IA Scholar Query: Combinatorics of Go.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgThu, 01 Dec 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Bringing a CURE into a Discrete Mathematics Course and Beyond
https://scholar.archive.org/work/ajhzbafhwnhffkzgnow5iuy6ka
Course-based Undergraduate Research Experiences (CUREs) have been well developed in the hard sciences, but math CUREs are all but absent from the literature. Like biology and chemistry, math programs suffer from a lack of research experiences and many students are not able to participate in programs like REUs (Research Experiences for Undergraduates). CUREs are a great alternative, but the current definition of CURE (see [1] ) has potential barriers when applied to mathematics (e.g. time, novelty of project). Our solution to these barriers was to develop a math CURE pathway in which students complete "Math CUREs" in targeted courses. After finishing the pathway (or part of the pathway), students complete a research project in at least one of the following areas: Lie theory, representation theory, or combinatorics. The focus of this paper is the math CURE implemented in a discrete mathematics course for math and computer science majors. We share our experiences with the development and implementation of this CURE over several iterations as well as the impact of the CURE on students experiences through participant survey data obtained from this CURE.Lipika Deka, Peri Shereen, Jeffrey Wandwork_ajhzbafhwnhffkzgnow5iuy6kaThu, 01 Dec 2022 00:00:00 GMTComputational Estimation by Scientific Data Mining with Classical Methods to Automate Learning Strategies of Scientists
https://scholar.archive.org/work/xm6nxk3ydretplyy7666q2ozua
Experimental results are often plotted as 2-dimensional graphical plots (aka graphs) in scientific domains depicting dependent versus independent variables to aid visual analysis of processes. Repeatedly performing laboratory experiments consumes significant time and resources, motivating the need for computational estimation. The goals are to estimate the graph obtained in an experiment given its input conditions, and to estimate the conditions that would lead to a desired graph. Existing estimation approaches often do not meet accuracy and efficiency needs of targeted applications. We develop a computational estimation approach called AutoDomainMine that integrates clustering and classification over complex scientific data in a framework so as to automate classical learning methods of scientists. Knowledge discovered thereby from a database of existing experiments serves as the basis for estimation. Challenges include preserving domain semantics in clustering, finding matching strategies in classification, striking a good balance between elaboration and conciseness while displaying estimation results based on needs of targeted users, and deriving objective measures to capture subjective user interests. These and other challenges are addressed in this work. The AutoDomainMine approach is used to build a computational estimation system, rigorously evaluated with real data in Materials Science. Our evaluation confirms that AutoDomainMine provides desired accuracy and efficiency in computational estimation. It is extendable to other science and engineering domains as proved by adaptation of its sub-processes within fields such as Bioinformatics and Nanotechnology.Aparna S. Vardework_xm6nxk3ydretplyy7666q2ozuaMon, 31 Oct 2022 00:00:00 GMTSecurity and privacy recommendation of mobile app for Arabic speaking
https://scholar.archive.org/work/tqcfmynberc3hgpxqumaxyn7ma
<p>There is an enormous number of mobile apps, leading users to be concerned about the security and privacy of their data. But few users are aware of what is meant by app permissions, which sometimes do not illustrate what kind of data is gathered. Therefore, users are still concerned about security risks and privacy, with little knowledge and experience of what security and privacy awareness. Users depend on ratings, which may be fake, or keep track of their sense to install an app, and an enormous number of users do not like to read reviews. To solve this issue, we propose a recommender system that reads users' reviews, and which exposes flaws, violations and third-party policies or the quality of a user's experience. In order to design and implement our recommender, we conduct a survey which supports two significant points: to detect the level of security and privacy awareness between users, and to gather new words into a dictionary of a recommender system, which assists to classify each review on the correct level, which can indeed reveal the scale of security and privacy in an app.</p>Hameed Almubarak, Mohamed Khairallah Khouja, Ahmed Jedidiwork_tqcfmynberc3hgpxqumaxyn7maSat, 01 Oct 2022 00:00:00 GMTCompletion and Embedding Problems for Combinatorial Designs
https://scholar.archive.org/work/cvk2kik2b5artcfkh2dp3g3gei
Combinatorial design theory studies arrangements and combinations of discrete objects according to different rules. Applications of designs are not only limited to analysis of experiments, but also useful in network analysis, cryptography and communication protocols, error correcting codes, mathematical biology, algorithm design, tournament scheduling, lotteries, etc. The topic of when a partial combinatorial design can be completed or embedded has attracted a great deal of interest over the years. In this thesis, we investigate four topics related to the completion or embedding of partial H-designs. We make progress on partial Steiner triple systems, partial block designs and partial star designs.AJANI RUWANDHIKA CHULANGI DE VAS GUNASEKARAwork_cvk2kik2b5artcfkh2dp3g3geiSat, 06 Aug 2022 00:00:00 GMTSwarm Control for Distributed Construction: A Computational Complexity Perspective
https://scholar.archive.org/work/guilhsv4cffm3lcfljbsqngaie
Over the last 20 years, human interaction with robot swarms has been investigated as a means to mitigate problems associated with the control and coordination of such swarms by either human teleoperation or completely autonomous swarms. Ongoing research seeks to characterize those situations in which such interaction is both viable and preferable. In this paper, we contribute to this effort by giving the first computational complexity analyses of problems associated with algorithm, environmental influence, and leader selection methods for the control of swarms performing distributed construction tasks. These analyses are done relative to a simple model in which swarms of deterministic finite-state robots operate in a synchronous error-free manner in 2D grid-based environments. We show that all three of our problems are polynomial-time intractable in general and remain intractable under a number of plausible restrictions (both individually and in many combinations) on robot controllers, environments, target structures, and sequences of swarm control commands. We also give the first restrictions relative to which these problems are tractable, as well as discussions of the implications of our results for both the design and deployment of swarm control assistance software tools and the human control of swarms.Todd Wareham, Ronald de Haan, Andrew Vardy, Iris van Rooijwork_guilhsv4cffm3lcfljbsqngaieFri, 05 Aug 2022 00:00:00 GMTComputing Real Numbers with Large-Population Protocols Having a Continuum of Equilibria
https://scholar.archive.org/work/fdjsn7ibbff3ziqp2fqu65g54i
Bournez, Fraigniaud, and Koegler [Bournez et al., 2012] defined a number in [0,1] as computable by their Large-Population Protocol (LPP) model, if the proportion of agents in a set of marked states converges to said number over time as the population grows to infinity. The notion, however, restricts the ordinary differential equations (ODEs) associated with an LPP to have only finitely many equilibria. This restriction places an intrinsic limitation on the model. As a result, a number is computable by an LPP if and only if it is algebraic, namely, not a single transcendental number can be computed under this notion. In this paper, we lift the finitary requirement on equilibria. That is, we consider systems with a continuum of equilibria. We show that essentially all numbers in [0,1] that are computable by bounded general-purpose analog computers (GPACs) or chemical reaction networks (CRNs) can also be computed by LPPs under this new definition. This implies a rich series of numbers (e.g., the reciprocal of Euler's constant, π/4, Euler's γ, Catalan's constant, and Dottie number) are all computable by LPPs. Our proof is constructive: We develop an algorithm that transfers bounded GPACs/CRNs into LPPs. Our algorithm also fixes a gap in Bournez et al.'s construction of LPPs designed to compute any arbitrary algebraic number in [0,1].Xiang Huang, Rachel N. Huls, Thomas E. Ouldridge, Shelley F. J. Wickhamwork_fdjsn7ibbff3ziqp2fqu65g54iThu, 04 Aug 2022 00:00:00 GMTLIPIcs, Volume 238, DNA 28, Complete Volume
https://scholar.archive.org/work/627o3xn4vbbgpdox5dwolgcuny
LIPIcs, Volume 238, DNA 28, Complete VolumeThomas E. Ouldridge, Shelley F. J. Wickhamwork_627o3xn4vbbgpdox5dwolgcunyThu, 04 Aug 2022 00:00:00 GMTAlgebraic groups in non-commutative probability theory revisited
https://scholar.archive.org/work/qi7y3gzhirhmdbfto3uuqhfu7u
The role of coalgebras as well as algebraic groups in non-commutative probability has long been advocated by the school of von Waldenfels and Sch\"urmann. Another algebraic approach was introduced more recently, based on shuffle and pre-Lie calculus, and resulting in another construction of groups of characters encoding the behaviour of states. Comparing the two, the first approach, recast recently in a general categorical language by Manzel and Sch\"urmann, can be seen as largely driven by the theory of universal products, whereas the second construction builds on Hopf algebras and a suitable algebraization of the combinatorics of noncrossing set partitions. Although both address the same phenomena, moving between the two viewpoints is not obvious. We present here an attempt to unify the two approaches by making explicit the Hopf algebraic connections between them. Our presentation, although relying largely on classical ideas as well as results closely related to Manzel and Sch\"urmann's aforementioned work, is nevertheless original on several points and fills a gap in the free probability literature. In particular, we systematically use the language and techniques of algebraic groups together with shuffle group techniques to prove that two notions of algebraic groups naturally associated with free, respectively Boolean and monotone, probability theories identify. We also obtain explicit formulas for various Hopf algebraic structures and detail arguments that had been left implicit in the literature.Ilya Chevyrev and Kurusch Ebrahimi-Fard and Frédéric Patraswork_qi7y3gzhirhmdbfto3uuqhfu7uThu, 04 Aug 2022 00:00:00 GMTDirac-type theorems in random hypergraphs
https://scholar.archive.org/work/radpwtwh4replhtyszkmn4v6jm
For positive integers d0 and any "not too small" p, we prove that a random k-uniform hypergraph G with n vertices and edge probability p typically has the property that every spanning subgraph of G with minimum degree at least (1+ε)m_d(k,n)p has a perfect matching. One interesting aspect of our proof is a "non-constructive" application of the absorbing method, which allows us to prove a bound in terms of m_d(k,n) without actually knowing its value.Asaf Ferber, Matthew Kwanwork_radpwtwh4replhtyszkmn4v6jmThu, 04 Aug 2022 00:00:00 GMTCalogero-Moser spaces vs unipotent representations
https://scholar.archive.org/work/jmtyfwgcknd6ph3ms2ljroatdy
Lusztig's classification of unipotent representations of finite reductive groups depends only on the associated Weyl group W (endowed with its Frobenius automorphism). All the structural questions (families, Harish-Chandra series, partition into blocks...) have an answer in a combinatorics that can be entirely built directly from W. Over the years, we have noticed that the same combinatorics seems to be encoded in the Poisson geometry of a Calogero-Moser space associated with W (roughly speaking, families correspond to ℂ^×-fixed points, Harish-Chandra series correspond to symplectic leaves, blocks correspond to symplectic leaves in the fixed point subvariety under the action of a root of unity). The aim of this survey is to gather all these observations, state precise conjectures and provide general facts and examples supporting these conjectures.Cédric Bonnaféwork_jmtyfwgcknd6ph3ms2ljroatdyThu, 04 Aug 2022 00:00:00 GMTSubstructures in Latin squares
https://scholar.archive.org/work/7s5oc53pq5g5djqancnbkzs7zm
We prove several results about substructures in Latin squares. First, we explain how to adapt our recent work on high-girth Steiner triple systems to the setting of Latin squares, resolving a conjecture of Linial that there exist Latin squares with arbitrarily high girth. As a consequence, we see that the number of order-n Latin squares with no intercalate (i.e., no 2×2 Latin subsquare) is at least (e^-9/4n-o(n))^n^2. Equivalently, ℙ[𝐍=0]≥ e^-n^2/4-o(n^2)=e^-(1+o(1))𝔼𝐍, where 𝐍 is the number of intercalates in a uniformly random order-n Latin square. In fact, extending recent work of Kwan, Sah, and Sawhney, we resolve the general large-deviation problem for intercalates in random Latin squares, up to constant factors in the exponent: for any constant 0<δ≤1 we have ℙ[𝐍≤(1-δ)𝔼𝐍]=exp(-Θ(n^2)) and for any constant δ>0 we have ℙ[𝐍≥(1+δ)𝔼𝐍]=exp(-Θ(n^4/3log n)). Finally, as an application of some new general tools for studying substructures in random Latin squares, we show that in almost all order-n Latin squares, the number of cuboctahedra (i.e., the number of pairs of possibly degenerate 2×2 submatrices with the same arrangement of symbols) is of order n^4, which is the minimum possible. As observed by Gowers and Long, this number can be interpreted as measuring "how associative" the quasigroup associated with the Latin square is.Matthew Kwan, Ashwin Sah, Mehtaab Sawhney, Michael Simkinwork_7s5oc53pq5g5djqancnbkzs7zmThu, 04 Aug 2022 00:00:00 GMTTotal stability and Auslander-Reiten theory for Dynkin quivers
https://scholar.archive.org/work/e5jnx5knmnfktamdjglx5prbfi
This paper concerns stability functions for Dynkin quivers, in the generality introduced by Rudakov. We show that relatively few inequalities need to be satisfied for a stability function to be totally stable (i.e. to make every indecomposable stable). Namely, a stability function μ is totally stable if and only if μ(τ V) < μ(V) for every almost split sequences 0 →τ V → E → V → 0 where E is indecomposable. These can be visualized as those sequences around the "border" of the Auslander-Reiten quiver.Yariana Diaz, Cody Gilbert, Ryan Kinserwork_e5jnx5knmnfktamdjglx5prbfiThu, 04 Aug 2022 00:00:00 GMTSuper Catalan Numbers and Fourier Summation over Finite Fields
https://scholar.archive.org/work/waql5bdudfdfxc3v4ikyn7apze
We study polynomial summation over unit circles over finite fields of odd characteristic, obtaining a purely algebraic integration theory without recourse to infinite procedures. There are nonetheless strong parallels to classical integration theory over a circle, and we show that the super Catalan numbers and closely related rational numbers lie at the heart of both theories. This gives a uniform analytic meaning to these up to now somewhat mysterious numbers. Our derivation utilises the three-fold symmetry of chromogeometry between Euclidean and relativistic geometries, and we find that the Fourier summation formulas we derive in these two different settings are closely connected.Kevin Limanta, Norman J. Wildbergerwork_waql5bdudfdfxc3v4ikyn7apzeWed, 03 Aug 2022 00:00:00 GMTNon-planar BCFW Grassmannian Geometries
https://scholar.archive.org/work/nk5du4z4ynerna2ckaxwxyy3qm
In this paper, we study non-adjacent BCFW recursion relations and their connection to positive geometry. For an adjacent BCFW shift, the n-point N^kMHV tree-level amplitude in N=4 SYM theory is expressed as a sum over planar on-shell diagrams, corresponding to canonical dlog forms on the cells in the positive Grassmannian G_+(k,n). Non-adjacent BCFW shifts naturally lead to an expansion of the amplitude in terms of a different set of objects, which do not manifest the cyclic ordering and the hidden Yangian symmetry of the amplitude. We show that these terms can be interpreted as dlog forms on the non-planar Grassmannian geometries, generalizing the cells of the positive Grassmannian G_+(k,n) to a larger class of objects which live in G(k,n). We focus mainly on the case of NMHV amplitudes and discuss in detail the Grassmannian geometries. We also propose an alternative way to calculate the associated on-shell functions and dlog forms using an intriguing connection between Grassmannian configurations and the geometry in the kinematical space.Shruti Paranjape, Jaroslav Trnka, Minshan Zhengwork_nk5du4z4ynerna2ckaxwxyy3qmWed, 03 Aug 2022 00:00:00 GMTAsymptotic freeness through unitaries generated by polynomials of Wigner matrices
https://scholar.archive.org/work/m2ue7o4hmfhexok2vftgfpku74
We study products of functions applied in self-adjoint polynomials in deterministic matrices and independent Wigner matrices; we compute the deterministic approximations of such products and control the fluctuations. We focus on minimizing the assumption of smoothness on those functions while optimizing the error term with respect to N, the size of the matrices. As an application, we build on the idea that the long-time Heisenberg evolution associated to Wigner matrices generates asymptotic freeness as first shown in [8]. More precisely given P a self-adjoint non-commutative polynomial and Y^N a d-tuple of independent Wigner matrices, we prove that the quantum evolution associated to the operator P(Y^N) yields asymptotic freeness for large times.Félix Parraud, Kevin Schnelliwork_m2ue7o4hmfhexok2vftgfpku74Wed, 03 Aug 2022 00:00:00 GMTStability version of Dirac's theorem and its applications for generalized Turán problems
https://scholar.archive.org/work/xivx32prunc7po4n743qs2q7w4
In 1952, Dirac proved that every 2-connected n-vertex graph with the minimum degree k+1 contains a cycle of length at least min{n, 2(k+1)}. Here we obtain a stability version of this result by characterizing those graphs with minimum degree k and circumference at most 2k+1. We present applications of the above-stated result by obtaining generalized Turán numbers. In particular, for all ℓ≥ 5 we determine how many copies of a five-cycle as well as four-cycle are necessary to guarantee that the graph has circumference larger than ℓ. In addition, we give a new proof of Luo's Theorem for cliques using our stability result.Xiutao Zhu, Ervin Győri, Zhen He, Zequn Lv, Nika Salia, Chuanqi Xiaowork_xivx32prunc7po4n743qs2q7w4Wed, 03 Aug 2022 00:00:00 GMTSafety Analysis Methods for Complex Systems in Aviation
https://scholar.archive.org/work/ptsnvz3syvf6fbszsyuhng4evu
Each new concept of operation and equipment generation in aviation becomes more automated, integrated and interconnected. In the case of Unmanned Aircraft Systems (UAS), this evolution allows drastically decreasing aircraft weight and operational cost, but these benefits are also realized in highly automated manned aircraft and ground Air Traffic Control (ATC) systems. The downside of these advances is overwhelmingly more complex software and hardware, making it harder to identify potential failure paths. Although there are mandatory certification processes based on broadly accepted standards, such as ARP4754 and its family, ESARR 4 and others, these standards do not allow proof or disproof of safety of disruptive technology changes, such as GBAS Precision Approaches, Autonomous UAS, aircraft self-separation and others. In order to leverage the introduction of such concepts, it is necessary to develop solid knowledge on the foundations of safety in complex systems and use this knowledge to elaborate sound demonstrations of either safety or unsafety of new system designs. These demonstrations at early design stages will help reducing costs both on development of new technology as well as reducing the risk of such technology causing accidents when in use. This paper presents some safety analysis methods which are not in the industry standards but which we identify as having benefits for analyzing safety of advanced technological concepts in aviation.Ítalo Romani de Oliveira, José Alexandre T. Guerreiro Fregnani, Gláucia Costa Balvedi, Michael L. Ulrey, Jeffery D. Musiakwork_ptsnvz3syvf6fbszsyuhng4evuWed, 03 Aug 2022 00:00:00 GMT𝒩=2^* Schur indices
https://scholar.archive.org/work/f6anqlkirne5fiohfzabli5gv4
We find closed-form expressions for the Schur indices of 4d 𝒩=2^* super Yang-Mills theory with unitary gauge groups for arbitrary ranks via the Fermi-gas formulation. They can be written as a sum over the Young diagrams associated with spectral zeta functions of an ideal Fermi-gas system. These functions are expressed in terms of the twisted Weierstrass functions, generating functions for quasi-Jacobi forms. The indices lie in the polynomial ring generated by the Kronecker theta function and the Weierstrass functions which contains the polynomial ring of the quasi-Jacobi forms. The grand canonical ensemble allows for another simple exact form of the indices as infinite series. In addition, we find that the unflavored Schur indices and their limits can be expressed in terms of several generating functions for combinatorial objects, including sum of triangular numbers, generalized sums of divisors and overpartitions.Yasuyuki Hatsuda, Tadashi Okazakiwork_f6anqlkirne5fiohfzabli5gv4Tue, 02 Aug 2022 00:00:00 GMTOn Good 2-Query Locally Testable Codes from Sheaves on High Dimensional Expanders
https://scholar.archive.org/work/l6ic3hvtnjfcppkjp6nvsiz2vm
We expose a strong connection between good 2-query locally testable codes (LTCs) and high dimensional expanders. Here, an LTC is called good if it has constant rate and linear distance. Our emphasis in this work is on LTCs testable with only 2 queries, which are of particular interest to theoretical computer science. This is done by introducing a new object called a sheaf that is put on top of a high dimensional expander. Sheaves are vastly studied in topology. Here, we introduce sheaves on simplicial complexes. Moreover, we define a notion of an expanding sheaf that has not been studied before. We present a framework to get good infinite families of 2-query LTCs from expanding sheaves on high dimensional expanders, utilizing towers of coverings of these high dimensional expanders. Starting with a high dimensional expander and an expanding sheaf, our framework produces an infinite family of codes admitting a 2-query tester. We show that if the initial sheaved high dimensional expander satisfies some conditions, which can be checked in constant time, then these codes form a family of good 2-query LTCs. We give candidates for sheaved high dimensional expanders which can be fed into our framework, in the form of an iterative process which conjecturally produces such candidates given a high dimensional expander and a special auxiliary sheaf. (We could not verify the prerequisites of our framework for these candidates directly because of computational limitations.) We analyse this process experimentally and heuristically, and identify some properties of the fundamental group of the high dimensional expander at hand which are sufficient (but not necessary) to get the desired sheaf, and consequently an infinite family of good 2-query LTCs.Uriya A. First, Tali Kaufmanwork_l6ic3hvtnjfcppkjp6nvsiz2vmTue, 02 Aug 2022 00:00:00 GMTExploring variational quantum eigensolver ansatzes for the long-range XY model
https://scholar.archive.org/work/ztxbjqazjnabng4y5uoe7mwxta
Finding the ground state energy and wavefunction of a quantum many-body system is a key problem in quantum physics and chemistry. We study this problem for the long-range XY model by using the variational quantum eigensolver (VQE) algorithm. We consider VQE ansatzes with full and linear entanglement structures consisting of different building gates: the CNOT gate, the controlled-rotation (CRX) gate, and the two-qubit rotation (TQR) gate. We find that the full-entanglement CRX and TQR ansatzes can sufficiently describe the ground state energy of the long-range XY model. In contrast, only the full-entanglement TQR ansatz can represent the ground state wavefunction with a fidelity close to one. In addition, we find that instead of using full-entanglement ansatzes, restricted-entanglement ansatzes where entangling gates are applied only between qubits that are a fixed distance from each other already suffice to give acceptable solutions. Using the entanglement entropy to characterize the expressive powers of the VQE ansatzes, we show that the full-entanglement TQR ansatz has the highest expressive power among them.Jia-Bin You, Dax Enshan Koh, Jian Feng Kong, Wen-Jun Ding, Ching Eng Png, Lin Wuwork_ztxbjqazjnabng4y5uoe7mwxtaTue, 02 Aug 2022 00:00:00 GMT