Related papers: Linear Combinations of Unordered Data Vectors
Submodular functions have been studied extensively in machine learning and data mining. In particular, the optimization of submodular functions over the integer lattice (integer submodular functions) has recently attracted much interest,…
A vector addition system (VAS) with an initial and a final marking and transition labels induces a language. In part because the reachability problem in VAS remains far from being well-understood, it is difficult to devise decision…
In the present paper the unconditional convergence and the invertibility of multipliers is investigated. Multipliers are operators created by (frame-like) analysis, multiplication by a fixed symbol, and resynthesis. Sufficient and/or…
We study safety verification for multithreaded programs with recursive parallelism (i.e. unbounded thread creation and recursion) as well as unbounded integer variables. Since the threads in each program configuration are structured in a…
Under consideration are mathematical models of heat and mass transfer. We study inverse problems of recovering lower-order coefficients in a second order parabolic equation. The coefficients are representable in the form of a finite…
Previous compact representations of permutations have focused on adding a small index on top of the plain data $<\pi(1), \pi(2),...\pi(n)>$, in order to efficiently support the application of the inverse or the iterated permutation. In this…
Permutation entropy measures the complexity of deterministic time series via a data symbolic quantization consisting of rank vectors called ordinal patterns or just permutations. The reasons for the increasing popularity of this entropy in…
Gaussian elimination answers any question about a finitely presented vector space. However, a "uniform family" of such presentations--given as generic relations among an unspecified number of generators--is susceptible to elimination only…
We revisit evaluation of logical formulas that allow both uninterpreted relations, constrained to be finite, as well as an interpreted vocabulary over an infinite domain. This formalism was denoted embedded finite model theory in the past.…
Given a primitive collection of vectors in the integer lattice, we count the number of ways it can be extended to a basis by vectors with sup-norm bounded by $T$, producing an asymptotic estimate as $T \to \infty$. This problem can be…
A set is introreducible if it can be computed by every infinite subset of itself. Such a set can be thought of as coding information very robustly. We investigate introreducible sets and related notions. Our two main results are that the…
Sets of desirable gambles constitute a quite general type of uncertainty model with an interesting geometrical interpretation. We give a general discussion of such models and their rationality criteria. We study exchangeability assessments…
Neural networks appear to have mysterious generalization properties when using parameter counting as a proxy for complexity. Indeed, neural networks often have many more parameters than there are data points, yet still provide good…
We study generalized sums of linear orders. These are binary operations that, given linear orders $A$ and $B$, return an order $A \oplus B$ that can be decomposed as an isomorphic copy of $A$ interleaved with a copy of $B$. We show that…
The advent of modern data collection and processing techniques has seen the size, scale, and complexity of data grow exponentially. A seminal step in leveraging these rich datasets for downstream inference is understanding the…
High-dimensional data, where the dimension of the feature space is much larger than sample size, arise in a number of statistical applications. In this context, we construct the generalized multivariate sign transformation, defined as a…
An infinite set is orbit-finite if, up to permutations of the underlying structure of atoms, it has only finitely many elements. We study a generalisation of linear programming where constraints are expressed by an orbit-finite system of…
Pattern matching is a powerful tool which is part of many functional programming languages as well as computer algebra systems such as Mathematica. Among the existing systems, Mathematica offers the most expressive pattern matching.…
The dynamics of recombination in genetics leads to an interesting nonlinear differential equation, which has a natural generalization to a measure valued version. The latter can be solved explicitly under rather general circumstances. It…
In semantics and in programming practice, algebraic concepts such as monads or, essentially equivalently, (large) Lawvere theories are a well-established tool for modelling generic side-effects. An important issue in this context are…