Related papers: On Multisequences and their extensions
This text is a conceptual introduction to mixed effects modeling with linguistic applications, using the R programming environment. The reader is introduced to linear modeling and assumptions, as well as to mixed effects/multilevel…
This paper is devoted to the performance study of the Linear Minimum Mean Squared Error estimator for multidimensional signals in the large dimension regime. Such an estimator is frequently encountered in wireless communications and in…
In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of…
We establish $L^p$ estimates for multilinear multipliers acting on $(n-1)$-tuples of functions on $\mathbb{R}^d$. We assume that the multiplier satisfies symbol estimates outside a linear subspace of dimension $m$. The difficulty of proving…
We investigate the problem of transforming an input sequence into a high-dimensional output sequence in order to transcribe polyphonic audio music into symbolic notation. We introduce a probabilistic model based on a recurrent neural…
We study the extension estimates for paraboloids in d-dimensional vector spaces over finite fields F_q with q elements. We use the connection between L^2 based restriction estimates and L^p\to L^r extension estimates for paraboloids. As a…
Type theories with multi-clocked guarded recursion provide a flexible framework for programming with coinductive types encoding productivity in types. Combining this with solutions to general guarded domain equations one can also construct…
We use the concept of the half of a lower-triangular matrix to define a transformation on integer sequences. We explore the properties of this transformation, including in some cases a study of the Hankel transform of the transformed…
Despite the great success of large language models (LLMs), efficiently controlling the length of the output sequence still remains a challenge. In this paper, we propose Hansel, an efficient framework for length control in LLMs without…
Nonlinear complexity, as an important measure for assessing the randomness of sequences, is defined as the length of the shortest feedback shift registers that can generate a given sequence. In this paper, the structure of n-periodic binary…
Short fixed-length inputs are the main bottleneck of deep learning methods in long time-series forecasting tasks. Prolonging input length causes overfitting, rapidly deteriorating accuracy. Our research indicates that the overfitting is a…
In a multiplex network, a set of nodes is connected by different types of interactions, each represented as a separate layer within the network. Multiplexes have emerged as a key instrument for modeling large-scale complex systems, due to…
We show that the expected value for the linear complexity of $m$-multisequences of length $n$ is E_n^{(m)} = n m/(m+1) + O(1).
The authors recently introduced so-called Vandermonde nets. These digital nets share properties with the well-known polynomial lattices. For example, both can be constructed via component-by-component search algorithms. A striking…
Sequence models, and particularly Linear Recurrent Neural Networks (LRNNs) of the form $\mathbf{h}_{k+1} = \mathbf{W} \mathbf{h}_{k} + \mathbf{y}_k + \mathbf{b}$, are widely applicable in time-series analysis for dynamical systems, yet, as…
This paper studies the high-dimensional mixed linear regression (MLR) where the output variable comes from one of the two linear regression models with an unknown mixing proportion and an unknown covariance structure of the random…
A q-ary linear code of dimension k is called a maximum weight spectrum (MWS) code if it has the maximum possible number (viz. (q^k-1)/(q-1)) of different non-zero weights. We construct MWS codes from quasi-minimal codes, thus obtaining of…
Willems' fundamental lemma enables a trajectory-based characterization of linear systems through data-based Hankel matrices. However, in the presence of measurement noise, we ask: Is this noisy Hankel-based model expressive enough to…
L\"uroth series, like regular continued fractions, provide an interesting identification of real numbers with infinite sequences of integers. These sequences give deep arithmetic and measure-theoretic properties of subsets of numbers…
Given a finite-dimensional vector space $V$ over the finite field $\mathbb{F}_q$ and a subspace $W$ of $V$, we consider the problem of counting linear transformations $T:W\to V$ which have prescribed invariant factors. The case $W=V$ is a…