Phase imaging is gaining importance due to its applications in fields like biomedical and material characterization. In applications, it can provide quantitative information missing label-free microscopy modalities. One of the most prominent methods phase quantification Transport-of-Intensity Equation (TIE). TIE often requires multiple acquisitions at different defocus distances, which not always feasible a clinical setting hardware constraints. To address this issue, we propose use...

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others. We investigate the of three fundamental algorithmic problems these classes: enumeration, counting uniform generation solutions, show that they have several desirable properties respect. Both classes are defined terms nondeterministic transducers (NL...

Conjunctive queries are one of the most common class used in database systems, and best studied literature. A seminal result Grohe, Schwentick, Segoufin (STOC 2001) demonstrates that for every G graphs, evaluation all conjunctive whose underlying graph is tractable if, only has bounded treewidth. In this work, we extend characterization to counting problem queries. Specifically, C with treewidth, introduce first fully polynomial-time randomized approximation scheme (FPRAS) answers a query C,...

Phase imaging is gaining importance due to its applications in fields like biomedical and material characterization. In applications, it can provide quantitative information missing label-free microscopy modalities. One of the most prominent methods phase quantification Transport-of-Intensity Equation (TIE). TIE often requires multiple acquisitions at different defocus distances, which not always feasible a clinical setting. To address this issue, we propose use chromatic aberrations induce...

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, that provide a unifying framework for efficient query evaluation in areas such as information extraction and graph databases, among others. We investigate the of three fundamental algorithmic problems these classes: enumeration, counting, uniform generation solutions, show they have several desirable properties respect. Both classes are defined terms non-deterministic transducers...

We study two simple yet general complexity classes, which provide a unifying framework for efficient query evaluation in areas like graph databases and information extraction, among others. investigate the of three fundamental algorithmic problems these classes: enumeration, counting uniform generation solutions, show that they have several desirable properties this respect. Both classes are defined terms non deterministic logarithmic-space transducers (NL transducers). For first class, we...

Data stream processing systems enable querying over sliding windows of streams data. Efficient index structures for the streaming window are a crucial building block to operations such as aggregation and joins. This paper proposes SWIX, novel memory-efficient learned windows. Unlike conventional indexes that rely on tree achieve logarithmic query cost, SWIX has flat structure uses substantially less memory enables efficient execution while having low cost maintenance when inserting (and...

Learned indexes leverage machine learning models to accelerate query answering in databases, showing impressive practical performance. However, theoretical understanding of these methods remains incomplete. Existing research suggests that learned have superior asymptotic complexity compared their non-learned counterparts, but findings been established under restrictive probabilistic assumptions. Specifically, for a sorted array with $n$ elements, it has shown can find key $O(\log(\log n))$...

Encoding information in combinations of pre-synthesised deoxyribonucleic acid (DNA) strands (referred to as motifs) is an interesting approach DNA storage that could potentially circumvent the prohibitive costs nucleotide-by-nucleotide synthesis. Based on our analysis empirical data set from HelixWorks, we propose two channel models for this setup (with and without interference) analyse their fundamental limits. We a coding scheme approaches those limits by leveraging all available at output...

Inverse problems aim to determine parameters from observations, a crucial task in engineering and science. Lately, generative models, especially diffusion have gained popularity this area for their ability produce realistic solutions good mathematical properties. Despite success, an important drawback of models is sensitivity the choice variance schedule, which controls dynamics process. Fine-tuning schedule specific applications but time-costly does not guarantee optimal result. We propose...

Counting the number of words a certain length accepted by non-deterministic finite automaton (NFA) is fundamental problem, which has many applications in different areas such as graph databases, knowledge compilation, and information extraction. Along with this, generating uniformly at random also relevant particularly scenarios where returning varied outputs desirable feature.

In this work, we study two simple yet general complexity classes, based on logspace Turing machines, which provide a unifying framework for efficient query evaluation in areas like information extraction and graph databases, among others. We investigate the of three fundamental algorithmic problems these classes: enumeration, counting uniform generation solutions, show that they have several desirable properties respect. Both classes are defined terms non-deterministic transducers (NL...

Conjunctive queries are one of the most common class used in database systems, and best studied literature. A seminal result Grohe, Schwentick, Segoufin (STOC 2001) demonstrates that for every $G$ graphs, evaluation all conjunctive whose underlying graph is tractable if, only has bounded treewidth. In this work, we extend characterization to counting problem queries. Specifically, $C$ with treewidth, introduce first fully polynomial-time randomized approximation scheme (FPRAS) answers a...

Counting the answers to a query is fundamental problem in databases, with several applications evaluation, optimization, and visualization of queries. Unfortunately, counting #P-hard most cases, so it unlikely be solvable polynomial time. Recently, new results on approximate have been developed, specifically by showing that some problems automata theory admit fully polynomial-time randomized approximation schemes. These implications for query; particular, graph conjunctive In this work, we...