@inproceedings{7966,
abstract = {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.},
author = {Auerbach, Benedikt and Giacon, Federico and Kiltz, Eike},
booktitle = {Advances in Cryptology – EUROCRYPT 2020},
isbn = {9783030457266},
issn = {0302-9743},
pages = {475--506},
publisher = {Springer Nature},
title = {{Everybody’s a target: Scalability in public-key encryption}},
doi = {10.1007/978-3-030-45727-3_16},
volume = {12107},
year = {2020},
}
@inproceedings{6163,
abstract = {We propose a new non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. Every grid point, each represented by integer 3-coordinates, corresponds to rhombic dodecahedron centroid. Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. A characterization of a 3D digital sphere with relevant topological features is proposed as well with the help of a 48 symmetry that comes with the new coordinate system.},
author = {Biswas, Ranita and Largeteau-Skapin, Gaëlle and Zrour, Rita and Andres, Eric},
booktitle = {Lecture Notes in Computer Science},
isbn = {9783662464465},
issn = {0302-9743},
location = {Marne-la-Vallée, France},
pages = {27--37},
publisher = {Springer Berlin Heidelberg},
title = {{Rhombic dodecahedron grid—coordinate system and 3D digital object definitions}},
doi = {10.1007/978-3-030-14085-4_3},
volume = {11414},
year = {2019},
}
@inproceedings{7147,
abstract = {The expression of a gene is characterised by its transcription factors and the function processing them. If the transcription factors are not affected by gene products, the regulating function is often represented as a combinational logic circuit, where the outputs (product) are determined by current input values (transcription factors) only, and are hence independent on their relative arrival times. However, the simultaneous arrival of transcription factors (TFs) in genetic circuits is a strong assumption, given that the processes of transcription and translation of a gene into a protein introduce intrinsic time delays and that there is no global synchronisation among the arrival times of different molecular species at molecular targets.
In this paper, we construct an experimentally implementable genetic circuit with two inputs and a single output, such that, in presence of small delays in input arrival, the circuit exhibits qualitatively distinct observable phenotypes. In particular, these phenotypes are long lived transients: they all converge to a single value, but so slowly, that they seem stable for an extended time period, longer than typical experiment duration. We used rule-based language to prototype our circuit, and we implemented a search for finding the parameter combinations raising the phenotypes of interest.
The behaviour of our prototype circuit has wide implications. First, it suggests that GRNs can exploit event timing to create phenotypes. Second, it opens the possibility that GRNs are using event timing to react to stimuli and memorise events, without explicit feedback in regulation. From the modelling perspective, our prototype circuit demonstrates the critical importance of analysing the transient dynamics at the promoter binding sites of the DNA, before applying rapid equilibrium assumptions.},
author = {Guet, Calin C and Henzinger, Thomas A and Igler, Claudia and Petrov, Tatjana and Sezgin, Ali},
booktitle = {17th International Conference on Computational Methods in Systems Biology},
isbn = {9783030313036},
issn = {1611-3349},
location = {Trieste, Italy},
pages = {155--187},
publisher = {Springer Nature},
title = {{Transient memory in gene regulation}},
doi = {10.1007/978-3-030-31304-3_9},
volume = {11773},
year = {2019},
}
@inproceedings{7159,
abstract = {Cyber-physical systems (CPS) and the Internet-of-Things (IoT) result in a tremendous amount of generated, measured and recorded time-series data. Extracting temporal segments that encode patterns with useful information out of these huge amounts of data is an extremely difficult problem. We propose shape expressions as a declarative formalism for specifying, querying and extracting sophisticated temporal patterns from possibly noisy data. Shape expressions are regular expressions with arbitrary (linear, exponential, sinusoidal, etc.) shapes with parameters as atomic predicates and additional constraints on these parameters. We equip shape expressions with a novel noisy semantics that combines regular expression matching semantics with statistical regression. We characterize essential properties of the formalism and propose an efficient approximate shape expression matching procedure. We demonstrate the wide applicability of this technique on two case studies. },
author = {Ničković, Dejan and Qin, Xin and Ferrere, Thomas and Mateis, Cristinel and Deshmukh, Jyotirmoy},
booktitle = {19th International Conference on Runtime Verification},
isbn = {9783030320782},
issn = {0302-9743},
location = {Porto, Portugal},
pages = {292--309},
publisher = {Springer Nature},
title = {{Shape expressions for specifying and extracting signal features}},
doi = {10.1007/978-3-030-32079-9_17},
volume = {11757},
year = {2019},
}
@inbook{6726,
abstract = {Randomness is an essential part of any secure cryptosystem, but many constructions rely on distributions that are not uniform. This is particularly true for lattice based cryptosystems, which more often than not make use of discrete Gaussian distributions over the integers. For practical purposes it is crucial to evaluate the impact that approximation errors have on the security of a scheme to provide the best possible trade-off between security and performance. Recent years have seen surprising results allowing to use relatively low precision while maintaining high levels of security. A key insight in these results is that sampling a distribution with low relative error can provide very strong security guarantees. Since floating point numbers provide guarantees on the relative approximation error, they seem a suitable tool in this setting, but it is not obvious which sampling algorithms can actually profit from them. While previous works have shown that inversion sampling can be adapted to provide a low relative error (Pöppelmann et al., CHES 2014; Prest, ASIACRYPT 2017), other works have called into question if this is possible for other sampling techniques (Zheng et al., Eprint report 2018/309). In this work, we consider all sampling algorithms that are popular in the cryptographic setting and analyze the relationship of floating point precision and the resulting relative error. We show that all of the algorithms either natively achieve a low relative error or can be adapted to do so.},
author = {Walter, Michael},
booktitle = {Progress in Cryptology – AFRICACRYPT 2019},
editor = {Buchmann, J and Nitaj, A and Rachidi, T},
isbn = {9783030236953},
issn = {0302-9743},
location = {Rabat, Morocco},
pages = {157--180},
publisher = {Springer Nature},
title = {{Sampling the integers with low relative error}},
doi = {10.1007/978-3-030-23696-0_9},
volume = {11627},
year = {2019},
}
@inproceedings{6942,
abstract = {Graph games and Markov decision processes (MDPs) are standard models in reactive synthesis and verification of probabilistic systems with nondeterminism. The class of 𝜔 -regular winning conditions; e.g., safety, reachability, liveness, parity conditions; provides a robust and expressive specification formalism for properties that arise in analysis of reactive systems. The resolutions of nondeterminism in games and MDPs are represented as strategies, and we consider succinct representation of such strategies. The decision-tree data structure from machine learning retains the flavor of decisions of strategies and allows entropy-based minimization to obtain succinct trees. However, in contrast to traditional machine-learning problems where small errors are allowed, for winning strategies in graph games and MDPs no error is allowed, and the decision tree must represent the entire strategy. In this work we propose decision trees with linear classifiers for representation of strategies in graph games and MDPs. We have implemented strategy representation using this data structure and we present experimental results for problems on graph games and MDPs, which show that this new data structure presents a much more efficient strategy representation as compared to standard decision trees.},
author = {Ashok, Pranav and Brázdil, Tomáš and Chatterjee, Krishnendu and Křetínský, Jan and Lampert, Christoph and Toman, Viktor},
booktitle = {16th International Conference on Quantitative Evaluation of Systems},
isbn = {9783030302801},
issn = {0302-9743},
location = {Glasgow, United Kingdom},
pages = {109--128},
publisher = {Springer Nature},
title = {{Strategy representation by decision trees with linear classifiers}},
doi = {10.1007/978-3-030-30281-8_7},
volume = {11785},
year = {2019},
}
@inbook{7453,
abstract = {We illustrate the ingredients of the state-of-the-art of model-based approach for the formal design and verification of cyber-physical systems. To capture the interaction between a discrete controller and its continuously evolving environment, we use the formal models of timed and hybrid automata. We explain the steps of modeling and verification in the tools Uppaal and SpaceEx using a case study based on a dual-chamber implantable pacemaker monitoring a human heart. We show how to design a model as a composition of components, how to construct models at varying levels of detail, how to establish that one model is an abstraction of another, how to specify correctness requirements using temporal logic, and how to verify that a model satisfies a logical requirement.},
author = {Alur, Rajeev and Giacobbe, Mirco and Henzinger, Thomas A and Larsen, Kim G. and Mikučionis, Marius},
booktitle = {Computing and Software Science},
editor = {Steffen, Bernhard and Woeginger, Gerhard},
isbn = {9783319919072},
issn = {0302-9743},
pages = {452--477},
publisher = {Springer Nature},
title = {{Continuous-time models for system design and analysis}},
doi = {10.1007/978-3-319-91908-9_22},
volume = {10000},
year = {2019},
}
@inproceedings{7411,
abstract = {Proofs of sequential work (PoSW) are proof systems where a prover, upon receiving a statement χ and a time parameter T computes a proof ϕ(χ,T) which is efficiently and publicly verifiable. The proof can be computed in T sequential steps, but not much less, even by a malicious party having large parallelism. A PoSW thus serves as a proof that T units of time have passed since χ
was received.
PoSW were introduced by Mahmoody, Moran and Vadhan [MMV11], a simple and practical construction was only recently proposed by Cohen and Pietrzak [CP18].
In this work we construct a new simple PoSW in the random permutation model which is almost as simple and efficient as [CP18] but conceptually very different. Whereas the structure underlying [CP18] is a hash tree, our construction is based on skip lists and has the interesting property that computing the PoSW is a reversible computation.
The fact that the construction is reversible can potentially be used for new applications like constructing proofs of replication. We also show how to “embed” the sloth function of Lenstra and Weselowski [LW17] into our PoSW to get a PoSW where one additionally can verify correctness of the output much more efficiently than recomputing it (though recent constructions of “verifiable delay functions” subsume most of the applications this construction was aiming at).},
author = {Abusalah, Hamza M and Kamath Hosdurg, Chethan and Klein, Karen and Pietrzak, Krzysztof Z and Walter, Michael},
booktitle = {Advances in Cryptology – EUROCRYPT 2019},
isbn = {9783030176556},
issn = {0302-9743},
location = {Darmstadt, Germany},
pages = {277--291},
publisher = {Springer International Publishing},
title = {{Reversible proofs of sequential work}},
doi = {10.1007/978-3-030-17656-3_10},
volume = {11477},
year = {2019},
}
@inproceedings{6822,
abstract = {In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the qualitative winner or quantitative payoff of the game. In bidding games, in each turn, we hold an auction between the two players to determine which player moves the token. Bidding games have largely been studied with concrete bidding mechanisms that are variants of a first-price auction: in each turn both players simultaneously submit bids, the higher
bidder moves the token, and pays his bid to the lower bidder in Richman bidding, to the bank in poorman bidding, and in taxman bidding, the bid is split between the other player and the bank according to a predefined constant factor. Bidding games are deterministic games. They have an intriguing connection with a fragment of stochastic games called
randomturn games. We study, for the first time, a combination of bidding games with probabilistic behavior; namely, we study bidding games that are played on Markov decision processes, where the players bid for the right to choose the next action, which determines the probability distribution according to which the next vertex is chosen. We study parity and meanpayoff bidding games on MDPs and extend results from the deterministic bidding setting to the probabilistic one.},
author = {Avni, Guy and Henzinger, Thomas A and Ibsen-Jensen, Rasmus and Novotny, Petr},
booktitle = { Proceedings of the 13th International Conference of Reachability Problems},
isbn = {978-303030805-6},
issn = {0302-9743},
location = {Brussels, Belgium},
pages = {1--12},
publisher = {Springer},
title = {{Bidding games on Markov decision processes}},
doi = {10.1007/978-3-030-30806-3_1},
volume = {11674},
year = {2019},
}
@inproceedings{6462,
abstract = {A controller is a device that interacts with a plant. At each time point,it reads the plant’s state and issues commands with the goal that the plant oper-ates optimally. Constructing optimal controllers is a fundamental and challengingproblem. Machine learning techniques have recently been successfully applied totrain controllers, yet they have limitations. Learned controllers are monolithic andhard to reason about. In particular, it is difficult to add features without retraining,to guarantee any level of performance, and to achieve acceptable performancewhen encountering untrained scenarios. These limitations can be addressed bydeploying quantitative run-timeshieldsthat serve as a proxy for the controller.At each time point, the shield reads the command issued by the controller andmay choose to alter it before passing it on to the plant. We show how optimalshields that interfere as little as possible while guaranteeing a desired level ofcontroller performance, can be generated systematically and automatically usingreactive synthesis. First, we abstract the plant by building a stochastic model.Second, we consider the learned controller to be a black box. Third, we mea-surecontroller performanceandshield interferenceby two quantitative run-timemeasures that are formally defined using weighted automata. Then, the problemof constructing a shield that guarantees maximal performance with minimal inter-ference is the problem of finding an optimal strategy in a stochastic2-player game“controller versus shield” played on the abstract state space of the plant with aquantitative objective obtained from combining the performance and interferencemeasures. We illustrate the effectiveness of our approach by automatically con-structing lightweight shields for learned traffic-light controllers in various roadnetworks. The shields we generate avoid liveness bugs, improve controller per-formance in untrained and changing traffic situations, and add features to learnedcontrollers, such as giving priority to emergency vehicles.},
author = {Avni, Guy and Bloem, Roderick and Chatterjee, Krishnendu and Henzinger, Thomas A and Konighofer, Bettina and Pranger, Stefan},
booktitle = {31st International Conference on Computer-Aided Verification},
isbn = {9783030255398},
issn = {0302-9743},
location = {New York, NY, United States},
pages = {630--649},
publisher = {Springer},
title = {{Run-time optimization for learned controllers through quantitative games}},
doi = {10.1007/978-3-030-25540-4_36},
volume = {11561},
year = {2019},
}
@inproceedings{6493,
abstract = {We present two algorithmic approaches for synthesizing linear hybrid automata from experimental data. Unlike previous approaches, our algorithms work without a template and generate an automaton with nondeterministic guards and invariants, and with an arbitrary number and topology of modes. They thus construct a succinct model from the data and provide formal guarantees. In particular, (1) the generated automaton can reproduce the data up to a specified tolerance and (2) the automaton is tight, given the first guarantee. Our first approach encodes the synthesis problem as a logical formula in the theory of linear arithmetic, which can then be solved by an SMT solver. This approach minimizes the number of modes in the resulting model but is only feasible for limited data sets. To address scalability, we propose a second approach that does not enforce to find a minimal model. The algorithm constructs an initial automaton and then iteratively extends the automaton based on processing new data. Therefore the algorithm is well-suited for online and synthesis-in-the-loop applications. The core of the algorithm is a membership query that checks whether, within the specified tolerance, a given data set can result from the execution of a given automaton. We solve this membership problem for linear hybrid automata by repeated reachability computations. We demonstrate the effectiveness of the algorithm on synthetic data sets and on cardiac-cell measurements.},
author = {Garcia Soto, Miriam and Henzinger, Thomas A and Schilling, Christian and Zeleznik, Luka},
booktitle = {31st International Conference on Computer-Aided Verification},
isbn = {9783030255398},
issn = {0302-9743},
keywords = {Synthesis, Linear hybrid automaton, Membership},
location = {New York City, NY, USA},
pages = {297--314},
publisher = {Springer},
title = {{Membership-based synthesis of linear hybrid automata}},
doi = {10.1007/978-3-030-25540-4_16},
volume = {11561},
year = {2019},
}
@inproceedings{6482,
abstract = {Computer vision systems for automatic image categorization have become accurate and reliable enough that they can run continuously for days or even years as components of real-world commercial applications. A major open problem in this context, however, is quality control. Good classification performance can only be expected if systems run under the specific conditions, in particular data distributions, that they were trained for. Surprisingly, none of the currently used deep network architectures have a built-in functionality that could detect if a network operates on data from a distribution it was not trained for, such that potentially a warning to the human users could be triggered. In this work, we describe KS(conf), a procedure for detecting such outside of specifications (out-of-specs) operation, based on statistical testing of the network outputs. We show by extensive experiments using the ImageNet, AwA2 and DAVIS datasets on a variety of ConvNets architectures that KS(conf) reliably detects out-of-specs situations. It furthermore has a number of properties that make it a promising candidate for practical deployment: it is easy to implement, adds almost no overhead to the system, works with all networks, including pretrained ones, and requires no a priori knowledge of how the data distribution could change. },
author = {Sun, Rémy and Lampert, Christoph},
isbn = {9783030129385},
issn = {0302-9743},
location = {Stuttgart, Germany},
pages = {244--259},
publisher = {Springer Nature},
title = {{KS(conf): A light-weight test if a ConvNet operates outside of Its specifications}},
doi = {10.1007/978-3-030-12939-2_18},
volume = {11269},
year = {2019},
}
@inproceedings{6164,
abstract = {In this paper, we propose an algorithm to build discrete spherical shell having integer center and real-valued inner and outer radii on the face-centered cubic (FCC) grid. We address the problem by mapping it to a 2D scenario and building the shell layer by layer on hexagonal grids with additive manufacturing in mind. The layered hexagonal grids get shifted according to need as we move from one layer to another and forms the FCC grid in 3D. However, we restrict our computation strictly to 2D in order to utilize symmetry and simplicity.},
author = {Koshti, Girish and Biswas, Ranita and Largeteau-Skapin, Gaëlle and Zrour, Rita and Andres, Eric and Bhowmick, Partha},
booktitle = {Lecture Notes in Computer Science},
isbn = {9783030052874},
issn = {0302-9743},
location = {Porto, Portugal},
pages = {82--96},
publisher = {Springer},
title = {{Sphere construction on the FCC grid interpreted as layered hexagonal grids in 3D}},
doi = {10.1007/978-3-030-05288-1_7},
volume = {11255},
year = {2018},
}
@inproceedings{6941,
abstract = {Bitcoin has become the most successful cryptocurrency ever deployed, and its most distinctive feature is that it is decentralized. Its underlying protocol (Nakamoto consensus) achieves this by using proof of work, which has the drawback that it causes the consumption of vast amounts of energy to maintain the ledger. Moreover, Bitcoin mining dynamics have become less distributed over time.
Towards addressing these issues, we propose SpaceMint, a cryptocurrency based on proofs of space instead of proofs of work. Miners in SpaceMint dedicate disk space rather than computation. We argue that SpaceMint’s design solves or alleviates several of Bitcoin’s issues: most notably, its large energy consumption. SpaceMint also rewards smaller miners fairly according to their contribution to the network, thus incentivizing more distributed participation.
This paper adapts proof of space to enable its use in cryptocurrency, studies the attacks that can arise against a Bitcoin-like blockchain that uses proof of space, and proposes a new blockchain format and transaction types to address these attacks. Our prototype shows that initializing 1 TB for mining takes about a day (a one-off setup cost), and miners spend on average just a fraction of a second per block mined. Finally, we provide a game-theoretic analysis modeling SpaceMint as an extensive game (the canonical game-theoretic notion for games that take place over time) and show that this stylized game satisfies a strong equilibrium notion, thereby arguing for SpaceMint ’s stability and consensus.},
author = {Park, Sunoo and Kwon, Albert and Fuchsbauer, Georg and Gazi, Peter and Alwen, Joel F and Pietrzak, Krzysztof Z},
booktitle = {22nd International Conference on Financial Cryptography and Data Security},
isbn = {9783662583869},
issn = {0302-9743},
location = {Nieuwpoort, Curacao},
pages = {480--499},
publisher = {Springer Nature},
title = {{SpaceMint: A cryptocurrency based on proofs of space}},
doi = {10.1007/978-3-662-58387-6_26},
volume = {10957},
year = {2018},
}
@inproceedings{5801,
abstract = {Space filling circles and spheres have various applications in mathematical imaging and physical modeling. In this paper, we first show how the thinnest (i.e., 2-minimal) model of digital sphere can be augmented to a space filling model by fixing certain “simple voxels” and “filler voxels” associated with it. Based on elementary number-theoretic properties of such voxels, we design an efficient incremental algorithm for generation of these space filling spheres with successively increasing radius. The novelty of the proposed technique is established further through circular space filling on 3D digital plane. As evident from a preliminary set of experimental result, this can particularly be useful for parallel computing of 3D Voronoi diagrams in the digital space.},
author = {Dwivedi, Shivam and Gupta, Aniket and Roy, Siddhant and Biswas, Ranita and Bhowmick, Partha},
isbn = {9783319662718},
issn = {0302-9743},
location = {Vienna, Austria},
pages = {347--359},
publisher = {Springer International Publishing},
title = {{Fast and Efficient Incremental Algorithms for Circular and Spherical Propagation in Integer Space}},
doi = {10.1007/978-3-319-66272-5_28},
volume = {10502},
year = {2017},
}
@inproceedings{5802,
abstract = {This papers introduces a definition of digital primitives based on focal points and weighted distances (with positive weights). The proposed definition is applicable to general dimensions and covers in its gamut various regular curves and surfaces like circles, ellipses, digital spheres and hyperspheres, ellipsoids and k-ellipsoids, Cartesian k-ovals, etc. Several interesting properties are presented for this class of digital primitives such as space partitioning, topological separation, and connectivity properties. To demonstrate further the potential of this new way of defining digital primitives, we propose, as extension, another class of digital conics defined by focus-directrix combination.},
author = {Andres, Eric and Biswas, Ranita and Bhowmick, Partha},
isbn = {9783319662718},
issn = {0302-9743},
location = {Vienna, Austria},
pages = {388--398},
publisher = {Springer International Publishing},
title = {{Digital Primitives Defined by Weighted Focal Set}},
doi = {10.1007/978-3-319-66272-5_31},
volume = {10502},
year = {2017},
}
@inbook{5803,
abstract = {Different distance metrics produce Voronoi diagrams with different properties. It is a well-known that on the (real) 2D plane or even on any 3D plane, a Voronoi diagram (VD) based on the Euclidean distance metric produces convex Voronoi regions. In this paper, we first show that this metric produces a persistent VD on the 2D digital plane, as it comprises digitally convex Voronoi regions and hence correctly approximates the corresponding VD on the 2D real plane. Next, we show that on a 3D digital plane D, the Euclidean metric spanning over its voxel set does not guarantee a digital VD which is persistent with the real-space VD. As a solution, we introduce a novel concept of functional-plane-convexity, which is ensured by the Euclidean metric spanning over the pedal set of D. Necessary proofs and some visual result have been provided to adjudge the merit and usefulness of the proposed concept.},
author = {Biswas, Ranita and Bhowmick, Partha},
booktitle = {Combinatorial image analysis},
isbn = {9783319591070},
issn = {0302-9743},
location = {Plovdiv, Bulgaria},
pages = {93--104},
publisher = {Springer International Publishing},
title = {{Construction of Persistent Voronoi Diagram on 3D Digital Plane}},
doi = {10.1007/978-3-319-59108-7_8},
volume = {10256},
year = {2017},
}
@inbook{5805,
author = {Sen, Nabhasmita and Biswas, Ranita and Bhowmick, Partha},
booktitle = {Computational Topology in Image Context},
isbn = {9783319394404},
issn = {0302-9743},
location = {Marseille, France},
pages = {253--264},
publisher = {Springer International Publishing},
title = {{On Some Local Topological Properties of Naive Discrete Sphere}},
doi = {10.1007/978-3-319-39441-1_23},
volume = {9667},
year = {2016},
}
@inproceedings{5806,
abstract = {Although the concept of functional plane for naive plane is studied and reported in the literature in great detail, no similar study is yet found for naive sphere. This article exposes the first study in this line, opening up further prospects of analyzing the topological properties of sphere in the discrete space. We show that each quadraginta octant Q of a naive sphere forms a bijection with its projected pixel set on a unique coordinate plane, which thereby serves as the functional plane of Q, and hence gives rise to merely mono-jumps during back projection. The other two coordinate planes serve as para-functional and dia-functional planes for Q, as the former is ‘mono-jumping’ but not bijective, whereas the latter holds neither of the two. Owing to this, the quadraginta octants form symmetry groups and subgroups with equivalent jump conditions. We also show a potential application in generating a special class of discrete 3D circles based on back projection and jump bridging by Steiner voxels. A circle in this class possesses 4-symmetry, uniqueness, and bounded distance from the underlying real sphere and real plane.},
author = {Biswas, Ranita and Bhowmick, Partha},
booktitle = {Discrete Geometry for Computer Imagery},
isbn = {9783319323596},
issn = {0302-9743},
location = {Nantes, France},
pages = {256--267},
publisher = {Springer International Publishing},
title = {{On Functionality of Quadraginta Octants of Naive Sphere with Application to Circle Drawing}},
doi = {10.1007/978-3-319-32360-2_20},
volume = {9647},
year = {2016},
}
@inbook{5809,
abstract = {A discrete spherical circle is a topologically well-connected 3D circle in the integer space, which belongs to a discrete sphere as well as a discrete plane. It is one of the most important 3D geometric primitives, but has not possibly yet been studied up to its merit. This paper is a maiden exposition of some of its elementary properties, which indicates a sense of its profound theoretical prospects in the framework of digital geometry. We have shown how different types of discretization can lead to forbidden and admissible classes, when one attempts to define the discretization of a spherical circle in terms of intersection between a discrete sphere and a discrete plane. Several fundamental theoretical results have been presented, the algorithm for construction of discrete spherical circles has been discussed, and some test results have been furnished to demonstrate its practicality and usefulness.},
author = {Biswas, Ranita and Bhowmick, Partha and Brimkov, Valentin E.},
booktitle = {Combinatorial image analysis},
isbn = {9783319261447},
issn = {0302-9743},
location = {Kolkata, India},
pages = {86--100},
publisher = {Springer},
title = {{On the Connectivity and Smoothness of Discrete Spherical Circles}},
doi = {10.1007/978-3-319-26145-4_7},
volume = {9448},
year = {2016},
}