Related papers: Covering Point Patterns
A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most…
Recently, Transformer-based encoder-decoder models have demonstrated strong performance in multilingual speech recognition. However, the decoder's autoregressive nature and large size introduce significant bottlenecks during inference.…
Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing…
We study a two-parameter family of one-dimensional maps and related (a,b)-continued fractions suggested for consideration by Don Zagier. We prove that the associated natural extension maps have attractors with finite rectangular structure…
We study the univariate moment problem of piecewise-constant density functions on the interval $[0,1]$ and its consequences for an inference problem in population genetics. We show that, up to closure, any collection of $n$ moments is…
Patterns, which are collections of elements arranged in regular or near-regular arrangements, are an important graphic art form and widely used due to their elegant simplicity and aesthetic appeal. When a pattern is encoded as a flat image…
We refine the bit complexity analysis of an algorithm for the computation of at least one point per connected component of a smooth real algebraic set, yielding exponential speedup (with respect to the number of variables) compared to prior…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
This paper investigates variable-length stop-feedback codes for memoryless channels in point-to-point, multiple access, and random access communication scenarios. The proposed codes employ $L$ decoding times $n_1, n_2, \dots, n_L$ for the…
For many measure preserving dynamical systems $(\Omega,T,m)$ the successive hitting times to a small set is well approximated by a Poisson process on the real line. In this work we define a new process obtained from recording not only the…
We study data structure problems related to document indexing and pattern matching queries and our main contribution is to show that the pointer machine model of computation can be extremely useful in proving high and unconditional lower…
We study learning algorithms that are restricted to using a small amount of information from their input sample. We introduce a category of learning algorithms we term $d$-bit information learners, which are algorithms whose output conveys…
In the successive refinement problem, a fixed-length sequence emitted from an information source is encoded into two codewords by two encoders in order to give two reconstructions of the sequence. One of two reconstructions is obtained by…
Biological and machine pattern recognition systems face a common challenge: Given sensory data about an unknown object, classify the object by comparing the sensory data with a library of internal representations stored in memory. In many…
We study the witness-counting problem: given a set of vectors $V$ in the $d$-dimensional vector space over $\mathbb{F}_2$, a target vector $t$, and an integer $k$, count all ways to sum-up exactly $k$ different vectors from $V$ to reach…
PointNet, which is the widely used point-wise embedding method and known as a universal approximator for continuous set functions, can process one million points per second. Nevertheless, real-time inference for the recent development of…
Pebble transducers are nested two-way transducers which can drop marks (named "pebbles") on their input word. Such machines can compute functions whose output size is polynomial in the size of their input. They can be seen as simple…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
The increasing demand for accurate representations of 3D scenes, combined with immersive technologies has led point clouds to extensive popularity. However, quality point clouds require a large amount of data and therefore the need for…
We propose new estimates for the frontier of a set of points. They are defined as kernel estimates covering all the points and whose associated support is of smallest surface. The estimates are written as linear combinatio- ns of kernel…