@article{9627,
abstract = {We compute the deficiency spaces of operators of the form 𝐻𝐴⊗̂ 𝐼+𝐼⊗̂ 𝐻𝐵, for symmetric 𝐻𝐴 and self-adjoint 𝐻𝐵. This enables us to construct self-adjoint extensions (if they exist) by means of von Neumann's theory. The structure of the deficiency spaces for this case was asserted already in Ibort et al. [Boundary dynamics driven entanglement, J. Phys. A: Math. Theor. 47(38) (2014) 385301], but only proven under the restriction of 𝐻𝐵 having discrete, non-degenerate spectrum.},
author = {Lenz, Daniel and Weinmann, Timon and Wirth, Melchior},
issn = {14643839},
journal = {Proceedings of the Edinburgh Mathematical Society},
pages = {1--15},
publisher = {Cambridge University Press},
title = {{Self-adjoint extensions of bipartite Hamiltonians}},
doi = {10.1017/S0013091521000080},
year = {2021},
}
@article{9647,
abstract = {Gene expression is regulated by the set of transcription factors (TFs) that bind to the promoter. The ensuing regulating function is often represented as a combinational logic circuit, where output (gene expression) is determined by current input values (promoter bound TFs) only. However, the simultaneous arrival of TFs is a strong assumption, since transcription and translation of genes introduce intrinsic time delays and there is no global synchronisation among the arrival times of different molecular species at their targets. We present an experimentally implementable genetic circuit with two inputs and one output, which in the presence of small delays in input arrival, exhibits qualitatively distinct population-level phenotypes, over timescales that are longer than typical cell doubling times. From a dynamical systems point of view, these phenotypes represent long-lived transients: although they converge to the same value eventually, they do so after a very long time span. The key feature of this toy model genetic circuit is that, despite having only two inputs and one output, it is regulated by twenty-three distinct DNA-TF configurations, two of which are more stable than others (DNA looped states), one promoting and another blocking the expression of the output gene. Small delays in input arrival time result in a majority of cells in the population quickly reaching the stable state associated with the first input, while exiting of this stable state occurs at a slow timescale. In order to mechanistically model the behaviour of this genetic circuit, we used a rule-based modelling language, and implemented a grid-search to find parameter combinations giving rise to long-lived transients. Our analysis shows that in the absence of feedback, there exist path-dependent gene regulatory mechanisms based on the long timescale of transients. The behaviour of this toy model circuit suggests that gene regulatory networks can exploit event timing to create phenotypes, and it opens the possibility that they could use event timing to memorise events, without regulatory feedback. The model reveals the importance of (i) mechanistically modelling the transitions between the different DNA-TF states, and (ii) employing transient analysis thereof.},
author = {Petrov, Tatjana and Igler, Claudia and Sezgin, Ali and Henzinger, Thomas A and Guet, Calin C},
issn = {03043975},
journal = {Theoretical Computer Science},
publisher = {Elsevier},
title = {{Long lived transients in gene regulation}},
doi = {10.1016/j.tcs.2021.05.023},
year = {2021},
}
@inproceedings{9646,
abstract = {We consider the fundamental problem of deriving quantitative bounds on the probability that a given assertion is violated in a probabilistic program. We provide automated algorithms that obtain both lower and upper bounds on the assertion violation probability. The main novelty of our approach is that we prove new and dedicated fixed-point theorems which serve as the theoretical basis of our algorithms and enable us to reason about assertion violation bounds in terms of pre and post fixed-point functions. To synthesize such fixed-points, we devise algorithms that utilize a wide range of mathematical tools, including repulsing ranking supermartingales, Hoeffding's lemma, Minkowski decompositions, Jensen's inequality, and convex optimization. On the theoretical side, we provide (i) the first automated algorithm for lower-bounds on assertion violation probabilities, (ii) the first complete algorithm for upper-bounds of exponential form in affine programs, and (iii) provably and significantly tighter upper-bounds than the previous approaches. On the practical side, we show our algorithms can handle a wide variety of programs from the literature and synthesize bounds that are remarkably tighter than previous results, in some cases by thousands of orders of magnitude.},
author = {Wang, Jinyi and Sun, Yican and Fu, Hongfei and Chatterjee, Krishnendu and Goharshady, Amir Kafshdar},
booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
isbn = {9781450383912},
location = {Online},
pages = {1171--1186},
publisher = {Association for Computing Machinery},
title = {{Quantitative analysis of assertion violations in probabilistic programs}},
doi = {10.1145/3453483.3454102},
year = {2021},
}
@inproceedings{9645,
abstract = {We consider the fundamental problem of reachability analysis over imperative programs with real variables. Previous works that tackle reachability are either unable to handle programs consisting of general loops (e.g. symbolic execution), or lack completeness guarantees (e.g. abstract interpretation), or are not automated (e.g. incorrectness logic). In contrast, we propose a novel approach for reachability analysis that can handle general and complex loops, is complete, and can be entirely automated for a wide family of programs. Through the notion of Inductive Reachability Witnesses (IRWs), our approach extends ideas from both invariant generation and termination to reachability analysis.
We first show that our IRW-based approach is sound and complete for reachability analysis of imperative programs. Then, we focus on linear and polynomial programs and develop automated methods for synthesizing linear and polynomial IRWs. In the linear case, we follow the well-known approaches using Farkas' Lemma. Our main contribution is in the polynomial case, where we present a push-button semi-complete algorithm. We achieve this using a novel combination of classical theorems in real algebraic geometry, such as Putinar's Positivstellensatz and Hilbert's Strong Nullstellensatz. Finally, our experimental results show we can prove complex reachability objectives over various benchmarks that were beyond the reach of previous methods.},
author = {Asadi, Ali and Chatterjee, Krishnendu and Fu, Hongfei and Goharshady, Amir Kafshdar and Mahdavi, Mohammad},
booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
isbn = {9781450383912},
location = {Online},
pages = {772--787},
publisher = {Association for Computing Machinery},
title = {{Polynomial reachability witnesses via Stellensätze}},
doi = {10.1145/3453483.3454076},
year = {2021},
}
@inproceedings{9644,
abstract = {We present a new approach to proving non-termination of non-deterministic integer programs. Our technique is rather simple but efficient. It relies on a purely syntactic reversal of the program's transition system followed by a constraint-based invariant synthesis with constraints coming from both the original and the reversed transition system. The latter task is performed by a simple call to an off-the-shelf SMT-solver, which allows us to leverage the latest advances in SMT-solving. Moreover, our method offers a combination of features not present (as a whole) in previous approaches: it handles programs with non-determinism, provides relative completeness guarantees and supports programs with polynomial arithmetic. The experiments performed with our prototype tool RevTerm show that our approach, despite its simplicity and stronger theoretical guarantees, is at least on par with the state-of-the-art tools, often achieving a non-trivial improvement under a proper configuration of its parameters.},
author = {Chatterjee, Krishnendu and Goharshady, Ehsan Kafshdar and Novotný, Petr and Zikelic, Dorde},
booktitle = {Proceedings of the 42nd ACM SIGPLAN International Conference on Programming Language Design and Implementation},
isbn = {9781450383912},
location = {Online},
pages = {1033--1048},
publisher = {Association for Computing Machinery},
title = {{Proving non-termination by program reversal}},
doi = {10.1145/3453483.3454093},
year = {2021},
}
@article{9649,
abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. manifolds defined as the zero set of some multivariate vector-valued smooth function f : Rd → Rd−n. A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear (PL) approximation based on a triangulation T of the ambient space Rd. In this paper, we give conditions under which the PL-approximation of an isomanifold is topologically equivalent to the isomanifold. The conditions are easy to satisfy in the sense that they can always be met by taking a sufficiently
fine triangulation T . This contrasts with previous results on the triangulation of manifolds where, in arbitrary dimensions, delicate perturbations are needed to guarantee topological correctness, which leads to strong limitations in practice. We further give a bound on the Fréchet distance between the original isomanifold and its PL-approximation. Finally we show analogous results for the PL-approximation of an isomanifold with boundary.},
author = {Boissonnat, Jean-Daniel and Wintraecken, Mathijs},
journal = {Foundations of Computational Mathematics },
publisher = {Springer Nature},
title = {{The topological correctness of PL approximations of isomanifolds}},
doi = {10.1007/s10208-021-09520-0},
year = {2021},
}
@inproceedings{9678,
abstract = {We introduce a new graph problem, the token dropping game, and we show how to solve it efficiently in a distributed setting. We use the token dropping game as a tool to design an efficient distributed algorithm for stable orientations and more generally for locally optimal semi-matchings. The prior work by Czygrinow et al. (DISC 2012) finds a stable orientation in O(Δ^5) rounds in graphs of maximum degree Δ, while we improve it to O(Δ^4) and also prove a lower bound of Ω(Δ). For the more general problem of locally optimal semi-matchings, the prior upper bound is O(S^5) and our new algorithm runs in O(C · S^4) rounds, which is an improvement for C = o(S); here C and S are the maximum degrees of customers and servers, respectively.},
author = {Brandt, Sebastian and Keller, Barbara and Rybicki, Joel and Suomela, Jukka and Uitto, Jara},
booktitle = {Annual ACM Symposium on Parallelism in Algorithms and Architectures},
isbn = {9781450380706},
location = { Virtual Event, United States},
pages = {129--139},
title = {{Efficient load-balancing through distributed token dropping}},
doi = {10.1145/3409964.3461785},
year = {2021},
}
@inproceedings{9441,
abstract = {Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e. submanifolds of ℝ^d defined as the zero set of some multivariate multivalued smooth function f: ℝ^d → ℝ^{d-n}, where n is the intrinsic dimension of the manifold. A natural way to approximate a smooth isomanifold M is to consider its Piecewise-Linear (PL) approximation M̂ based on a triangulation 𝒯 of the ambient space ℝ^d. In this paper, we describe a simple algorithm to trace isomanifolds from a given starting point. The algorithm works for arbitrary dimensions n and d, and any precision D. Our main result is that, when f (or M) has bounded complexity, the complexity of the algorithm is polynomial in d and δ = 1/D (and unavoidably exponential in n). Since it is known that for δ = Ω (d^{2.5}), M̂ is O(D²)-close and isotopic to M, our algorithm produces a faithful PL-approximation of isomanifolds of bounded complexity in time polynomial in d. Combining this algorithm with dimensionality reduction techniques, the dependency on d in the size of M̂ can be completely removed with high probability. We also show that the algorithm can handle isomanifolds with boundary and, more generally, isostratifolds. The algorithm for isomanifolds with boundary has been implemented and experimental results are reported, showing that it is practical and can handle cases that are far ahead of the state-of-the-art. },
author = {Boissonnat, Jean-Daniel and Kachanovich, Siargey and Wintraecken, Mathijs},
booktitle = {37th International Symposium on Computational Geometry (SoCG 2021)},
isbn = {978-3-95977-184-9},
issn = {1868-8969},
location = {Virtual},
pages = {17:1--17:16},
publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
title = {{Tracing isomanifolds in Rd in time polynomial in d using Coxeter-Freudenthal-Kuhn triangulations}},
doi = {10.4230/LIPIcs.SoCG.2021.17},
volume = {189},
year = {2021},
}
@inproceedings{9620,
abstract = {In this note, we introduce a distributed twist on the classic coupon collector problem: a set of m collectors wish to each obtain a set of n coupons; for this, they can each sample coupons uniformly at random, but can also meet in pairwise interactions, during which they can exchange coupons. By doing so, they hope to reduce the number of coupons that must be sampled by each collector in order to obtain a full set. This extension is natural when considering real-world manifestations of the coupon collector phenomenon, and has been remarked upon and studied empirically (Hayes and Hannigan 2006, Ahmad et al. 2014, Delmarcelle 2019).
We provide the first theoretical analysis for such a scenario. We find that “coupon collecting with friends” can indeed significantly reduce the number of coupons each collector must sample, and raises interesting connections to the more traditional variants of the problem. While our analysis is in most cases asymptotically tight, there are several open questions raised, regarding finer-grained analysis of both “coupon collecting with friends,” and of a long-studied variant of the original problem in which a collector requires multiple full sets of coupons.},
author = {Alistarh, Dan-Adrian and Davies, Peter},
booktitle = {Structural Information and Communication Complexity},
isbn = {9783030795269},
issn = {1611-3349},
location = {Wrocław, Poland},
pages = {3--12},
publisher = {Springer Nature},
title = {{Collecting coupons is faster with friends}},
doi = {10.1007/978-3-030-79527-6_1},
volume = {12810},
year = {2021},
}
@inproceedings{9200,
abstract = {Formal design of embedded and cyber-physical systems relies on mathematical modeling. In this paper, we consider the model class of hybrid automata whose dynamics are defined by affine differential equations. Given a set of time-series data, we present an algorithmic approach to synthesize a hybrid automaton exhibiting behavior that is close to the data, up to a specified precision, and changes in synchrony with the data. A fundamental problem in our synthesis algorithm is to check membership of a time series in a hybrid automaton. Our solution integrates reachability and optimization techniques for affine dynamical systems to obtain both a sufficient and a necessary condition for membership, combined in a refinement framework. The algorithm processes one time series at a time and hence can be interrupted, provide an intermediate result, and be resumed. We report experimental results demonstrating the applicability of our synthesis approach.},
author = {Garcia Soto, Miriam and Henzinger, Thomas A and Schilling, Christian},
booktitle = {HSCC '21: Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control},
isbn = {9781450383394},
keywords = {hybrid automaton, membership, system identification},
location = {Nashville, TN, United States},
pages = {2102.12734},
publisher = {Association for Computing Machinery},
title = {{Synthesis of hybrid automata with affine dynamics from time-series data}},
doi = {10.1145/3447928.3456704},
year = {2021},
}