Related papers: Special orientable sequences
In this paper we give constructions for infinite sequences of finite non-linear locally recoverable codes $\mathcal C\subseteq \prod\limits^N_{i=1}\mathbb F_{q_i}$ over a product of finite fields arising from basis expansions in algebraic…
Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector…
Orthogonal designs are fundamental mathematical notions used in the construction of space time block codes for wireless transmissions. Designs have two important parameters, the rate and the decoding delay; the main problem of the theory is…
One of the important applications of Golay complementary sets (GCSs) is the reduction of peak-to-mean envelope power ratio (PMEPR) in orthogonal frequency division multiplexing (OFDM) systems. OFDM has played a major role in modern wireless…
To increase the information capacity of DNA storage, composite DNA letters were introduced. We propose a novel channel model for composite DNA in which composite sequences are decomposed into ordered standard non-composite sequences. The…
Sequence memory is an essential attribute of natural and artificial intelligence that enables agents to encode, store, and retrieve complex sequences of stimuli and actions. Computational models of sequence memory have been proposed where…
Probabilistic message-passing algorithms are developed for routing transmissions in multi-wavelength optical communication networks, under node and edge-disjoint routing constraints and for various objective functions. Global routing…
Cyclic codes over finite fields are widely implemented in data storage systems, communication systems, and consumer electronics, as they have very efficient encoding and decoding algorithms. They are also important in theory, as they are…
We study the problem of modeling a binary operation that satisfies some algebraic requirements. We first construct a neural network architecture for Abelian group operations and derive a universal approximation property. Then, we extend it…
The paper contains two natural constructions of extreme hyperspace selections generated by special ordinal decompositions of the underlying space. These constructions are very efficient not only in simplifying arguments but also in…
We present a new recursive generation algorithm for prefix normal words. These are binary strings with the property that no substring has more 1s than the prefix of the same length. The new algorithm uses two operations on binary strings,…
The partial sums of integer sequences that count the occurrences of a specific pattern in the binary expansion of positive integers have been investigated by different authors since the 1950s. In this note, we introduce generalized pattern…
Optimal Transport has recently gained interest in machine learning for applications ranging from domain adaptation, sentence similarities to deep learning. Yet, its ability to capture frequently occurring structure beyond the "ground…
Evolutionary algorithms are wildly used in unmanned aerial vehicle path planning for their flexibility and effectiveness. Nevertheless, they are so sensitive to the change of environment that can't adapt to all scenarios. Due to this…
The problem of predicting a sequence $x_1,x_2,...$ generated by a discrete source with unknown statistics is considered. Each letter $x_{t+1}$ is predicted using information on the word $x_1x_2... x_t$ only. In fact, this problem is a…
This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…
Representing visual data using compact binary codes is attracting increasing attention as binary codes are used as direct indices into hash table(s) for fast non-exhaustive search. Recent methods show that ranking binary codes using…
Discrete structures are currently second-class in differentiable programming. Since functions over discrete structures lack overt derivatives, differentiable programs do not differentiate through them and limit where they can be used. For…
A bi-level optimization framework (BiOPT) was proposed in [3] for convex composite optimization, which is a generalization of bi-level unconstrained minimization framework (BLUM) given in [20]. In this continuation paper, we introduce a…
The brain is targeted for processing temporal sequence information. It remains largely unclear how the brain learns to store and retrieve sequence memories. Here, we study how recurrent networks of binary neurons learn sequence attractors…