20 results for “smooth sequences”
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This paper uses ergodic theory to study statistical properties of smooth sequences over the odd alphabet {1,3}, defining a notion of type for those sequences and proving unique ergodicity for subshift…
This paper analyzes the computational complexity of evaluating recurrent functions, showing that the complexity depends heavily on how the input offsets are encoded and the structure of the recurrence…
The paper proposes a novel method using random walks and equitable partitions to derive an inequality for the total variation distance of codes, generalizing existing bounds for finite abelian groups.
The paper introduces Singularity-aware Adam (S-Adam), a novel optimizer that stabilizes deep learning training in non-smooth loss landscapes by dynamically damping updates based on local geometric ins…
This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.
This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.
This paper presents methods for ranking and unranking permutations avoiding a pattern of length three in lexicographic or colexicographic order.
The paper proves that the reversible elementary second order cellular automaton rule 115 is periodic when started on finite initial configurations.
The paper introduces BlockGen, a blockwise sequence model, to investigate the performance of uniform-state versus masked diffusion models when generating sequences block-by-block, showing that the per…
The paper formally models structure-informed multiple sequence alignment (MSA-S) as an NP-complete optimization problem, establishing a strong computational complexity baseline for the field.
The paper uses majorization theory to analyze lattice reduction, showing that local swaps smooth the Gram-Schmidt profile and deriving variational and telescoping identities for the worst-case profile…
This paper settles the complexity of three sketching problems in graphs and distributions.
The paper systematically investigates the conditions under which linear layers in AES-like ciphers avoid related-differential structures, proving that the MDS property is necessary and identifying spe…
The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…
The paper proposes a novel set of combined cellular automaton (CA)-based pseudo-random number generators (PRNGs) that overcome the weak equidistribution issues of existing CA-based PRNGs, achieving ma…
This paper systematically analyzes binomial functions over $\mathbb{F}_{p^n}$ in characteristic 3, providing a classification and rigorous proof of specific classes of exponents that yield extremely l…
The paper introduces QuITE, a plug-and-play embedding module that uses learnable query tokens to effectively embed irregular multivariate time series data into latent representations compatible with e…
The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…
The paper introduces a software platform for generating and analyzing pseudo-random sequences (like LFSR and Mersenne Twister), demonstrating that while these classical generators are efficient, quant…