sequence w ε(a, b)∗ or w ε(a, b)w, such that Σ|w| i=0 w(i)λi equals t? The problem turns out to relate to many fields of mathematics and computer science, and its decidability question is surprisingly hard to solve. We solve the finite version of the problem, and show the hardness of the infinite version, linking it to various areas and open problems in mathematics and computer science: β-expansions, discounted-sum automata, piecewise affine maps, and generalizations of the Cantor set. We provide some partial results to the infinite version, among which are solutions to its restriction to eventually-periodic sequences and to the cases that λ λ 1/2 or λ = 1/n, for every n ε N. We use our results for solving some open problems on discounted-sum automata, among which are the exact-value problem for nondeterministic automata over finite words and the universality and inclusion problems for functional automata. },
author = {Boker, Udi and Henzinger, Thomas A and Otop, Jan},
issn = {2664-1690},
pages = {20},
publisher = {IST Austria},
title = {{The target discounted-sum problem}},
doi = {10.15479/AT:IST-2015-335-v1-1},
year = {2015},
}
@misc{5440,
abstract = {Evolution occurs in populations of reproducing individuals. The structure of the population affects the outcome of the evolutionary process. Evolutionary graph theory is a powerful approach to study this phenomenon. There are two graphs. The interaction graph specifies who interacts with whom for payoff in the context of evolution. The replacement graph specifies who competes with whom for reproduction. The vertices of the two graphs are the same, and each vertex corresponds to an individual of the population. The fitness (or the reproductive rate) is a non-negative number, and depends on the payoff. A key quantity is the fixation probability of a new mutant. It is defined as the probability that a newly introduced mutant (on a single vertex) generates a lineage of offspring which eventually takes over the entire population of resident individuals. The basic computational questions are as follows: (i) the qualitative question asks whether the fixation probability is positive; and (ii) the quantitative approximation question asks for an approximation of the fixation probability. Our main results are as follows: First, we consider a special case of the general problem, where the residents do not reproduce. We show that the qualitative question is NP-complete, and the quantitative approximation question is #P-complete, and the hardness results hold even in the special case where the interaction and the replacement graphs coincide. Second, we show that in general both the qualitative and the quantitative approximation questions are PSPACE-complete. The PSPACE-hardness result for quantitative approximation holds even when the fitness is always positive.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Nowak, Martin},
issn = {2664-1690},
pages = {18},
publisher = {IST Austria},
title = {{The complexity of evolutionary games on graphs}},
doi = {10.15479/AT:IST-2015-323-v2-2},
year = {2015},
}
@misc{5441,
abstract = {We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural problems that arise in program analysis. We consider that each component of the concurrent system is a graph with constant treewidth, a property satisfied by the controlflow graphs of most programs. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis. The study of multiple queries allows us to consider the tradeoff between the resource usage of the one-time preprocessing and for each individual query. The traditional approach constructs the product graph of all components and applies the best-known graph algorithm on the product. In this approach, even the answer to a single query requires the transitive closure (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time. Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time, each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results showing that the worst-case running time of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (i.e., improving the worst-case bound for the shortest path problem in general graphs). Preliminary experimental results show that our algorithms perform favorably on several benchmarks.},
author = {Chatterjee, Krishnendu and Ibsen-Jensen, Rasmus and Goharshady, Amir and Pavlogiannis, Andreas},
issn = {2664-1690},
pages = {24},
publisher = {IST Austria},
title = {{Algorithms for algebraic path properties in concurrent systems of constant treewidth components}},
doi = {10.15479/AT:IST-2015-340-v1-1},
year = {2015},
}
@misc{5442,
abstract = {We study algorithmic questions for concurrent systems where the transitions are labeled from a complete, closed semiring, and path properties are algebraic with semiring operations. The algebraic path properties can model dataflow analysis problems, the shortest path problem, and many other natural properties that arise in program analysis.
We consider that each component of the concurrent system is a graph with constant treewidth, and it is known that the controlflow graphs of most programs have constant treewidth. We allow for multiple possible queries, which arise naturally in demand driven dataflow analysis problems (e.g., alias analysis). The study of multiple queries allows us to consider the tradeoff between the resource usage of the \emph{one-time} preprocessing and for \emph{each individual} query. The traditional approaches construct the product graph of all components and apply the best-known graph algorithm on the product. In the traditional approach, even the answer to a single query requires the transitive closure computation (i.e., the results of all possible queries), which provides no room for tradeoff between preprocessing and query time.
Our main contributions are algorithms that significantly improve the worst-case running time of the traditional approach, and provide various tradeoffs depending on the number of queries. For example, in a concurrent system of two components, the traditional approach requires hexic time in the worst case for answering one query as well as computing the transitive closure, whereas we show that with one-time preprocessing in almost cubic time,
each subsequent query can be answered in at most linear time, and even the transitive closure can be computed in almost quartic time. Furthermore, we establish conditional optimality results that show that the worst-case running times of our algorithms cannot be improved without achieving major breakthroughs in graph algorithms (such as improving
the worst-case bounds for the shortest path problem in general graphs whose current best-known bound has not been improved in five decades). Finally, we provide a prototype implementation of our algorithms which significantly outperforms the existing algorithmic methods on several benchmarks.},
author = {Anonymous, 1 and Anonymous, 2 and Anonymous, 3 and Anonymous, 4},
issn = {2664-1690},
pages = {22},
publisher = {IST Austria},
title = {{Algorithms for algebraic path properties in concurrent systems of constant treewidth components}},
year = {2015},
}
@misc{5443,
abstract = {POMDPs are standard models for probabilistic planning problems, where an agent interacts with an uncertain environment. We study the problem of almost-sure reachability, where given a set of target states, the question is to decide whether there is a policy to ensure that the target set is reached with probability 1 (almost-surely). While in general the problem is EXPTIME-complete, in many practical cases policies with a small amount of memory suffice. Moreover, the existing solution to the problem is explicit, which first requires to construct explicitly an exponential reduction to a belief-support MDP. In this work, we first study the existence of observation-stationary strategies, which is NP-complete, and then small-memory strategies. We present a symbolic algorithm by an efficient encoding to SAT and using a SAT solver for the problem. We report experimental results demonstrating the scalability of our symbolic (SAT-based) approach.},
author = {Chatterjee, Krishnendu and Chmelik, Martin and Davies, Jessica},
issn = {2664-1690},
pages = {23},
publisher = {IST Austria},
title = {{A symbolic SAT-based algorithm for almost-sure reachability with small strategies in POMDPs}},
doi = {10.15479/AT:IST-2015-325-v2-1},
year = {2015},
}
@misc{5444,
abstract = {A comprehensive understanding of the clonal evolution of cancer is critical for understanding neoplasia. Genome-wide sequencing data enables evolutionary studies at unprecedented depth. However, classical phylogenetic methods often struggle with noisy sequencing data of impure DNA samples and fail to detect subclones that have different evolutionary trajectories. We have developed a tool, called Treeomics, that allows us to reconstruct the phylogeny of a cancer with commonly available sequencing technologies. Using Bayesian inference and Integer Linear Programming, robust phylogenies consistent with the biological processes underlying cancer evolution were obtained for pancreatic, ovarian, and prostate cancers. Furthermore, Treeomics correctly identified sequencing artifacts such as those resulting from low statistical power; nearly 7% of variants were misclassified by conventional statistical methods. These artifacts can skew phylogenies by creating illusory tumor heterogeneity among distinct samples. Importantly, we show that the evolutionary trees generated with Treeomics are mathematically optimal.},
author = {Reiter, Johannes and Makohon-Moore, Alvin and Gerold, Jeffrey and Bozic, Ivana and Chatterjee, Krishnendu and Iacobuzio-Donahue, Christine and Vogelstein, Bert and Nowak, Martin},
issn = {2664-1690},
pages = {25},
publisher = {IST Austria},
title = {{Reconstructing robust phylogenies of metastatic cancers}},
doi = {10.15479/AT:IST-2015-399-v1-1},
year = {2015},
}
@misc{5549,
abstract = {This repository contains the experimental part of the CAV 2015 publication Counterexample Explanation by Learning Small Strategies in Markov Decision Processes.
We extended the probabilistic model checker PRISM to represent strategies of Markov Decision Processes as Decision Trees.
The archive contains a java executable version of the extended tool (prism_dectree.jar) together with a few examples of the PRISM benchmark library.
To execute the program, please have a look at the README.txt, which provides instructions and further information on the archive.
The archive contains scripts that (if run often enough) reproduces the data presented in the publication.},
author = {Fellner, Andreas},
keywords = {Markov Decision Process, Decision Tree, Probabilistic Verification, Counterexample Explanation},
publisher = {IST Austria},
title = {{Experimental part of CAV 2015 publication: Counterexample Explanation by Learning Small Strategies in Markov Decision Processes}},
doi = {10.15479/AT:ISTA:28},
year = {2015},
}
@article{1383,
abstract = {In plants, vacuolar H+-ATPase (V-ATPase) activity acidifies both the trans-Golgi network/early endosome (TGN/EE) and the vacuole. This dual V-ATPase function has impeded our understanding of how the pH homeostasis within the plant TGN/EE controls exo- and endocytosis. Here, we show that the weak V-ATPase mutant deetiolated3 (det3) displayed a pH increase in the TGN/EE, but not in the vacuole, strongly impairing secretion and recycling of the brassinosteroid receptor and the cellulose synthase complexes to the plasma membrane, in contrast to mutants lacking tonoplast-localized V-ATPase activity only. The brassinosteroid insensitivity and the cellulose deficiency defects in det3 were tightly correlated with reduced Golgi and TGN/EE motility. Thus, our results provide strong evidence that acidification of the TGN/EE, but not of the vacuole, is indispensable for functional secretion and recycling in plants.},
author = {Yu, Luo and Scholl, Stefan and Doering, Anett and Yi, Zhang and Irani, Niloufer and Di Rubbo, Simone and Neumetzler, Lutz and Krishnamoorthy, Praveen and Van Houtte, Isabelle and Mylle, Evelien and Bischoff, Volker and Vernhettes, Samantha and Winne, Johan and Friml, Jirí and Stierhof, York and Schumacher, Karin and Persson, Staffan and Russinova, Eugenia},
journal = {Nature Plants},
number = {7},
publisher = {Nature Publishing Group},
title = {{V-ATPase activity in the TGN/EE is required for exocytosis and recycling in Arabidopsis}},
doi = {10.1038/nplants.2015.94},
volume = {1},
year = {2015},
}
@phdthesis{1399,
abstract = {This thesis is concerned with the computation and approximation of intrinsic volumes. Given a smooth body M and a certain digital approximation of it, we develop algorithms to approximate various intrinsic volumes of M using only measurements taken from its digital approximations. The crucial idea behind our novel algorithms is to link the recent theory of persistent homology to the theory of intrinsic volumes via the Crofton formula from integral geometry and, in particular, via Euler characteristic computations. Our main contributions are a multigrid convergent digital algorithm to compute the first intrinsic volume of a solid body in R^n as well as an appropriate integration pipeline to approximate integral-geometric integrals defined over the Grassmannian manifold.},
author = {Pausinger, Florian},
pages = {144},
publisher = {IST Austria},
title = {{On the approximation of intrinsic volumes}},
year = {2015},
}
@phdthesis{1400,
abstract = {Cancer results from an uncontrolled growth of abnormal cells. Sequentially accumulated genetic and epigenetic alterations decrease cell death and increase cell replication. We used mathematical models to quantify the effect of driver gene mutations. The recently developed targeted therapies can lead to dramatic regressions. However, in solid cancers, clinical responses are often short-lived because resistant cancer cells evolve. We estimated that approximately 50 different mutations can confer resistance to a typical targeted therapeutic agent. We find that resistant cells are likely to be present in expanded subclones before the start of the treatment. The dominant strategy to prevent the evolution of resistance is combination therapy. Our analytical results suggest that in most patients, dual therapy, but not monotherapy, can result in long-term disease control. However, long-term control can only occur if there are no possible mutations in the genome that can cause cross-resistance to both drugs. Furthermore, we showed that simultaneous therapy with two drugs is much more likely to result in long-term disease control than sequential therapy with the same drugs. To improve our understanding of the underlying subclonal evolution we reconstruct the evolutionary history of a patient's cancer from next-generation sequencing data of spatially-distinct DNA samples. Using a quantitative measure of genetic relatedness, we found that pancreatic cancers and their metastases demonstrated a higher level of relatedness than that expected for any two cells randomly taken from a normal tissue. This minimal amount of genetic divergence among advanced lesions indicates that genetic heterogeneity, when quantitatively defined, is not a fundamental feature of the natural history of untreated pancreatic cancers. Our newly developed, phylogenomic tool Treeomics finds evidence for seeding patterns of metastases and can directly be used to discover rules governing the evolution of solid malignancies to transform cancer into a more predictable disease.},
author = {Reiter, Johannes},
pages = {183},
publisher = {IST Austria},
title = {{The subclonal evolution of cancer}},
year = {2015},
}
@inproceedings{1424,
abstract = {We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data. These diagrams encode persistent homology, a widely used invariant in topological data analysis. While several avenues towards a statistical treatment of the diagrams have been explored recently, we follow an alternative route that is motivated by the success of methods based on the embedding of probability measures into reproducing kernel Hilbert spaces. In fact, a positive definite kernel on persistence diagrams has recently been proposed, connecting persistent homology to popular kernel-based learning techniques such as support vector machines. However, important properties of that kernel enabling a principled use in the context of probability measure embeddings remain to be explored. Our contribution is to close this gap by proving universality of a variant of the original kernel, and to demonstrate its effective use in twosample hypothesis testing on synthetic as well as real-world data.},
author = {Kwitt, Roland and Huber, Stefan and Niethammer, Marc and Lin, Weili and Bauer, Ulrich},
location = {Montreal, Canada},
pages = {3070 -- 3078},
publisher = {Neural Information Processing Systems},
title = {{Statistical topological data analysis-A kernel perspective}},
volume = {28},
year = {2015},
}
@inproceedings{1425,
abstract = {In this work we aim at extending the theoretical foundations of lifelong learning. Previous work analyzing this scenario is based on the assumption that learning tasks are sampled i.i.d. from a task environment or limited to strongly constrained data distributions. Instead, we study two scenarios when lifelong learning is possible, even though the observed tasks do not form an i.i.d. sample: first, when they are sampled from the same environment, but possibly with dependencies, and second, when the task environment is allowed to change over time in a consistent way. In the first case we prove a PAC-Bayesian theorem that can be seen as a direct generalization of the analogous previous result for the i.i.d. case. For the second scenario we propose to learn an inductive bias in form of a transfer procedure. We present a generalization bound and show on a toy example how it can be used to identify a beneficial transfer algorithm.},
author = {Pentina, Anastasia and Lampert, Christoph},
location = {Montreal, Canada},
pages = {1540 -- 1548},
publisher = {Neural Information Processing Systems},
title = {{Lifelong learning with non-i.i.d. tasks}},
volume = {2015},
year = {2015},
}
@inproceedings{1430,
abstract = {Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse their runtime on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrence of new mutations is much longer than the time it takes for a new beneficial mutation to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a (1+1)-type process where the probability of accepting a new genotype (improvements or worsenings) depends on the change in fitness. We present an initial runtime analysis of SSWM, quantifying its performance for various parameters and investigating differences to the (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient.},
author = {Paixao, Tiago and Sudholt, Dirk and Heredia, Jorge and Trubenova, Barbora},
booktitle = {Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation},
location = {Madrid, Spain},
pages = {1455 -- 1462},
publisher = {ACM},
title = {{First steps towards a runtime comparison of natural and artificial evolution}},
doi = {10.1145/2739480.2754758},
year = {2015},
}
@inproceedings{1474,
abstract = {Cryptographic access control offers selective access to encrypted data via a combination of key management and functionality-rich cryptographic schemes, such as attribute-based encryption. Using this approach, publicly available meta-data may inadvertently leak information on the access policy that is enforced by cryptography, which renders cryptographic access control unusable in settings where this information is highly sensitive. We begin to address this problem by presenting rigorous definitions for policy privacy in cryptographic access control. For concreteness we set our results in the model of Role-Based Access Control (RBAC), where we identify and formalize several different flavors of privacy, however, our framework should serve as inspiration for other models of access control. Based on our insights we propose a new system which significantly improves on the privacy properties of state-of-the-art constructions. Our design is based on a novel type of privacy-preserving attribute-based encryption, which we introduce and show how to instantiate. We present our results in the context of a cryptographic RBAC system by Ferrara et al. (CSF'13), which uses cryptography to control read access to files, while write access is still delegated to trusted monitors. We give an extension of the construction that permits cryptographic control over write access. Our construction assumes that key management uses out-of-band channels between the policy enforcer and the users but eliminates completely the need for monitoring read/write access to the data.},
author = {Ferrara, Anna and Fuchsbauer, Georg and Liu, Bin and Warinschi, Bogdan},
location = {Verona, Italy},
pages = {46--60},
publisher = {IEEE},
title = {{Policy privacy in cryptographic access control}},
doi = {10.1109/CSF.2015.11},
year = {2015},
}
@inproceedings{1481,
abstract = {Simple board games, like Tic-Tac-Toe and CONNECT-4, play an important role not only in the development of mathematical and logical skills, but also in the emotional and social development. In this paper, we address the problem of generating targeted starting positions for such games. This can facilitate new approaches for bringing novice players to mastery, and also leads to discovery of interesting game variants. We present an approach that generates starting states of varying hardness levels for player 1 in a two-player board game, given rules of the board game, the desired number of steps required for player 1 to win, and the expertise levels of the two players. Our approach leverages symbolic methods and iterative simulation to efficiently search the extremely large state space. We present experimental results that include discovery of states of varying hardness levels for several simple grid-based board games. The presence of such states for standard game variants like 4×4 Tic-Tac-Toe opens up new games to be played that have never been played as the default start state is heavily biased. },
author = {Ahmed, Umair and Chatterjee, Krishnendu and Gulwani, Sumit},
booktitle = {Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence},
location = {Austin, TX, USA},
pages = {745 -- 752},
publisher = {AAAI Press},
title = {{Automatic generation of alternative starting positions for simple traditional board games}},
volume = {2},
year = {2015},
}
@inproceedings{1483,
abstract = {Topological data analysis offers a rich source of valuable information to study vision problems. Yet, so far we lack a theoretically sound connection to popular kernel-based learning techniques, such as kernel SVMs or kernel PCA. In this work, we establish such a connection by designing a multi-scale kernel for persistence diagrams, a stable summary representation of topological features in data. We show that this kernel is positive definite and prove its stability with respect to the 1-Wasserstein distance. Experiments on two benchmark datasets for 3D shape classification/retrieval and texture recognition show considerable performance gains of the proposed method compared to an alternative approach that is based on the recently introduced persistence landscapes.},
author = {Reininghaus, Jan and Huber, Stefan and Bauer, Ulrich and Kwitt, Roland},
location = {Boston, MA, USA},
pages = {4741 -- 4748},
publisher = {IEEE},
title = {{A stable multi-scale kernel for topological machine learning}},
doi = {10.1109/CVPR.2015.7299106},
year = {2015},
}
@inproceedings{1495,
abstract = {Motivated by biological questions, we study configurations of equal-sized disks in the Euclidean plane that neither pack nor cover. Measuring the quality by the probability that a random point lies in exactly one disk, we show that the regular hexagonal grid gives the maximum among lattice configurations. },
author = {Edelsbrunner, Herbert and Iglesias Ham, Mabel and Kurlin, Vitaliy},
booktitle = {Proceedings of the 27th Canadian Conference on Computational Geometry},
location = {Ontario, Canada},
pages = {128--135},
publisher = {Queen's University},
title = {{Relaxed disk packing}},
volume = {2015-August},
year = {2015},
}