Related papers: Scalable Probabilistic Frames
We consider the safety evaluation of discrete time, stochastic systems over a finite horizon. Therefore, we discuss and link probabilistic invariance with reachability as well as reach-avoid problems. We show how to efficiently compute…
This paper examines the construction and properties of binary Parseval frames. We address two questions: When does a binary Parseval frame have a complementary Parseval frame? Which binary symmetric idempotent matrices are Gram matrices of…
Composite likelihood has shown promise in settings where the number of parameters $p$ is large due to its ability to break down complex models into simpler components, thus enabling inference even when the full likelihood is not tractable.…
High-dimensional data sets are commonly collected in many contemporary applications arising in various fields of scientific research. We present two views of finite samples in high dimensions: a probabilistic one and a nonprobabilistic one.…
Spin glasses are paradigmatic models that deliver concepts relevant for a variety of systems. However, rigorous analytical results are difficult to obtain for spin-glass models, in particular for realistic short-range models. Therefore…
Probability metrics constitute an important tool in probability theory and statistics \cite{DKS91}, \cite{R91}, \cite{Z83} as they are specific metrics on spaces of random variables which, by satisfying an extra condition, concord well with…
A graph is regularizable if it is possible to assign weights to its edges so that all nodes have the same degree. Weights can be positive, nonnegative or arbitrary as soon as the regularization degree is not null. Positive and nonnegative…
Probabilistic timed automata are classical timed automata extended with discrete probability distributions over edges. We introduce clock-dependent probabilistic timed automata, a variant of probabilistic timed automata in which transition…
We initiate a systematic study of lattices of thick subcategories for arbitrary essentially small triangulated categories. To this end we give several examples illustrating the various properties these lattices may, or may not, have and…
We consider frames in a finite-dimensional Hilbert space Hn where frames are exactly the spanning sets of the vector space. The diagram vector of a vector in R2 was previously defined using polar coordinates and was used to characterize…
Recent contributions in the field of quantum state tomography have shown that, despite the exponential growth of Hilbert space with the number of subsystems, tomography of one-dimensional quantum systems may still be performed efficiently…
Finite frame theory has a number of real-world applications. In applications like sparse signal processing, data transmission with robustness to erasures, and reconstruction without phase, there is a pressing need for deterministic…
The problem of searching for a model-based scene interpretation is analyzed within a probabilistic framework. Object models are formulated as generative models for range data of the scene. A new statistical criterion, the truncated object…
We investigate the problem of deciding whether a given preference profile is close to having a certain nice structure, as for instance single-peaked, single-caved, single-crossing, value-restricted, best-restricted, worst-restricted,…
A useful sampling-reconstruction model should be stable with respect to different kind of small perturbations, regardless whether they result from jitter, measurement errors, or simply from a small change in the model assumptions. In this…
We prove a result about producing new frames for general spline-type spaces by piecing together portions of known frames. Using spline-type spaces as models for the range of certain integral transforms, we obtain results for time-frequency…
The collection of $d \times N$ complex matrices with prescribed column norms and prescribed (nonzero) singular values forms a compact algebraic variety, which we refer to as a frame space. Elements of frame spaces -- i.e., frames -- are…
Alignment algorithms usually rely on simplified models of gaps for computational efficiency. Based on an isomorphism between alignments and physical helix-coil models, we show in statistical mechanics that alignments with realistic laws for…
The problem of constructing a necessary and sufficient condition for establishing the separability of continuous variable systems is revisited. Simon [R. Simon, Phys. Rev. Lett. 84, 2726 (2000)] pointed out that such a criterion may be…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…