An Optimal Algorithm for Tiling the Plane with a Translated Polyomino

We give a $O(n)$-time algorithm for determining whether translations of a polyomino with $n$ edges can tile the plane. The algorithm is also a $O(n)$-time algorithm for enumerating all such tilings that are also regular, and we prove that at most $\Theta(n)$ such tilings exist.Comment: In proceedings of ISAAC 201

Some Results on Sprout

Abstract. Sprout is a lightweight stream cipher proposed by Armknecht and Mikhalev at FSE 2015. It has a Grain-like structure with two State Registers of size 40 bits each, which is exactly half the state size of Grain v1. In spite of this, the cipher does not appear to lose in security against generic Time-Memory-Data Tradeoff attacks due to the novelty of its design. In this paper, we first present improved results on Key Recovery with partial knowledge of the internal state. We show that if 50 of the 80 bits of the internal state are guessed then the remaining bits along with the Secret Key can be found in a reasonable time using a SAT solver. Thereafter we show that it is possible to perform a distinguishing attack on the full Sprout stream cipher in the multiple IV setting using around 240 randomly chosen IVs on an average. The attack requires around 248 bits of memory. Thereafter we will show that for every Secret Key, there exist around 230 IVs for which the LFSR used in Sprout enters the all zero state during the Keystream generating phase. Using this observation, we will first show that it is possible to enumerate Key-IV pairs that produce keystream bits with period as small as 80. We will then outline a simple Key recovery attack that takes time equivalent to 266.7 encryptions with negligible memory requirement. This although is not the best attack reported against this cipher in terms of the Time complexity, it is the best in terms of the memory required to perform the attack

Hybrid Simulation Safety: Limbos and Zero Crossings

Physical systems can be naturally modeled by combining continuous and discrete models. Such hybrid models may simplify the modeling task of complex system, as well as increase simulation performance. Moreover, modern simulation engines can often efficiently generate simulation traces, but how do we know that the simulation results are correct? If we detect an error, is the error in the model or in the simulation itself? This paper discusses the problem of simulation safety, with the focus on hybrid modeling and simulation. In particular, two key aspects are studied: safe zero-crossing detection and deterministic hybrid event handling. The problems and solutions are discussed and partially implemented in Modelica and Ptolemy II

Optimal skeleton huffman trees revisited

A skeleton Huffman tree is a Huffman tree in which all disjoint maximal perfect subtrees are shrunk into leaves. Skeleton Huffman trees, besides saving storage space, are also used for faster decoding and for speeding up Huffman-shaped wavelet trees. In 2017 Klein et al. introduced an optimal skeleton tree: for given symbol frequencies, it has the least number of nodes among all optimal prefix-free code trees (not necessarily Huffman’s) with shrunk perfect subtrees. Klein et al. described a simple algorithm that, for fixed codeword lengths, finds a skeleton tree with the least number of nodes; with this algorithm one can process each set of optimal codeword lengths to find an optimal skeleton tree. However, there are exponentially many such sets in the worst case. We describe an (formula presented)-time algorithm that, given n symbol frequencies, constructs an optimal skeleton tree and its corresponding optimal code. © Springer Nature Switzerland AG 2020.Supported by the Russian Science Foundation (RSF), project 18-71-00002

A new multistage lattice vector quantization with adaptive subband thresholding for image compression

Lattice vector quantization (LVQ) reduces coding complexity and computation due to its regular structure. A new multistage LVQ (MLVQ) using an adaptive subband thresholding technique is presented and applied to image compression. The technique concentrates on reducing the quantization error of the quantized vectors by "blowing out" the residual quantization errors with an LVQ scale factor. The significant coefficients of each subband are identified using an optimum adaptive thresholding scheme for each subband. A variable length coding procedure using Golomb codes is used to compress the codebook index which produces a very efficient and fast technique for entropy coding. Experimental results using the MLVQ are shown to be significantly better than JPEG 2000 and the recent VQ techniques for various test images

Interaction of Imidazole Containing Hydroxamic Acids with Fe(III): Hydroxamate Versus Imidazole Coordination of the Ligands

Solution equilibrium studies on Fe(III) complexes formed with imidazole-4-carbohydroxamic acid (Im-4-Cha), N-Me-imidazole-4-carbohydroxamic acid (N-Me-Im-4-Cha), imidazole-4-acetohydroxamic acid (Im-4-Aha), and histidinehydroxamic acid (Hisha) have been performed by using pH-potentiometry, UV-visible spectrophotometry, EPR, ESI-MS, and H1-NMR methods. All of the obtained results demonstrate that the imidazole moiety is able to play an important role very often in the interaction with Fe(III), even if this metal ion prefers the hydroxamate chelates very much. If the imidazole moiety is in α-position to the hydroxamic one (Im-4-Cha and N-Me-Im-4-Cha) its coordination to the metal ion is indicated unambiguously by our results. Interestingly, parallel formation of (Nimidazole, Ohydroxamate), and (Ohydroxamate, Ohydroxamate) type chelates seems probable with N-Me-Im-4-Cha. The imidazole is in β-position to the hydroxamic moiety in Im-4-Aha and an intermolecular noncovalent (mainly H-bonding) interaction seems to organize the intermediate-protonated molecules in this system. Following the formation of mono- and bishydroxamato mononuclear complexes, only EPR silent species exists in the Fe(III)-Hisha system above pH 4, what suggests the rather significant “assembler activity” of the imidazole (perhaps together with the ammonium moiety)

Translation invariant extensions of finite volume measures

We investigate the following questions: Given a measure μΛ on configurations on a subset Λ of a lattice L, where a configuration is an element of ΩΛ for some fixed set Ω, does there exist a measure μ on configurations on all of L, invariant under some specified symme- try group of L, such that μΛ is its marginal on configurations on Λ? When the answer is yes, what are the properties, e.g., the entropies, of such measures? Our primary focus is the case in which L = Zd and the symmetries are the translations. For the case in which Λ is an interval in Z we give a simple necessary and sufficient condition, local translation invariance (LTI), for extendibility. For LTI measures we construct extensions having maximal entropy, which we show are Gibbs measures; this construction extends to the case in which L is the Bethe lattice. On Z we also consider extensions supported on periodic configurations, which are analyzed using de Bruijn graphs and which include the extensions with minimal entropy. When Λ ⊂ Z is not an interval, or when Λ ⊂ Zd with d > 1, the LTI condition is necessary but not sufficient for extendibility. For Zd with d > 1, extendibility is in some sense undecidable

DNA Barcode Goes Two-Dimensions: DNA QR Code Web Server

The DNA barcoding technology uses a standard region of DNA sequence for species identification and discovery. At present, “DNA barcode” actually refers to DNA sequences, which are not amenable to information storage, recognition, and retrieval. Our aim is to identify the best symbology that can represent DNA barcode sequences in practical applications. A comprehensive set of sequences for five DNA barcode markers ITS2, rbcL, matK, psbA-trnH, and CO1 was used as the test data. Fifty-three different types of one-dimensional and ten two-dimensional barcode symbologies were compared based on different criteria, such as coding capacity, compression efficiency, and error detection ability. The quick response (QR) code was found to have the largest coding capacity and relatively high compression ratio. To facilitate the further usage of QR code-based DNA barcodes, a web server was developed and is accessible at http://qrfordna.dnsalias.org. The web server allows users to retrieve the QR code for a species of interests, convert a DNA sequence to and from a QR code, and perform species identification based on local and global sequence similarities. In summary, the first comprehensive evaluation of various barcode symbologies has been carried out. The QR code has been found to be the most appropriate symbology for DNA barcode sequences. A web server has also been constructed to allow biologists to utilize QR codes in practical DNA barcoding applications