IA Scholar Query: Cardinality of Set Partitions.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgSat, 31 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling
https://scholar.archive.org/work/by4kwstrpzgk3fvpxqnu3yoeiq
Map labeling is a classical problem in cartography and geographic information systems that asks to place labels for area, line, and point features, with the goal to select and place the maximum number of independent (i.e., overlap-free) labels. A practically interesting case is point labeling with axis-parallel rectangular labels of common size. In a fully dynamic setting, at each timestep, either a new label appears or an existing label disappears. Then, the challenge is to maintain a maximum cardinality subset of pairwise independent labels with sublinear update time. Motivated by this, we study the maximal independent set ( MIS ) and maximum independent set ( Max-IS ) problems on fully dynamic (insertion/deletion model) sets of axis-parallel rectangles of two types: (i) uniform height and width and (ii) uniform height and arbitrary width; both settings can be modeled as rectangle intersection graphs. We present the first deterministic algorithm for maintaining an MIS (and thus a 4-approximate Max-IS ) of a dynamic set of uniform rectangles with polylogarithmic update time. This breaks the natural barrier of \( \Omega (\Delta) \) update time (where \( \Delta \) is the maximum degree in the graph) for vertex updates presented by Assadi et al. (STOC 2018). We continue by investigating Max-IS and provide a series of deterministic dynamic approximation schemes. For uniform rectangles, we first give an algorithm that maintains a 4-approximate Max-IS with \( O(1) \) update time. In a subsequent algorithm, we establish the trade-off between approximation quality \( 2(1+\frac{1}{k}) \) and update time \( O(k^2\log n) \) , for \( k\in \mathbb {N} \) . We conclude with an algorithm that maintains a 2-approximate Max-IS for dynamic sets of unit-height and arbitrary-width rectangles with \( O(\log ^2 n + \omega \log n) \) update time, where \( \omega \) is the maximum size of an independent set of rectangles stabbed by any horizontal line. We implement our algorithms and report the results of an experimental comparison exploring the trade-off between solution quality and update time for synthetic and real-world map labeling instances. We made several major observations in our empirical study. First, the original approximations are well above their respective worst-case ratios. Second, in comparison with the static approaches, the dynamic approaches show a significant speedup in practice. Third, the approximation algorithms show their predicted relative behavior. The better the solution quality, the worse the update times. Fourth, a simple greedy augmentation to the approximate solutions of the algorithms boost the solution sizes significantly in practice.Sujoy Bhore, Guangping Li, Martin Nöllenburgwork_by4kwstrpzgk3fvpxqnu3yoeiqSat, 31 Dec 2022 00:00:00 GMTHand2 delineates mesothelium progenitors and is reactivated in mesothelioma
https://scholar.archive.org/work/qg5kk5d6wnfvleqgg5mij3sedq
The mesothelium lines body cavities and surrounds internal organs, widely contributing to homeostasis and regeneration. Mesothelium disruptions cause visceral anomalies and mesothelioma tumors. Nonetheless, the embryonic emergence of mesothelia remains incompletely understood. Here, we track mesothelial origins in the lateral plate mesoderm (LPM) using zebrafish. Single-cell transcriptomics uncovers a post-gastrulation gene expression signature centered on hand2 in distinct LPM progenitor cells. We map mesothelial progenitors to lateral-most, hand2-expressing LPM and confirm conservation in mouse. Time-lapse imaging of zebrafish hand2 reporter embryos captures mesothelium formation including pericardium, visceral, and parietal peritoneum. We find primordial germ cells migrate with the forming mesothelium as ventral migration boundary. Functionally, hand2 loss disrupts mesothelium formation with reduced progenitor cells and perturbed migration. In mouse and human mesothelioma, we document expression of LPM-associated transcription factors including Hand2, suggesting re-initiation of a developmental program. Our data connects mesothelium development to Hand2, expanding our understanding of mesothelial pathologies.Karin D Prummel, Helena L Crowell, Susan Nieuwenhuize, Eline C Brombacher, Stephan Daetwyler, Charlotte Soneson, Jelena Kresoja-Rakic, Agnese Kocere, Manuel Ronner, Alexander Ernst, Zahra Labbaf, David E Clouthier, Anthony B Firulli, Héctor Sánchez-Iranzo, Sundar R Naganathan, Rebecca O'Rourke, Erez Raz, Nadia Mercader, Alexa Burger, Emanuela Felley-Bosco, Jan Huisken, Mark D Robinson, Christian Mosimannwork_qg5kk5d6wnfvleqgg5mij3sedqThu, 01 Dec 2022 00:00:00 GMTA logic-based Benders decomposition for microscopic railway timetable planning
https://scholar.archive.org/work/nxeu2ezyrjhwjcr44kgibmmjiu
Railway timetable planning is one of the key factors in the successful operation of a railway network. The timetable must satisfy all operational restrictions at a microscopic representation of the railway network, while maximizing transportation capacity for passengers and freight. The microscopic planning of a railway timetable is an NP-Hard problem, difficult to solve for large-scale railway networks, such as those of entire countries. In this work, we propose a logic Benders decomposition approach to solve the problem of microscopic railway timetable planning. Our decomposition exploits the typical structure of a railway with dense networks around major hubs and sparse connections in-between hubs. A logic Benders cut is designed, which we are able to compute effectively for all decomposed problems within our considered structure, using a SAT based algorithm we developed. Moreover, an aggregation scheme for Benders cuts is proposed to speed up the iterative process. Experiments on real-world cases of the Swiss Federal Railways show a clear improvement in scalability compared to a variety of benchmarks including centralized approaches.Florin Leutwiler, Francesco Cormanwork_nxeu2ezyrjhwjcr44kgibmmjiuThu, 01 Dec 2022 00:00:00 GMTEdge Open Packing sets in graphs
https://scholar.archive.org/work/647whwnjknhbjkmsrqz7qeb75i
In a graph $G=(V,E)$, two edges $e_1$ and $e_2$ are said to have a \emph{common edge} if there exists an edge $e\in E(G)$ different from $e_1$ and $e_2$ such that $e$ joins a vertex of $e_1$ to a vertex of $e_2$ in $G$. That is, $\left \langle e_1, e, e_2\right\rangle$ is either $P_4$ or $K_3$ in $G$. A non-empty set $D\subseteq E(G)$ is an \emph{edge open packing set} of a graph $G$ if no two edges of $D$ have a common edge in $G$. The maximum cardinality of an edge open packing set is the \emph{edge open packing number} of $G$ and is denoted by $\rho^{o}_e(G)$. In this paper, we initiate a study on this parameter.C. Gayathri, K. Karuppasamy, S. Saravanakumarwork_647whwnjknhbjkmsrqz7qeb75iWed, 05 Oct 2022 00:00:00 GMTCovering Properties of Sum-Rank Metric Codes
https://scholar.archive.org/work/bapkykg6ujdcxhaq6q5lp63jtq
The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance separable codes (i.e., the codes achieving the Singleton bound in the corresponding metric). In this work, we investigate the covering property of sum-rank metric codes to enrich the theory of sum-rank metric codes. We intend to answer the question: what is the minimum cardinality of a code given a sum-rank covering radius? We show the relations of this quantity between different metrics and provide several lower and upper bounds for sum-rank metric codes.Cornelia Ott, Hedongliang Liu, Antonia Wachter-Zehwork_bapkykg6ujdcxhaq6q5lp63jtqWed, 05 Oct 2022 00:00:00 GMTExtending Conformal Prediction to Hidden Markov Models with Exact Validity via de Finetti's Theorem for Markov Chains
https://scholar.archive.org/work/ml2jpckezzapfl6xzxxviucnci
Conformal prediction is a widely used method to quantify uncertainty in settings where the data is independent and identically distributed (IID), or more generally, exchangeable. Conformal prediction takes in a pre-trained classifier, a calibration dataset and a confidence level as inputs, and returns a function which maps feature vectors to subsets of classes. The output of the returned function for a new feature vector (i.e., a test data point) is guaranteed to contain the true class with the pre-specified confidence. Despite its success and usefulness in IID settings, extending conformal prediction to non-exchangeable (e.g., Markovian) data in a manner that provably preserves all desirable theoretical properties has largely remained an open problem. As a solution, we extend conformal prediction to the setting of a Hidden Markov Model (HMM) with unknown parameters. The key idea behind the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are then viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework and is general enough to be useful in many sequential prediction problems.Buddhika Nettasinghe, Samrat Chatterjee, Ramakrishna Tipireddy, Mahantesh Halappanavarwork_ml2jpckezzapfl6xzxxviucnciWed, 05 Oct 2022 00:00:00 GMTGraded Semigroups
https://scholar.archive.org/work/ygq2jflpivaydaveb3j4o6i3qu
We systematically develop a theory of graded semigroups, that is semigroups S partitioned by groups G, in a manner compatible with the multiplication on S. We define a smash product S#G, and show that when S has local units, the category S#G-Mod of sets admitting an S#G-action is isomorphic to the category S-Gr of graded sets admitting an appropriate S-action. We also show that when S is an inverse semigroup, it is strongly graded if and only if S-Gr is naturally equivalent to S_1-Mod, where S_1 is the partition of S corresponding to the identity element 1 of G. These results are analogous to well-known theorems of Cohen/Montgomery and Dade for graded rings. Moreover, we show that graded Morita equivalence implies Morita equivalence for semigroups with local units, evincing the wealth of information encoded by the grading of a semigroup. We also give a graded Vagner-Preston theorem, provide numerous examples of naturally-occurring graded semigroups, and explore connections between graded semigroups, graded rings, and graded groupoids. In particular, we introduce graded Rees matrix semigroups, and relate them to smash product semigroups. We pay special attention to graded graph inverse semigroups, and characterise those that produce strongly graded Leavitt path algebras.Roozbeh Hazrat, Zachary Mesyanwork_ygq2jflpivaydaveb3j4o6i3quWed, 05 Oct 2022 00:00:00 GMTGlossary of terms in the SPHERE project environment
https://scholar.archive.org/work/3rottguedfgpbcdv6fd76os4u4
"The Glossary of terms in the SPHERE project environment" is a 206 pages document that presents 1287 terms used during the project. It can help you identify the acronyms presented in the Acronyms document and consult the terms and their definition.Antoni Quintana, Enric Ortega Fontwork_3rottguedfgpbcdv6fd76os4u4Wed, 05 Oct 2022 00:00:00 GMTNonlinear approximation spaces for inverse problems
https://scholar.archive.org/work/vnnby3ppijcwnijijla3hf2qca
This paper is concerned with the ubiquitous inverse problem of recovering an unknown function u from finitely many measurements possibly affected by noise. In recent years, inversion methods based on linear approximation spaces were introduced in [MPPY15, BCDDPW17] with certified recovery bounds. It is however known that linear spaces become ineffective for approximating simple and relevant families of functions, such as piecewise smooth functions that typically occur in hyperbolic PDEs (shocks) or images (edges). For such families, nonlinear spaces [Devore98] are known to significantly improve the approximation performance. The first contribution of this paper is to provide with certified recovery bounds for inversion procedures based on nonlinear approximation spaces. The second contribution is the application of this framework to the recovery of general bidimensional shapes from cell-average data. We also discuss how the application of our results to n-term approximation relates to classical results in compressed sensing.Albert Cohen, Matthieu Dolbeault, Olga Mula, Agustin Somacalwork_vnnby3ppijcwnijijla3hf2qcaWed, 05 Oct 2022 00:00:00 GMTIntroSurvey of representation theory
https://scholar.archive.org/work/hchtz7q3sfckzgitewdq453gz4
There could be thousands of Introductions/Surveys of representation theory, given that it is an enormous field. This is just one of them, quite personal and informal. It has an increasing level of difficulty; the first part is intended for final year undergrads. We explain some basics of representation theory, notably Schur-Weyl duality and representations of the symmetric group. We then do the quantum version, introduce Kazhdan-Lusztig theory, quantum groups and their categorical versions. We then proceed to a survey of some recent advances in modular representation theory. We finish with twenty open problems and a song of despair.Nicolas Libedinskywork_hchtz7q3sfckzgitewdq453gz4Wed, 05 Oct 2022 00:00:00 GMTLabelled well-quasi-order for permutation classes
https://scholar.archive.org/work/didja3e3nvh7tf7omqczxqmteq
While the theory of labelled well-quasi-order has received significant attention in the graph setting, it has not yet been considered in the context of permutation patterns. We initiate this study here, and show how labelled well quasi order provides a lens through which to view and extend previous well-quasi-order results in the permutation patterns literature. Connections to the graph setting are emphasised throughout. In particular, we establish that a permutation class is labelled well-quasi-ordered if and only if its corresponding graph class is also labelled well-quasi-ordered.Robert Brignall, Vincent Vatterwork_didja3e3nvh7tf7omqczxqmteqWed, 05 Oct 2022 00:00:00 GMTCity products of right-angled buildings and their universal groups
https://scholar.archive.org/work/hbmbqlsmrnc35klynzbwzgn534
We introduce the notion of city products of right-angled buildings that produces a new right-angled building out of smaller ones. More precisely, if M is a right-angled Coxeter diagram of rank n and Δ_1,...,Δ_n are right-angled buildings, then we construct a new right-angled building Δ := cityproduct_M(Δ_1,...,Δ_n). We can recover the buildings Δ_1,...,Δ_n as residues of Δ, but we can also construct a skeletal building of type M from Δ that captures the large-scale geometry of Δ. We then proceed to study universal groups for city products of right-angled buildings, and we show that the universal group of Δ can be expressed in terms of the universal groups for the buildings Δ_1,...,Δ_n and the structure of M. As an application, we show the existence of many examples of pairs of different buildings of the same type that admit (topologically) isomorphic universal groups, thereby vastly generalizing a recent example by Lara Beßmann.Jens Bossaert, Tom De Medtswork_hbmbqlsmrnc35klynzbwzgn534Wed, 05 Oct 2022 00:00:00 GMTAn Analytic Propositional Proof System on Graphs
https://scholar.archive.org/work/x7ysr6kr7zacji2bx3m73mtnyu
In this paper we present a proof system that operates on graphs instead of formulas. Starting from the well-known relationship between formulas and cographs, we drop the cograph-conditions and look at arbitrary undirected) graphs. This means that we lose the tree structure of the formulas corresponding to the cographs, and we can no longer use standard proof theoretical methods that depend on that tree structure. In order to overcome this difficulty, we use a modular decomposition of graphs and some techniques from deep inference where inference rules do not rely on the main connective of a formula. For our proof system we show the admissibility of cut and a generalization of the splitting property. Finally, we show that our system is a conservative extension of multiplicative linear logic with mix, and we argue that our graphs form a notion of generalized connective.Matteo Acclavio, Ross Horne, Lutz Straßburgerwork_x7ysr6kr7zacji2bx3m73mtnyuWed, 05 Oct 2022 00:00:00 GMTTorsors for finite group schemes of bounded height
https://scholar.archive.org/work/e3kyqppmpjgk5g3vbnxb7gsvs4
Let F be a global field. Let G be a non trivial finite étale tame F-group scheme. We define height functions on the set of G-torsors over F, which generalize the usual heights such as discriminant. As an analogue of the Malle conjecture for group schemes, we formulate a conjecture on the asymptotic behaviour of the number of G-torsors over F of bounded height. The conjectured asymptotic is proven for the case when G is commutative. As an application of our theory, we prove that the inverse Galois problem has an affirmative answer for what we call semicommutative group schemes.Ratko Darda, Takehiko Yasudawork_e3kyqppmpjgk5g3vbnxb7gsvs4Wed, 05 Oct 2022 00:00:00 GMTMulticlass Learnability Beyond the PAC Framework: Universal Rates and Partial Concept Classes
https://scholar.archive.org/work/qde3vhsypbboleksmoygfx36mi
In this paper we study the problem of multiclass classification with a bounded number of different labels k, in the realizable setting. We extend the traditional PAC model to a) distribution-dependent learning rates, and b) learning rates under data-dependent assumptions. First, we consider the universal learning setting (Bousquet, Hanneke, Moran, van Handel and Yehudayoff, STOC '21), for which we provide a complete characterization of the achievable learning rates that holds for every fixed distribution. In particular, we show the following trichotomy: for any concept class, the optimal learning rate is either exponential, linear or arbitrarily slow. Additionally, we provide complexity measures of the underlying hypothesis class that characterize when these rates occur. Second, we consider the problem of multiclass classification with structured data (such as data lying on a low dimensional manifold or satisfying margin conditions), a setting which is captured by partial concept classes (Alon, Hanneke, Holzman and Moran, FOCS '21). Partial concepts are functions that can be undefined in certain parts of the input space. We extend the traditional PAC learnability of total concept classes to partial concept classes in the multiclass setting and investigate differences between partial and total concepts.Alkis Kalavasis, Grigoris Velegkas, Amin Karbasiwork_qde3vhsypbboleksmoygfx36miWed, 05 Oct 2022 00:00:00 GMTDistributed Extended Object Tracking Information Filter Over Sensor Networks
https://scholar.archive.org/work/rodahco4zfhsddhwcnrv7k2cm4
This work aims to design a distributed extended object tracking (EOT) system over a realistic network, where both the extent and kinematics are required to retain consensus within the entire network. To this end, we resort to the multiplicative error model (MEM) that allows the extent parameters of perpendicular axis-symmetric objects to have individual uncertainty. To incorporate the MEM into the information filter (IF) style, we use the moment-matching technique to derive two pair linear models with only additive noise. The separation is merely in a fashion, and the cross-correlation between states is preserved as parameters in each other's model. As a result, the closed-form expressions are transferred into an alternating iteration of two linear IFs. With the two models, a centralized IF is proposed wherein the measurements are converted into a summation of innovation parts. Later, under a sensor network with the communication nodes and sensor nodes, we present two distributed IFs through the consensus on information and consensus on measurement schemes, respectively. Moreover, we prove the estimation errors of the proposed filter are exponentially bounded in the mean square. The benefits are testified by numerical experiments in comparison to state-of-the-art filters in literature.Zhifei Li and Yan Liang and Linfeng Xu and Shuli Mawork_rodahco4zfhsddhwcnrv7k2cm4Wed, 05 Oct 2022 00:00:00 GMTSingle Round-trip Hierarchical ORAM via Succinct Indices
https://scholar.archive.org/work/jzjdn7rj7bg25nbzkov4ko63tu
Accesses to data stored remotely create a side channel that is known to leak information even if the content is encrypted. Oblivious RAM is a cryptographic primitive that provides confidentiality of access patterns in remote storage settings. To outsource a database of n blocks of B bits, traditional solutions restrict the client to 𝒪(B) bits of private memory. A class of solutions, known as Hierarchical ORAM, has achieved theoretically optimal bandwidth performance in this setting. Hierarchical ORAM distributes data blocks at the server across a hierarchy of hash tables, with the most recently accessed blocks in the lower levels of the hierarchy. Locating a block in the hierarchy requires a large number of round-trips of communication, with the server, per virtual access. Furthermore, rebuilding the hierarchy incurs a large concrete bandwidth overhead. Thus, Hierarchical ORAMs are seen as theoretical artefacts and have not been deployed in practice. For many applications, such as cloud storage, the client can afford a larger, ω(B)-bit, private memory allocation. With this premise, we introduce Rank ORAM, the first practical Hierarchical ORAM that takes advantage of a larger client. We construct a compact client-side data structure that keeps track of how recently data blocks have been accessed. Leveraging this information, Rank ORAM reduces both the number of round-trips of communication and the concrete bandwidth overhead of Hierarchical ORAM. In addition, Rank ORAM achieves a smaller client memory allocation than existing (non-Hierarchical) state-of-the-art practical ORAM schemes while maintaining comparable bandwidth performance. Our experiments on real network file-system traces demonstrate a reduction in client memory, against existing approaches, of a factor of 100.William Holland, Olga Ohrimenko, Anthony Wirthwork_jzjdn7rj7bg25nbzkov4ko63tuWed, 05 Oct 2022 00:00:00 GMTMahonian and Euler-Mahonian statistics for set partitions
https://scholar.archive.org/work/pv45j2egxjgmff543uud2gec3y
A partition of the set [n]:={1,2,...,n} is a collection of disjoint nonempty subsets (or blocks) of [n], whose union is [n]. In this paper we consider the following rarely used representation for set partitions: given a partition of [n] with blocks B_1,B_2,...,B_m satisfying max B_1<max B_2<⋯<max B_m, we represent it by a word w=w_1w_2... w_n such that i∈ B_w_i, 1≤ i≤ n. We prove that the Mahonian statistics INV, MAJ, MAJ_d, r-MAJ, Z, DEN, MAK, MAD are all equidistributed on set partitions via this representation, and that the Euler-Mahonian statistics (des, MAJ), (mstc, INV), (exc, DEN), (des, MAK) are all equidistributed on set partitions via this representation.Shao-Hua Liuwork_pv45j2egxjgmff543uud2gec3yWed, 05 Oct 2022 00:00:00 GMTPrivTrace: Differentially Private Trajectory Synthesis by Adaptive Markov Model
https://scholar.archive.org/work/takasn3ehjdn5cqtpyzysfcgca
Publishing trajectory data (individual's movement information) is very useful, but it also raises privacy concerns. To handle the privacy concern, in this paper, we apply differential privacy, the standard technique for data privacy, together with Markov chain model, to generate synthetic trajectories. We notice that existing studies all use Markov chain model and thus propose a framework to analyze the usage of the Markov chain model in this problem. Based on the analysis, we come up with an effective algorithm PrivTrace that uses the first-order and second-order Markov model adaptively. We evaluate PrivTrace and existing methods on synthetic and real-world datasets to demonstrate the superiority of our method.Haiming Wang, Zhikun Zhang, Tianhao Wang, Shibo He, Michael Backes, Jiming Chen, Yang Zhangwork_takasn3ehjdn5cqtpyzysfcgcaWed, 05 Oct 2022 00:00:00 GMTK-apices Of Minor-closed Graph Classes. I. Bounding The Obstructions
https://scholar.archive.org/work/geliif4ebrfzpgjcwpodot57di
Let G be a minor-closed graph class. We say that a graph G is a k-apex of G if G contains a set S of at most k vertices such that G∖ S belongs to G. We denote by A_k ( G) the set of all graphs that are k-apices of G. We prove that every graph in the obstruction set of A_k ( G), i.e., the minor-minimal set of graphs not belonging to A_k ( G), has size at most 2^2^2^2^ poly(k), where poly is a polynomial function whose degree depends on the size of the minor-obstructions of G. This bound drops to 2^2^ poly(k) when G excludes some apex graph as a minor.Ignasi Sau, Giannos Stamoulis, Dimitrios M. Thilikoswork_geliif4ebrfzpgjcwpodot57diWed, 05 Oct 2022 00:00:00 GMT