Fractional covers of Hypergraphs with bounded multi-intersection

Fractional (hyper-)graph theory is concerned with the specific problems that arise when fractional analogues of otherwise integer-valued (hyper-)graph invariants are considered. The focus of this paper is on fractional edge covers of hypergraphs. Our main technical result generalizes and unifies previous conditions under which the size of the support of fractional edge covers is bounded independently of the size of the hypergraph itself. This allows us to extend previous tractability results for checking if the fractional hypertree width of a given hypergraph is ≤ k for some constant k. We also show how our results translate to fractional vertex covers

Events in a Non-Commutative Space-Time

We treat the events determined by a quantum physical state in a noncommutative space-time, generalizing the analogous treatment in the usual Minkowski space-time based on positive-operator-valued measures (POVMs). We consider in detail the model proposed by Snyder in 1947 and calculate the POVMs defined on the real line that describe the measurement of a single coordinate. The approximate joint measurement of all the four space-time coordinates is described in terms of a generalized Wigner function (GWF). We derive lower bounds for the dispersion of the coordinate observables and discuss the covariance of the model under the Poincare' group. The unusual transformation law of the coordinates under space-time translations is interpreted as a failure of the absolute character of the concept of space-time coincidence. The model shows that a minimal length is compatible with Lorents covariance.Comment: 13 pages, revtex. Introductory part shortened and some arguments made more clea

The COVID-19 Pandemic Affects Seasonality, With Increasing Cases of New-Onset Type 1 Diabetes in Children, From the Worldwide SWEET Registry

Objective: To analyze whether the coronavirus disease 2019 (COVID-19) pandemic increased the number of cases or impacted seasonality of new-onset type 1 diabetes (T1D) in large pediatric diabetes centers globally. Research design and methods: We analyzed data on 17,280 cases of T1D diagnosed during 2018-2021 from 92 worldwide centers participating in the SWEET registry using hierarchic linear regression models. Results: The average number of new-onset T1D cases per center adjusted for the total number of patients treated at the center per year and stratified by age-groups increased from 11.2 (95% CI 10.1-12.2) in 2018 to 21.7 (20.6-22.8) in 2021 for the youngest age-group, <6 years; from 13.1 (12.2-14.0) in 2018 to 26.7 (25.7-27.7) in 2021 for children ages 6 to <12 years; and from 12.2 (11.5-12.9) to 24.7 (24.0-25.5) for adolescents ages 12-18 years (all P < 0.001). These increases remained within the expected increase with the 95% CI of the regression line. However, in Europe and North America following the lockdown early in 2020, the typical seasonality of more cases during winter season was delayed, with a peak during the summer and autumn months. While the seasonal pattern in Europe returned to prepandemic times in 2021, this was not the case in North America. Compared with 2018-2019 (HbA1c 7.7%), higher average HbA1c levels (2020, 8.1%; 2021, 8.6%; P < 0.001) were present within the first year of T1D during the pandemic. Conclusions: The slope of the rise in pediatric new-onset T1D in SWEET centers remained unchanged during the COVID-19 pandemic, but a change in the seasonality at onset became apparent.info:eu-repo/semantics/publishedVersio

Deep Eutectic Solvents (DESs) and their applications [forthcoming]

Deep Eutectic Solvents (DESs) and Their Application

MV-Datalog+-: Effective rule-based reasoning with uncertain observations

Modern applications combine information from a great variety of sources. Oftentimes, some of these sources, like machine-learning systems, are not strictly binary but associated with some degree of (lack of) confidence in the observation. We propose MV-Datalog and as extensions of Datalog and, respectively, to the fuzzy semantics of infinite-valued &#x141;ukasiewicz logic as languages for effectively reasoning in scenarios where such uncertain observations occur. We show that the semantics of MV-Datalog exhibits similar model theoretic properties as Datalog. In particular, we show that (fuzzy) entailment can be decided via minimal fuzzy models. We show that when they exist, such minimal fuzzy models are unique and can be characterised in terms of a linear optimisation problem over the output of a fixed-point procedure. On the basis of this characterisation, we propose similar many-valued semantics for rules with existential quantification in the head, extending

On the complexity of inductively learning guarded clauses

We investigate the computational complexity of mining guarded clauses from clausal datasets through the framework of inductive logic programming (ILP). We show that learning guarded clauses is NP-complete and thus one step below the Σ P 2 -complete task of learning Horn clauses on the polynomial hierarchy. Motivated by practical applications on large datasets we identify a natural tractable fragment of the problem. Finally, we also generalise all of our results to k-guarded clauses for constant k

Incremental updates of generalized hypertree decompositions

Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP so that it becomes a valid decomposition of a new CSP ′ produced by some modification of . Even though the problem is hard in theory, we propose and implement a framework for effectively updating GHDs. The experimental evaluation of our algorithm strongly suggests practical applicability

Fast parallel hypertree decompositions in logarithmic recursion depth

Various classic reasoning problems with natural hypergraph representations are known to be tractable when a hypertree decomposition (HD) of low width exists. The resulting algorithms are attractive for practical use in fields like databases and constraint satisfaction. However, algorithmic use of HDs relies on the difficult task of first computing a decomposition of the hypergraph underlying a given problem instance, which is then used to guide the algorithm for this particular instance. The performance of purely sequential methods for computing HDs is inherently limited, yet the problem is, theoretically, amenable to parallelisation. In this paper we propose the first algorithm for computing hypertree decompositions that is well-suited for parallelisation. The newly proposed algorithm log-k-decomp requires only a logarithmic number of recursion levels and additionally allows for highly parallelised pruning of the search space by restriction to so-called balanced separators. We provide a detailed experimental evaluation over the HyperBench benchmark and demonstrate that log-k-decomp outperforms the current state-of-the-art significantly.</p