Arbitrary Set Research Articles

Flow of temporal network properties under local aggregation and time shuffling: a tool for characterizing, comparing and classifying temporal networks

Abstract Although many tools have been developed and employed to characterize temporal networks (TNs), the issue of how to compare them remains largely open. It depends indeed on what features are considered as relevant, and on the way the differences in these features are quantified. In this paper, we propose to characterize TNs through their behavior under general transformations that are local in time: (i) a local time shuffling, which destroys correlations at time scales smaller than a given scale b, while preserving large time scales, and (ii) a local temporal aggregation on time windows of length n. By varying b and n, we obtain a flow of TNs, and flows of observable values, which encode the phenomenology of the TN on multiple time scales. We use a symbolic approach to summarize these flows into labels (strings of characters) describing their trends. These labels can then be used to compare TNs, validate models, or identify groups of networks with similar labels. Our procedure can be applied to any TN and with an arbitrary set of observables, and we illustrate it on an ensemble of data sets describing face-to-face interactions in various contexts, including both empirical and synthetic data.

Involvement in serious incident investigations: a qualitative documentary analysis of NHS trust policies in England

BackgroundThe considered shift from individual blame and sanctions towards a commitment to system-wide learning from incidents in healthcare has led to increased understanding of both the moral and epistemic importance of involving those affected. It is important to understand whether and how local policy describes and prompts involvement with a view to understanding the policy landscape for serious incident investigations in healthcare.This study aimed to explore the way in which involvement of those affected by serious incidents is represented in incident investigation policy documents across acute and mental health services in the English NHS, and to identify guidance for more effective construction of policy for meaningful involvement.MethodsWe conducted a documentary analysis of 43 local serious incident investigation policies to explore the way in which involvement in serious incident investigations is represented in policy documents across acute and mental health services in the NHS in England.ResultsThree headline findings were generated. First, we identified involvement as a concept was conspicuous by its absence in policy documents. Direct reference to support or involvement of those affected by serious incidents was lacking. Even where involvement and support were recognised as important, this was described as a passive process rather than there being moral or epistemic justification for more active contribution to learning. Second, learning from serious incidents was typically described as a high priority but the language used was unclear and ‘learning’ was more often positioned as construction of an arbitrary set of recommendations rather than a participatory process of deconstruction and reconstruction of specific systems and processes. Third, there was an emphasis placed on a just and open culture but paradoxically this was reinforced by expected compliance, positioning investigations as a tool through which action is governed rather than an opportunity to learn from and with the experiences and expertise of those affected.ConclusionsMore effective representation in policy of the moral and epistemic reasons for stakeholder involvement in serious incident investigations may lead to better understanding of its importance, thus increasing potential for organisational learning and reducing the potential for compounded harm. Moreover, understanding how structural elements of policy documents were central to the way in which the document is framed and received is significant for both local and national policy makers to enable more effective construction of healthcare policy documents to prompt meaningful action.

Adaptive Quotient Filters

Filters trade off accuracy for space and occasionally return false positive matches with a bounded error. Numerous systems use filters in fast memory to avoid performing expensive I/Os to slow storage. A fundamental limitation in traditional filters is that they do not change their representation upon seeing a false positive match. Therefore, the maximum false positive rate is only guaranteed for a single query, not for an arbitrary set of queries. We can improve the filter's performance on a stream of queries, especially on a skewed distribution, if we can adapt after encountering false positives. Adaptive filters, such as telescoping quotient filters and adaptive cuckoo filters, update their representation upon detecting a false positive to avoid repeating the same error in the future. Adaptive filters require an auxiliary structure, typically much larger than the main filter and often residing on slow storage, to facilitate adaptation. However, existing adaptive filters are not practical and have not been adopted in real-world systems for two main reasons. First, they offer weak adaptivity guarantees, meaning that fixing a new false positive can cause a previously fixed false positive to come back. Secondly, the sub-optimal design of the auxiliary structure results in adaptivity overheads so substantial that they can actually diminish overall system performance compared to a traditional filter. In this paper, we design and implement the \sysname, the first practical adaptive filter with minimal adaptivity overhead and strong adaptivity guarantees, which means that the performance and false-positive guarantees continue to hold even for adversarial workloads. The \sysname is based on the state-of-the-art quotient filter design and preserves all the critical features of the quotient filter such as cache efficiency and mergeability. Furthermore, we employ a new auxiliary structure design which results in considerably low adaptivity overhead and makes the \sysname practical in real systems. We evaluate the \sysname by using it to filter queries to an on-disk B-tree database and find no negative impact on insert or query performance compared to traditional filters. Against adversarial workloads, the \sysname preserves system performance, whereas traditional filters incur 2× slowdown from adversaries representing as low as 1% of the workload. Finally, we show that on skewed query workloads, the \sysname can reduce the false-positive rate 100× using negligible (1/1000th of a bit per item) space overhead.

Symmetric linear functionals on the Banach space generated by pseudometrics

In this work we consider the notion of $B$-equivalence of pseudometrics.Two pseudometrics $d_1$ and $d_2$ on a set $X$ are called $B$-equivalent, where $B$ is a subgroup of the group of all bijections on $X,$ if there exists an element $b$ of $B$ such that $d_1(x,y) = d_2(b(x),b(y))$ for every $x,y\in X,$ that is, $d_1$ can be obtained from $d_2$ by permutating elements of $X$ with the aid of the bijection $b.$The group $B$ generates the group $\widehat B$ of transformations of the set of all pseudometricson $X,$ elements of which act as $d(\cdot, \cdot)\mapsto d(b(\cdot),b(\cdot)),$ where $d$ is a pseudometrics on $X$ and $b\in B.$ A function $f$ on the set of all pseudometrics on $X$is called $\widehat B$-symmetric if $f$ is invariant under the action on its argument of elements of the group $\widehat B.$If two pseudometrics $d_1$ and $d_2$ are $B$-equivalent, then $f(d_1)=f(d_2)$ for every $\widehat B$-symmetric function $f.$ In general, the technique of symmetric functions is well-developed for the case of symmetric continuous polynomials and, in particular, for the case of symmetric continuous linear functionals on Banach spaces. To use this technique for the construction of $\widehat B$-symmetricfunctions on sets of pseudometrics, we map these sets to some appropriate Banach space $V$, which is isometrically isomorphic to the Banach space $\ell_1$of all absolutely summing real sequences. Weinvestigate symmetric (with respect to an arbitrary group of symmetry, elements of whichmap the standard Schauder basis of $\ell_1$ into itself) linear continuous functionalson $\ell_1.$ We obtain the complete description of the structure of these functionals.Also we establish analogical results for symmetric linear continuous functionals on the space $V.$ These results are used for the construction of $\widehat B$-symmetric functionals on the set of all pseudometrics on an arbitrary set $X$ for the following case:the group $B$ of bijections on $X,$ that generates the group $\widehat B,$ is such that the set of all $x\in X,$ for which there exists $b\in B$ such that $b(x)\neq x,$is finite.

Approximations of system W for inference from strongly and weakly consistent belief bases

In this article, we investigate approximations of the inductive inference operator system W that has been shown to exhibit desirable inference properties and to extend both system Z, and thus rational closure, and c-inference. For versions of these inference operators that are extended to also cover inference from belief bases that are only weakly consistent, we first show that extended system Z and extended c-inference are captured by extended system W. Then we introduce general functions for generating inductive inference operators: the combination of two inductive inference operators by union, and the completion of an inductive inference operator by an arbitrary set of axioms. We construct the least inductive inference operator extending system Z and c-inference that is closed under system P and show that it is still strictly extended by extended system W. Furthermore, we introduce an inductive inference operator that strictly extends extended system W and that is strictly extended by lexicographic inference. This leads to a comprehensive map of inference relations between rational closure and extended c-inference on the one side and lexicographic inference on the other side with extended system W and its approximations at its centre, where all relationships also hold for the unextended versions.

Two-set inequalities for the binary knapsack polyhedra

This paper presents two-set inequalities, a class of valid inequalities for knapsack and multiple knapsack problems. Two-set inequalities are generated from two arbitrary sets of variables from a knapsack constraint. This class of cutting planes is not a traditional type of lifting since a valid inequality over a restricted space is not required to start. Furthermore, they cannot be derived using any existing lifting technique. The paper presents a quadratic algorithm to efficiently generate many two-set inequalities. Conditions for facet-defining two-set inequalities are also derived. Computational experiments tested these inequalities as pre-processing cuts versus CPLEX, a high-performance mathematical programming solver, at default settings. Overall, two-set inequalities reduced the time to solve some benchmark multiple knapsack instances to up to 80%. Computational results also showed the potential of this new class of cutting planes to solve computationally challenging binary integer programs.

A quantum algorithm for the lattice-Boltzmann method advection-diffusion equation

We present a versatile and efficient quantum algorithm based on the Lattice Boltzmann method (LBM) approximate solution of the linear advection-diffusion equation (ADE). We emphasize that the LBM approximation modifies the diffusion term of the underlying exact ADE and leads to a modified equation (mADE). Due to its versatility in terms of operator splitting, the proposed quantum LBM algorithm for the mADE provides a building block for future quantum algorithms to solve the linearized Navier-Stokes equation on quantum computers. We split the algorithm into four operations: initialization, collision, streaming, and calculation of the macroscopic quantities. We propose general quantum building blocks for each operator, which adapt intrinsically from the general three-dimensional case to smaller dimensions and apply to arbitrary lattice-velocity sets. Based on (sub-linear) amplitude data encoding, we propose improved initialization and collision operations with reduced complexity and efficient sampling-based simulation. Quantum streaming algorithms are based on previous developments. The proposed quantum algorithm allows for the computation of successive time steps, requiring full state measurement and reinitialization after every time step. It is validated by comparison with a digital implementation and based on analytical solutions in one and two dimensions. Furthermore, we demonstrate the versatility of the quantum algorithm for two cases with non-uniform advection velocities in two and three dimensions. Various velocity sets are considered to further highlight the flexibility of the algorithm. We benchmark our optimized quantum algorithm against previous methods employed in sampling-based quantum simulators. We demonstrate sampling efficiency, with sampling accelerated convergence requiring fewer shots.

Graph realization of distance sets

The Distance Realization problem is defined as follows. Given an n×n matrix D of nonnegative integers, interpreted as inter-vertex distances, find an n-vertex weighted or unweighted graph G realizing D, i.e., whose inter-vertex distances satisfy distG(i,j)=Di,j for every 1≤i<j≤n, or decide that no such realizing graph exists. The problem was studied for general weighted and unweighted graphs, as well as for cases where the realizing graph is restricted to a specific family of graphs (e.g., trees or bipartite graphs). An extension of Distance Realization that was studied in the past is where each entry in the matrix D may contain a range of consecutive permissible values. We refer to this extension as Range Distance Realization (or Range-DR). Restricting each range to at most k values yields the problem k-Range Distance Realization (or k-Range-DR). The current paper introduces a new extension of Distance Realization, in which each entry Di,j of the matrix may contain an arbitrary set of acceptable values for the distance between i and j, for every 1≤i<j≤n. We refer to this extension as Set Distance Realization (Set-DR), and to the restricted problem where each entry may contain at most k values as k-Set Distance Realization (or k-Set-DR).We first show that 2-Range-DR is NP-hard for unweighted graphs (implying the same for 2-Set-DR). Next we prove that 2-Set-DR is NP-hard for unweighted and weighted trees.Finally, we explore Set-DR where the realization is restricted to the families of stars, paths, cycles, or caterpillars. For the weighted case, our positive results are that there exist polynomial time algorithms for the 2-Set-DR problem on stars, paths and cycles, and for the 1-Set-DR problem on caterpillars. On the hardness side, we prove that 6-Set-DR is NP-hard for stars and 5-Set-DR is NP-hard for paths, cycles and caterpillars. For the unweighted case, our results are the same, except for the case of unweighted stars, for which k-Set-DR is polynomially solvable for any k.

Antisaturation fixed-time backstepping fuzzy integral sliding mode control for automatic landing of fixed-wing unmanned aerial vehicles

This paper proposes a robust adaptive fixed-time control for automatic landing systems (ALS) of small-scale fixed-wing UAVs exposed to wind disturbances, parametric uncertainties, and input saturation. The control structure consists of three subsystems, i.e., the guidance system, the attitude control system, and the thrust control system. Considering the landing geometry, the guidance system computes the desired Euler angles to stabilize the dynamics of altitude deviation, lateral deviation, and lateral speed. An auxiliary system is designed to compensate for the effect of input saturation in the attitude control system. The fixed-time method, the backstepping control (BSC), the fuzzy logic control (FLC), and the integral sliding mode control (ISMC) techniques are adopted to synthesize the control law. All three functional parts of the proposed ALS are equipped with a fixed-time fuzzy sliding mode disturbance observer (FSMDO). FLC computes the gains of signum functions adaptively to attenuate the chattering. Fixed-time convergence of the system errors to an arbitrary residual set is proved by comprehensive stability analysis. Finally, the comparative simulation results verify the better dynamic response and stronger robustness under the proposed ALS.

Snapshottable Stores

We say that an imperative data structure is snapshottable or supports snapshots if we can efficiently capture its current state, and restore a previously captured state to become the current state again. This is useful, for example, to implement backtracking search processes that update the data structure during search. Inspired by a data structure proposed in 1978 by Baker, we present a snapshottable store , a bag of mutable references that supports snapshots. Instead of capturing and restoring an array, we can capture an arbitrary set of references (of any type) and restore all of them at once. This snapshottable store can be used as a building block to support snapshots for arbitrary data structures, by simply replacing all mutable references in the data structure by our store references. We present use-cases of a snapshottable store when implementing type-checkers and automated theorem provers. Our implementation is designed to provide a very low overhead over normal references, in the common case where the capture/restore operations are infrequent. Read and write in store references are essentially as fast as in plain references in most situations, thanks to a key optimisation we call record elision . In comparison, the common approach of replacing references by integer indices into a persistent map incurs a logarithmic overhead on reads and writes, and sophisticated algorithms typically impose much larger constant factors. The implementation, which is inspired by Baker’s and the OCaml implementation of persistent arrays by Conchon and Filliâtre, is both fairly short and very hard to understand: it relies on shared mutable state in subtle ways. We provide a mechanized proof of correctness of its core using the Iris framework for the Coq proof assistant.

Boundary determination for hybrid imaging from a single measurement

Abstract We recover the conductivity σ at the boundary of a domain from a combination of Dirichlet and Neumann boundary data and generalized power/current density data at the boundary, from a single quite arbitrary set of data, in AET or CDII. The argument is elementary, algebraic and local. More generally, we consider the variable exponent p ⁢ ( ⋅ ) {p(\,\cdot\,)} -Laplacian as a forward model with the interior density data σ ⁢ | ∇ ⁡ u | q {\sigma|\nabla u|^{q}} , and find out that single measurement specifies the boundary conductivity when p - q ≥ 1 {p-q\geq 1} , and otherwise the measurement specifies two alternatives. We present heuristics for selecting between these alternatives. Both p and q may depend on the spatial variable x, but they are assumed to be a priori known. We illustrate the practical situations with numerical examples with the code available.

A simplex path integral and a simplex renormalization group for high-order interactions *

Modern theories of phase transitions and scale invariance are rooted in path integral formulation and renormalization groups (RGs). Despite the applicability of these approaches in simple systems with only pairwise interactions, they are less effective in complex systems with undecomposable high-order interactions (i.e. interactions among arbitrary sets of units). To precisely characterize the universality of high-order interacting systems, we propose a simplex path integral and a simplex RG (SRG) as the generalizations of classic approaches to arbitrary high-order and heterogeneous interactions. We first formalize the trajectories of units governed by high-order interactions to define path integrals on corresponding simplices based on a high-order propagator. Then, we develop a method to integrate out short-range high-order interactions in the momentum space, accompanied by a coarse graining procedure functioning on the simplex structure generated by high-order interactions. The proposed SRG, equipped with a divide-and-conquer framework, can deal with the absence of ergodicity arising from the sparse distribution of high-order interactions and can renormalize a system with intertwined high-order interactions at the p-order according to its properties at the q-order ( p⩽q ). The associated scaling relation and its corollaries provide support to differentiate among scale-invariant, weakly scale-invariant, and scale-dependent systems across different orders. We validate our theory in multi-order scale-invariance verification, topological invariance discovery, organizational structure identification, and information bottleneck analysis. These experiments demonstrate the capability of our theory to identify intrinsic statistical and topological properties of high-order interacting systems during system reduction.

Linkable ring signature scheme with stronger security guarantees

Ring signatures enable a user to sign messages on behalf of an arbitrary set of users, called the ring. The signer-anonymity property guarantees that the signature does not reveal which member of the ring signed the message. The notion of linkable ring signatures (LRS) is an extension of the concept of ring signatures such that there is a public way of determining whether two signatures have been produced by the same signer. However, the existing LRS schemes may not be competent in some scenarios since they exhibit a gap to bridge as reflected on the security guarantees such as the absence of quantum-resistance, inadequate security notions, and a reliance on the random oracle heuristic.In this paper, we present a framework for LRS that provides stronger security guarantees. We instantiate the framework from standard lattice assumptions and prove the security in the standard model. Furthermore, we implement our scheme and conduct experimental evaluations, which demonstrate that the performances are practical for typical settings.

Vector Quantization With Error Uniformly Distributed Over an Arbitrary Set

Vector Quantization With Error Uniformly Distributed Over an Arbitrary Set

REVIEW: Even amidst the pain, author manages to show kindness

Excommunicated. A multigenerational story of leaving the Exclusive Brethren, by Craig Hoyle. Auckland: Harper Collins, 2023. 327 pages. ISBN 9871775542018 IN THIS deeply personal memoir, Sunday Star-Times journalist Craig Hoyle turns his lens on his own family and the destructive effects upon them of their religion. Growing up in an Exclusive Brethren family meant closeness and warmth, but it also meant strict discipline, public prayers every day, and not really having schoolfriends for young Craig. It also meant there were family members nobody talked about because they had transgressed increasingly arbitrary sets of rules, or called out high-handed or incompetent leadership.

On some congruences and exponential sums

Let ε>0 be a fixed small constant, Fp be the finite field of p elements for prime p. We consider additive and multiplicative problems in Fp that involve intervals and arbitrary sets. Representative examples of our results are as follows. Let M be an arbitrary subset of Fp. If #M>p1/3+ε and H⩾p2/3 or if #M>p3/5+ε and H⩾p3/5+ε then all, but O(p1−δ) elements of Fp can be represented in the form hm with h∈[1,H] and m∈M, where δ>0 depends only on ε. Furthermore, let X be an arbitrary interval of length H and s be a fixed positive integer. IfH>p17/35+ε,#M>p17/35+ε, then the number T6(λ) of solutions to the congruencem1x1s+m2x2s+m3x3s+m4x4s+m5x5s+m6x6s≡λmodp,mi∈M,xi∈X,i=1,…,6, satisfiesT6(λ)=H6(#M)6p(1+O(p−δ)).

Remarks on context-free grammars with subregular control languages

A context-free grammar with control language is a pair (G,R) where G is a context-free grammar and R is a regular set over the set of productions of G. Its language consists of all terminal words where the sequence of applied productions belongs to R.We study context-free grammars with control languages belonging to subsets of the set of regular languages. We prove that we can obtain only context-free languages if we use regular commutative and strictly locally 1-testable languages. By strictly locally k-testable, k≥2, ordered, union-free, ordered, and regular circular control languages, we have no loss in the generative power, i.e., we generate the same family which is obtained by arbitrary regular control sets.

GENTANGLE: integrated computational design of gene entanglements.

The design of two overlapping genes in a microbial genome is an emerging technique for adding more reliable control mechanisms in engineered organisms for increased stability. The design of functional overlapping gene pairs is a challenging procedure, and computational design tools are used to improve the efficiency to deploy successful designs in genetically engineered systems. GENTANGLE (Gene Tuples ArraNGed in overLapping Elements) is a high-performance containerized pipeline for the computational design of two overlapping genes translated in different reading frames of the genome. This new software package can be used to design and test gene entanglements for microbial engineering projects using arbitrary sets of user-specified gene pairs. The GENTANGLE source code and its submodules are freely available on GitHub at https://github.com/BiosecSFA/gentangle. The DATANGLE (DATA for genTANGLE) repository contains related data and results and is freely available on GitHub at https://github.com/BiosecSFA/datangle. The GENTANGLE container is freely available on Singularity Cloud Library at https://cloud.sylabs.io/library/khyox/gentangle/gentangle.sif. The GENTANGLE repository wiki (https://github.com/BiosecSFA/gentangle/wiki), website (https://biosecsfa.github.io/gentangle/), and user manual contain detailed instructions on how to use the different components of software and data, including examples and reproducing the results. The code is licensed under the GNU Affero General Public License version 3 (https://www.gnu.org/licenses/agpl.html).

Valuations on power series rings in an arbitrary set of indeterminates

Valuations on power series rings in an arbitrary set of indeterminates

On the Existence and Uniqueness of Stationary Distributions for Some Piecewise Deterministic Markov Processes with State-Dependent Jump Intensity

In this paper, we consider a subclass of piecewise deterministic Markov processes with a Polish state space that involve a deterministic motion punctuated by random jumps, occurring in a Poisson-like fashion with some state-dependent rate, between which the trajectory is driven by one of the given semiflows. We prove that there is a one-to-one correspondence between stationary distributions of such processes and those of the Markov chains given by their post-jump locations. Using this result, we further establish a criterion guaranteeing the existence and uniqueness of the stationary distribution in a particular case, where the post-jump locations result from the action of a random iterated function system with an arbitrary set of transformations.