Split (1)

train · 617k rows

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_last_ process in S to write X, it will not see its own id, and will not stop.2 To obtain a name, a process starts at (r,c) = (0,0), and repeatedly executes the splitter at its current position (r,c). If the splitter returns right, it moves to (r,c+1); if down, it moves to (r+1,c); if stop, it stops, and returns the na...	{ "page_id": null, "source": 7357, "title": "from dpo" }
for Claim 4, replacing rows with columns and using Claim 2 instead of Claim 1. Iterating the preceding claims, the number of processes that reach row r is bounded by k-r for r ≤ k, and similarly the number that reach column c is bounded by k-c for c ≤ k. It follows that no process reaches row k or column k, which is wh...	{ "page_id": null, "source": 7357, "title": "from dpo" }
original names. Since we didn't prove anything about time complexity of the humongous-snapshot algorithm, we can't say much about the time complexity of this combined one. Moir and Anderson suggest using an O(Nk 2) algorithm of Borowsky and Gafni to get O(k 4) time for the combined algorithm. Faster algorithms have pro...	{ "page_id": null, "source": 7357, "title": "from dpo" }
where to watch all the other Marvel Television properties (Agents of SHIELD, the NetFlix Marvel shows, The Runaways, etc.) and promotional releases like webisodes should be viewed in the order. Relevant non-MCU films like the earlier Spider-Man franchises are also addressed there. Rather than hammer you all with that w...	{ "page_id": null, "source": 7359, "title": "from dpo" }
Infinity War 23) Captain Marvel 24) Avengers: Endgame 25) WandaVision, S1 (D+) 26) Falcon & the Winter Solider, S1 (D+) 27) Spider-Man: Far from Home 28) Spider-Man: No Way Home 29) Hawkeye, S1 (D+) 30) Guardians of the Galaxy Holiday Special (D+) 31) Loki, S1 (D+) 32) Ant-Man & ...	{ "page_id": null, "source": 7359, "title": "from dpo" }
Title: A Formal Framework for Complex Event Processing URL Source: Markdown Content: # A Formal Framework for Complex Event Processing # Alejandro Grez Pontificia Universidad Católica de Chile, Santiago, Chile Millennium Institute for Foundational Research on Data, Santiago, Chile ajgrez@uc.cl # Cristian Riveros Ponti...	{ "page_id": null, "source": 7361, "title": "from dpo" }
results. Finally, we gather the main results of this work to present an efficient and declarative framework for CEP. 2012 ACM Subject Classification Information systems → Data streams; Theory of computation → Data structures and algorithms for data management; Theory of computation → Database query languages (principle...	{ "page_id": null, "source": 7361, "title": "from dpo" }
applicable to real-life scenarios. Other design decisions, like query languages, are generally adapted to match computational models that can efficiently process data (see for example [50 ]). This has produced new data management and optimization techniques, generating promising results in the area [49, 1]. Unfortunate...	{ "page_id": null, "source": 7361, "title": "from dpo" }
], informally defined [ 26 ] or non-standard [ 22 , 5 ]. In practice this implies that, although finite state automata is a recurring approach in CEP, there is no general evaluation strategy with clear performance guarantees. Given this scenario, the goal of this paper is to give solid foundations to CEP systems in ter...	{ "page_id": null, "source": 7361, "title": "from dpo" }
we bring together our results to present a formal framework for evaluating CEL. A. Grez, C. Riveros, and M. Ugarte 5:3 Related work. Active Database Management Systems (ADSMS) and Data Stream Manage-ment Systems (DSMS) process data streams, and thus they are usually associated with CEP systems. Both technologies aim to...	{ "page_id": null, "source": 7361, "title": "from dpo" }
proposals (e.g. CEDR[ 15 ], TESLA[ 22 ], PBCED[ 7]) are defined with a formal semantics but they do not include iteration. An exception is Cayuga[ 25 ], but its language does not allow reusing variables and sequencing is non-associative, which results in an unintuitive semantics. Our framework is comparable to these sy...	{ "page_id": null, "source": 7361, "title": "from dpo" }
a first scenario, assume that there are three sensors, and each of them can measure both temperature (in Celsius degrees) and relative humidity (as the percentage of vapor in the air). Each sensor is assigned an id in {0, 1, 2}. The events produced by the sensors consist of the id of the sensor and a measurement of tem...	{ "page_id": null, "source": 7361, "title": "from dpo" }
one of type humidity (H). The events of type temperature and humidity are given names x and y, respectively, and the two events are filtered to select only those pairs (x, y ) representing a high temperature followed by a low humidity measured by sensor 0. What should the evaluation of ϕ1 over the stream in Figure 1 re...	{ "page_id": null, "source": 7361, "title": "from dpo" }
24 , 9, 50 , 2, 17 ]. But although it detects a set of possible fires, it restricts the order in which the two events occur: the temperature must be measured before the humidity. Naturally, this could prevent the detection of a fire in which the humidity was measured first. This motivates the introduction of disjunctio...	{ "page_id": null, "source": 7361, "title": "from dpo" }
26 ]). Coming back to our example, the formula for measuring temperatures whenever an increase of humidity is detected by sensor 1 is: ϕ3 = [H AS x ; (T AS y FILTER y.id = 1)+ ; H AS z] FILTER (x.hum 60 ∧ x.id = 1 ∧ z.id = 1) Intuitively, variables x and z witness the increase of humidity from less than 30% to more th...	{ "page_id": null, "source": 7361, "title": "from dpo" }
+ must allow for skipping arbitrary events. This implies that the complex events {3, 6, 7} and {3, 4, 7} are also part of the output. The previous discussion raises an interesting question: are users interested in all complex events? Are some complex events more informative than others? Coming back to the output of ϕ3 ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
framework, we illustrate one more common feature of CEP, namely correlation . Correlation is introduced by filtering events with predicates that involve more than one event. For example, consider that we want to see how does temperature change at some location whenever there is an increase of humidity, like in ϕ3. What...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Schemas, Tuples and Streams. Let A be a set of attribute names and D a set of values. A database schema R is a finite set of relation names, where each R ∈ R is associated to a tuple of attributes in A denoted by att (R). If R is a relation name, then an R-tuple is a function t ∶ att (R) → D. The type of an R-tuple t i...	{ "page_id": null, "source": 7361, "title": "from dpo" }
the predicate of all tuples that have a humidity attribute of less than 30 . We consider that checking if a tuple t is in a predicate P takes time O(S tS) , and that every atom P (¯x) has constant size (and thus the size of a formula is independent of the type of predicates). We assume a fixed set of predicates P (i.e....	{ "page_id": null, "source": 7361, "title": "from dpo" }
defined as a non-empty and finite set of indices. As mentioned in Section 2, a complex event contains the positions of the events that witness the matching of a formula over a stream, and moreover, they are the final output of evaluating a formula over a stream. We denote by SCS the size of C and by min (C) and max (C)...	{ "page_id": null, "source": 7361, "title": "from dpo" }
U ⊆ X and two valuations ν1 and ν2, the valuation ν1[ν2~U ] is defined by ν1ν2~U = ν2(x) if x ∈ U and by ν1ν2~U = ν1(x) otherwise. We are ready to define the semantics of a core-CEL formula ϕ. Given a complex event C and a stream S, we say that C is in the evaluation of ϕ over S under valuation ν (C ∈ ⟦ϕ⟧( S, ν )) if...	{ "page_id": null, "source": 7361, "title": "from dpo" }
C D T 2 0 1 9 5:8 A Formal Framework for Complex Event Processing that x will be already assigned (because R AS x occurs outside the subformula). This is precisely where other frameworks fail to formalize iteration, as without this construct it is not easy to correlate the variables inside + with the ones outside, as w...	{ "page_id": null, "source": 7361, "title": "from dpo" }
and MAX are useful selection strategies from a semantic point of view. We define each selection strategy below, giving the motivation and formal semantics. STRICT. As the name suggest, STRICT or strict-contiguity keeps only the complex events that are contiguous in the stream. To motivate this, recall that formula ϕ1 i...	{ "page_id": null, "source": 7361, "title": "from dpo" }
read ” (*). In practice, skip-till-next-match is defined by an evaluation algorithm that greedily adds an event to the output whenever a sequential operator is used, or adds as many events as possible whenever an iteration operator is used. The fact that the semantics is only defined A. Grez, C. Riveros, and M. Ugarte ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
S, ν ), if max (C) = max (C′) then C′ ≤next C. In other words, C must be the ≤next -maximum match among all matches that end in max (C). In our running example, we have that {1, 8} matches NXT (ϕ1) but {5, 8} does not. Furthermore, {3, 4, 6, 7} matches NXT (ϕ4) while {3, 4, 7} and {3, 6, 7} do not. Note that we compare...	{ "page_id": null, "source": 7361, "title": "from dpo" }
it does not come from a greedy heuristic like NXT does. MAX. A more ambitious selection strategy is to keep the maximal complex events in terms of set inclusion, which could be naturally more useful because these complex events are the most informative . Formally, given a CEL formula ϕ we say that C ∈ ⟦MAX (ϕ)⟧( S, ν )...	{ "page_id": null, "source": 7361, "title": "from dpo" }
formulas. Although CEL has well-defined semantics, there are some formulas whose semantics can be unintuitive. Consider for example the formula ϕ5 = (H AS x) FILTER (y.tmp ≤ 30 ). Here, x will be naturally bound to the only element in a complex event, but y will not add a new position to the output. By the semantics of...	{ "page_id": null, "source": 7361, "title": "from dpo" }
there is another subformula ψx such that x ∈ bound (ψx) and ψ is a subformula of ψx. This definition allows for including filters with variables defined in a wider scope. For example, formula ϕ4 in Section 2 is well-formed although it has the not-well-formed formula (T AS y FILTER y.id = x.id )+ as a subformula. One ca...	{ "page_id": null, "source": 7361, "title": "from dpo" }
the case. Formally, we say that two CEL formulas ϕ and ψ are equivalent, denoted by ϕ ≡ ψ, if ⟦ϕ⟧( S) = ⟦ψ⟧( S) for every stream S.A. Grez, C. Riveros, and M. Ugarte 5:11 I Theorem 2. Given a core-CEL formula ϕ, there is a safe formula ϕ′ such that ϕ ≡ ϕ′ and Sϕ′S is at most exponential in SϕS. By this result, we can r...	{ "page_id": null, "source": 7361, "title": "from dpo" }
holds that ¯x = {x} and ϕ′ = R AS x for some R and x. In other words, all filters containing unary predicates are applied directly to the definitions of their variables. For instance, formula ϕ′ > 1 is in LP-normal form while formulas ϕ1 and ϕ2 are not. Note that non-unary predicates are not restricted, and they can be...	{ "page_id": null, "source": 7361, "title": "from dpo" }
model for CEL In this section, we introduce a formal computational model for evaluating CEL formulas called complex event automata (CEA for short). Similar to classical database management systems (DBMS), it is useful to have a formal model that stands between the query language I C D T 2 0 1 9 5:12 A Formal Framework ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
of boolean answers. A well known extension for FSA are Finite State Transducers [ 16 ], which are capable of producing an output whenever an input element is read. Our computational model follows the same approach: CEA are allowed to generate and output complex events when reading a stream. Recall from Section 5 that U...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Section 5). Given a stream S and n ∈ N, we define the set of complex events of A over S at position n as ⟦A⟧n(S) = {events (ρ) S ρ ∈ Run n(A, S )} and the set of all complex events as ⟦A⟧( S) = ⋃n ⟦A⟧n(S). Note that ⟦A⟧( S) can be infinite, but ⟦A⟧n(S) is finite. Consider as an example the CEA A depicted in Figure 2. I...	{ "page_id": null, "source": 7361, "title": "from dpo" }
of complex events. Here P(x)∶= > type (x)=Hand P′(x)∶=type (x)=T∧x.temp >40 . formula ϕ4 needs unbounded memory to store candidate events seen in the past, and thus, it calls for a more sophisticated model (e.g. data automata [ 45 ]). Of course one would like to have a full-fledged model for CEL, but to this end we mus...	{ "page_id": null, "source": 7361, "title": "from dpo" }
However, we show that the output is of linear size if ϕ′ is safe, and of exponential size otherwise, suggesting that restricting the language to safe formulas allows for more efficient evaluation. We have described the compilation process without considering selection strategies. To include them, we extend our notation...	{ "page_id": null, "source": 7361, "title": "from dpo" }
for Complex Event Processing I/O-deterministic CEA. To evaluate CEA in practice we will focus on the class of the so-called I/O-deterministic CEA (for Input/Output deterministic). A CEA A = (Q, ∆, I, F ) is I/O-deterministic if SIS = 1 and for any two transitions (p, P 1, m 1, q 1) and (p, P 2, m 2, q 2),either P1 and ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
would like to compute complex events in one pass and using a restricted amount of resources. Streaming algorithms [ 34 , 28 ] are a natural starting point as they usually restrict the time allowed to process each tuple and the space needed to process the first n items of a stream (e.g., constant or logarithmic in n). H...	{ "page_id": null, "source": 7361, "title": "from dpo" }
]precisely for defining efficiency whenever generating the output might use considerable time. Formally, it requires the existence of a routine Enumerate that receives D as input and outputs all complex events in ⟦A⟧n(S) without repetitions, while spending a constant amount of time before and after each output. Natural...	{ "page_id": null, "source": 7361, "title": "from dpo" }
I Theorem 7. For every I/O-deterministic CEA A, there is a CEP evaluation algorithm with SAS-update time. Furthermore, if A is any CEA, there is a CEP evaluation algorithm with 2SAS-update time. We can further extend the CEP evaluation algorithm for I/O-deterministic CEA to any selection strategies by using the results...	{ "page_id": null, "source": 7361, "title": "from dpo" }
an exponentially larger formula. To avoid this, in many cases one can apply local rewriting rules [3 , 41 ]. For example, in Section 2 we converted ϕ1 into ϕ′ > 1 by applying a filter push , avoiding the exponential I C D T 2 0 1 9 5:16 A Formal Framework for Complex Event Processing blow-up of Theorem 3. Unfortunately...	{ "page_id": null, "source": 7361, "title": "from dpo" }
this same direction, we envision as future work a generalization of the concept behind selection strategies, together with a thorough study of their expressive power. Finally, we have focused on the fundamental features of CEP languages, leaving other features outside to keep the language and analysis simple. These fea...	{ "page_id": null, "source": 7361, "title": "from dpo" }
2006. A. Grez, C. Riveros, and M. Ugarte 5:17 11 Alexander Artikis, Alessandro Margara, Martin Ugarte, Stijn Vansummeren, and Matthias Weidlich. Complex Event Recognition Languages: Tutorial. In DEBS , pages 7–10. ACM, 2017. 12 Alexander Artikis, Marek Sergot, and Georgios Paliouras. An event calculus for event recogni...	{ "page_id": null, "source": 7361, "title": "from dpo" }
and Walker White. A general algebra and implementation for monitoring event streams. Technical report, Cornell University, 2005. 26 Alan Demers, Johannes Gehrke, Mingsheng Hong, Mirek Riedewald, and Walker White. Towards expressive publish/subscribe systems. In EDBT , 2006. 27 Antony Galton and Juan Carlos Augusto. Two...	{ "page_id": null, "source": 7361, "title": "from dpo" }
L Todd Heberlein, and Karl N Levitt. Network intrusion detection. IEEE network , 1994. 40 Peter Pietzuch, Brian Shand, and Jean Bacon. A framework for event composition in distributed systems. In Middleware , 2003. 41 Raghu Ramakrishnan and Johannes Gehrke. Database management systems (3 ed.) . McGraw-Hill, 2003. 42 BS...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Title: Improving automated GUI testing by learning to avoid infeasible tests URL Source: Markdown Content: This is a repository copy of Improving automated GUI testing by learning to avoid infeasible tests .White Rose Research Online URL for this paper: Version: Accepted Version Proceedings Paper: Walkinshaw, N. (202...	{ "page_id": null, "source": 7361, "title": "from dpo" }
are controlled through a graphical user interface (GUI). When it comes to automated test selection, however, GUIs present two major challenges: (1) It is difficult to automatically identify feasible, non-trivial sequences of GUI interactions (test cases), and (2) each attempt at a test case execution can take a long ti...	{ "page_id": null, "source": 7361, "title": "from dpo" }
cases’ amount to potentially complex sequences of widget clicks, drags, gestures, etc. In this paper we investigate a solution for scenarios where there is no capability of analysing and querying the run-time GUI state. We may, for example, be interested in testing an application across a multitude of platforms. We con...	{ "page_id": null, "source": 7361, "title": "from dpo" }
its capacity to distinguish between positive and negative examples to produce models that are capable of distinguishing between interaction sequences that have been attempted, and sequences that are likely to be invalid or lead to time-outs. > • We present an algorithm that uses the resulting model to filter-out and pr...	{ "page_id": null, "source": 7361, "title": "from dpo" }
as an Event Flow Graph . This is a graph that contains labels corresponding to GUI events, where transitions indicate the order in which these events are deemed to be possible. Definition 1: An EFG is a directed graph (V, E, I ), where each element v ∈ V corresponds to an event in the GUI. E is a set of edges (vi, v j ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
the target API or OS platform. They can only be re-engineered to an alternative platform if it offers a comparable interface with runtime access to the underlying GUI state. B. State Machines Definition 2: A Deterministic Finite Automaton (DFA) is a quituple (Q, Σ, ∆, F, q 0), where Q is a finite set of states, Σ is a ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
to the possible (and impossible) sequences of elements in Σ (denoted Σ∗). The set of all possible sequences in a DFA is referred to as its language . To define this formally, we draw on the inductive definition for an extended transition function ˆδ used by Hopcroft et al. . For a state q and a string w,the extended tr...	{ "page_id": null, "source": 7361, "title": "from dpo" }
, , and is detailed in Algorithm 1. In essence, the approach starts from two sets of sequences: S+ - a set of sequences that are accepted by the subject, and S− - a set of sequences that are not. From these it constructs a tree-shaped automaton (a ‘prefix-tree automaton’) that exactly represents a given set of sequence...	{ "page_id": null, "source": 7361, "title": "from dpo" }
inference. The idea was first ex-plored by Mariani et al. with the AutoBlackTest approach , which used QLearning to infer behaviours from the GUI under test as it is being tested, and to then use this as a basis for selecting new inputs. Subsequently, Choi et al. developed the SwiftHand Android testing tool (which is...	{ "page_id": null, "source": 7361, "title": "from dpo" }
before testing). All test executions are treated the same – regardless of whether they terminated successfully or ended in a time-out and had to be aborted. In the terms of the state merging algorithm presented in Algorithm 1, all of the traces belong to set S+ and S− is empty. This severely hampers model inference; wi...	{ "page_id": null, "source": 7361, "title": "from dpo" }
testing scenario . For the sake of practicality, we seek to limit our practical requirements where possible. We describe the key components (and distinguish between those that are absolutely necessary and those that are desirable) with respect to the GUI-testing setup illustrated in the grey-shaded elements in Figure 1...	{ "page_id": null, "source": 7361, "title": "from dpo" }
of GUI functionali-ties. This is challenging because test cases can require a long time to execute. Although GUI Rippers may have the EFG graph, these can be of limited practical use because of their scale, and the fact that many paths through them are infeasible in practice. For example, the ripped EFG for the smalles...	{ "page_id": null, "source": 7361, "title": "from dpo" }
where \|F inalT estSet \| = i ∗ j > 1 Select( T, i, j ) begin > 2 F inalT estSet ← ∅ ; > 3 S+ ← ∅ ; > 4 S− ← ∅ ; > 5 for 1 to i do > 6 P otential ← T \ F inalT estSet ; > 7 if S+ ∪ S− 6 = ∅ then > 8 DF A ← inf erDF A (S+, S −); > 9 P otential ← P otential ∩ L(DF A ); > 10 T ests ← randomSelection (P otential, j ); > 11 F...	{ "page_id": null, "source": 7361, "title": "from dpo" }
A random sub-set of size j is selected from P otential ,is stored as a separate set T ests , and is added to F inalT estSet .12-13 Each of the tests t ∈ T ests is executed. The execute function returns the sub-sequence of elements e in t that are successfully executed. In practice tests are executed by using whatever t...	{ "page_id": null, "source": 7361, "title": "from dpo" }
many of the proposed tests will invariably not be feasible). IV. P RELIMINARY EVALUATION The goal of our technique is to identify test sets that are ‘efficient’. By skipping tests that are infeasible, it should be possible to spend a greater proportion of the testing effort on meaningful tests that ultimately exercise ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
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large pool of tests), we repeat each run 30 times with different random seeds. As our baseline, we randomly pick the same number of test cases from the pool of candidate test cases that collectively cover the vertices of the EFG (as described in Section III-C). This amounts to a generic coverage-driven GUI testing tech...	{ "page_id": null, "source": 7361, "title": "from dpo" }
interactions than those that are selected at random. When the test runs from all the systems are taken together, the average sequence length achieved from the random selections at the final iteration is 2.41, versus 3.06 for inference-based testing. For all systems apart from JEdit the difference in sequence length is ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
testing are already evident between 100 and 150 iterations, in which case the time-overhead would be significantly lower. Summary The findings are promising. The inclusion of inference supported by negative results leads to longer sequences, which probe aspects of software behaviour that are not reached by random execu...	{ "page_id": null, "source": 7361, "title": "from dpo" }
gauge the extent to which the behaviour of the underlying source code has been executed. This is notoriously imprecise at estimating test adequacy; test set can achieve a high level of statement coverage but still miss out on many aspects of program behaviour. Since we are more interested in using code coverage as a re...	{ "page_id": null, "source": 7361, "title": "from dpo" }
T. Su, G. Meng, Y. Chen, K. Wu, W. Yang, Y. Yao, G. Pu, Y. Liu, and Z. Su, “Guided, stochastic model-based gui testing of android apps,” in Proceedings of the 2017 11th Joint Meeting on Foundations of Software Engineering . ACM, 2017, pp. 245–256. K. J. Lang, B. A. Pearlmutter, and R. A. Price, “Results of the Abbadin...	{ "page_id": null, "source": 7361, "title": "from dpo" }
annual international conference on Mobile systems, applications, and services . ACM, 2014, pp. 204–217. L. Mariani, M. Pezze, O. Riganelli, and M. Santoro, “Autoblacktest: Automatic black-box testing of interactive applications,” in 2012 IEEE Fifth International Conference on Software Testing, Verification and Validat...	{ "page_id": null, "source": 7361, "title": "from dpo" }
W. Biermann and R. Krishnaswamy, “Constructing programs from example computations,” IEEE Transactions on Software Engineering ,no. 3, pp. 141–153, 1976. J. Cook and A. Wolf, “Discovering models of software processes from event-based data,” ACM Transactions on Software Engineering and Methodology , vol. 7, no. 3, pp. 2...	{ "page_id": null, "source": 7361, "title": "from dpo" }
user interface testing using variable finite state machines,” in Fault-Tolerant Computing, 1997. FTCS-27. Digest of Papers., Twenty-Seventh Annual International Symposium on . IEEE, 1997, pp. 80–88. R. S. Sutton and A. G. Barto, Reinforcement learning: An introduction .MIT press Cambridge, 1998, vol. 1, no. 1. G. Bae...	{ "page_id": null, "source": 7361, "title": "from dpo" }
as SwiftHand. Algorithm 3: EFG-supported compatibility function Input : A DFA D and an EFG E. Result : A boolean. > 1 ChoosePair(E, D) begin > 2 merge ← f alse ; > 3 while (Bi, B j ) ← ChoosePair (QD ) ∧ ¬ merge do > 4 Events ← in (D, B i)∪in (D, B j ); > 5 Dest D ←out (D, B i)∪out (D, B j ); > 6 Dest E ← ∅ ; > 7 for e...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Title: OWR-2019-46 URL Source: Markdown Content: ## Mathematisches Forschungsinstitut Oberwolfach Report No. 46/2019 DOI: 10.4171/OWR/2019/46 ## Mini-Workshop: Degeneration Techniques in Representation Theory Organized by Evgeny Feigin, Moscow Ghislain Fourier, Aachen Martina Lanini, Rome 6 October – 12 October 2019 A...	{ "page_id": null, "source": 7361, "title": "from dpo" }
research. The mini-courses were given by Chris Manon (USA), Syu Kato (Japan) and Julianna Tymoczko (USA). The talks of Chris Manon were devoted to the description of various aspects of the Khovanskii bases with applications in commutative algebra, algebraic geom-etry and the theory of Newton-Okounkov bodies. The lectur...	{ "page_id": null, "source": 7361, "title": "from dpo" }
the study of various aspects of the moduli spaces of maps to the flag varieties of simple finite-dimensional Lie groups. In particular, they carry information about degenerations of the maps into the so-called quasi-maps. In his talks Syu Kato gave an overview of the modern state-of-art in the understanding of algebro-...	{ "page_id": null, "source": 7361, "title": "from dpo" }
properties of the maximal flat degeneration were presented. Summarizing, the workshop was very successful: not only we were able to dis-cuss various new results obtained by several groups working in different countries, but we also paved the way for the future research, formulating open problems and discussing new dire...	{ "page_id": null, "source": 7361, "title": "from dpo" }
FFLV polytopes . . . . . . . . . . . . 2893 Martha Precup (joint with Megumi Harada) Hessenberg Varieties and the Stanley–Stembridge Conjecture . . . . . . . . . . 2896 Lara Bossinger Positive initial ideals and the FFLV polytope . . . . . . . . . . . . . . . . . . . . . . . . 2899 Ilya Dumanski Global Demazure modules...	{ "page_id": null, "source": 7361, "title": "from dpo" }
g = n ⊕ h ⊕ n− be a triangular decomposition. For a positive root β ∈ ∆+, fix 0 6 = fβ ∈ n− to be a root vector of weight −β. By assigning deg( fβ ) = 1 we obtain the classical PBW (Poincar´ e-Birkhoff-Witt) filtration on the universal enveloping algebra U (n−) whose associated graded algebra is isomorphic to U (n−,a )...	{ "page_id": null, "source": 7361, "title": "from dpo" }
n−,a acts nilpotently on V a(λ), the abelianized group N −,a := exp( n−,a )acts on V a(λ). Feigin defined the degenerate flag variety Fan := N −,a · [vaρ ] ⊆ P(V a(ρ)) where ρ is the sum of fundamental weights. Recall that the classical type A flag variety Fn admits various realizations: (1) highest weight orbit: exp(...	{ "page_id": null, "source": 7361, "title": "from dpo" }
quiver Grassmannian approach. Such a description is further generalized in [2, 3] where we classify the linear maps f := ( f1, · · · , f n−2) ∈ End( Cn)n−2 such that the scheme Ff > n := {(V1, · · · , V n−1) \| fi(Vi) ⊆ Vi+1 } ⊆ > n−1 ∏ > k=1 Gr k(Cn)enjoys nice geometric properties (normal, irreducible, being a flat de...	{ "page_id": null, "source": 7361, "title": "from dpo" }
and M. Reineke. Linear degenerations of flag varieties . Math. Z., 287 (2017), no. 1–2, 615–654. G. Cerulli Irelli, X. Fang, E. Feigin, G. Fourier and M. Reineke, Linear degenerations of flag varieties: partial flags, defining equations, and group actions , to appear in Math. Z. G. Cerulli Irelli, E. Feigin and M. Re...	{ "page_id": null, "source": 7361, "title": "from dpo" }
flag manifolds reflects the representation theoretic pattern of a (sim-ply connected) semi-simple algebraic group G and its Lie algebra g. It is already apparent in the Borel-Weil theorem, that states the nef line bundle of the full flag variety B of G is in bijection with the set of isomorphism classes of the irreduci...	{ "page_id": null, "source": 7361, "title": "from dpo" }
B of degree β, where β is an element of the non-negative span of the positive coroots of G, identified with the effective classes in H2(B, Z). Since QG(β) admits a resolution of singularities by a variant of the space of stable maps, this opened a possibility to connect the theory of semi-infinite flag manifolds with t...	{ "page_id": null, "source": 7361, "title": "from dpo" }
picture, we recover QG(β) as a partic-ular case of the Richardson variety of Qrat > G . This makes it possible to reasonably understand the coordinate rings of Qrat > G and QG(β) from representation-theoretic perspective, and also exhibits the higher cohomology vanishing of their natural nef line bundles. The proofs of...	{ "page_id": null, "source": 7361, "title": "from dpo" }
that was further polished to the K-theoretic J-function calculation in Braverman-Finkelberg [6, 7]. There, the main geometric portion was to (essentially) guarantee that QG(β) is normal and has rational singularities. Thanks to the reconstruction theorem, the knowledge of the J-fuction is enough to recover the ring str...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Workshop, July 14-20, 2003, Montr´ eal, Canada , volume 38 of CRM Proc. Lecture Notes, pages 113–132. Amer. Math. Soc., Providence, RI, 2004. A. Braverman and M. Finkelberg. Semi-infinite Schubert varieties and quantum K-theory of flag manifolds , J. Amer. Math. Soc., 27 no. 4 1147–1168, 2014. A. Braverman and M. Fin...	{ "page_id": null, "source": 7361, "title": "from dpo" }
several equivalent descriptions, including:. • A function h : {1, 2, . . . , n } → { 1, 2, . . . , n } with h(i) ≥ h(i − 1) for all i (nondecreasing) and h(i) ≥ i for all i (upper-triangular). • A subspace H of gl n with [ H, b] ⊆ H and H ⊃ b. • A subset MH of roots so that if α ∈ M H , β ∈ Φ+, α +β ∈ Φ then α ∈ M H (n...	{ "page_id": null, "source": 7361, "title": "from dpo" }
kinds of singularities do they have; characterize the pieces of cells in each component; identify which permutation flags are in the closure of a given Hessenberg Schubert cell. Equivariant cohomology of Hessenberg varieties. If X is regular semisimple (namely X has n distinct eigenvalues), we have special tools to com...	{ "page_id": null, "source": 7361, "title": "from dpo" }
t n]n! : if w ↔ (ij )w is an edge in EH then ( ti − tj )\|(pw − p(ij )w ) } We describe methods and questions about bases for H∗ > T (Hess (X, h ) like: • how to interpret “upper-triangular bases” for equivariant cohomology • a formula for the upper-triangular (Schubert) basis of H∗ > T (G/B ) [1, Ap-pendix D], • when...	{ "page_id": null, "source": 7361, "title": "from dpo" }
is its Jordan type, and ˜Kλμ (N )(q) is a particular normalization of Kostka-Foulkes polynomials [13, III. Sect.7, 7.11 and Ex. 6]. The left action, which descends to Hessenberg varieties, is the monodromy ac-tion . A version of Equation (1) applies, replacing b with H and replacing the rank of λ with the multiplicity ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
, 12(3):213–235, 1988. Lucas Fresse. Betti numbers of Springer fibers in type A.J. Algebra , 322(7):2566–2579, 2009. Mini-Workshop: Degeneration Techniques in Representation Theory 2883 Mark Goresky, Robert Kottwitz, and Robert MacPherson. Equivariant cohomology, Koszul duality, and the localization theorem. Invent. ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
classification theorem for flat toric families of finite type. These three topics share Khovanskii bases as a common feature. Khovanskii bases and computations in algebras (joint with Kiumars Kaveh) The theory of Khovanskii bases generalizes SAGBI bases, which is itself an ana-logue of the theory of Gr¨ obner bases for...	{ "page_id": null, "source": 7361, "title": "from dpo" }
are subalgebras and monomial orders with no finite SAGBI basis. To remedy this situation, we generalize to the setting of a valuation v : A \ { 0} → Zd, where Zd is equipped with a group order ≺. The associated graded algebra gr v(A) plays the role of in ≺(A). We define a Khovanskii basis to be a set B ⊂ A whose image ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
on A with Khovanskii basis B. In it is also shown that the initial ideals found in Σ Γ(I) are the same as those found by classical Gr¨ obner theory (ie Zd = Z). The following is a consequence. Theorem 1. [Kaveh-M] A positively graded domain A has a full rank valuation v : A \ { 0} → Zd with finite Khovanskii basis B ⊂...	{ "page_id": null, "source": 7361, "title": "from dpo" }
we let the special fiber of the degeneration belong to a larger class of varieties. The complexity of a variety X equipped with an effective action by an algebraic torus T is dim (X) − rank (T ). In this way, complexity-1 varieties are a natural relaxation of toric varieties. Altmann and Hausen have constructed a comb...	{ "page_id": null, "source": 7361, "title": "from dpo" }
prime cones σ1 and σ2 share a facet σ1 ∩σ2 = τ , one can then consider a corresponding valuation into OΣ, where Σ is the fan defined by σ1, σ 2, τ ; this is the natural setting for considering mutations between the Newton-Okounkov bodies associated to the prime cones σ1, σ 2. With these constructions as motivation, it ...	{ "page_id": null, "source": 7361, "title": "from dpo" }
Smith in . Theorem 3 and its corollaries suggest a new way to construct toric vector bun-dles, and other toric families. Let k[TN ] be the coordinate ring of the torus TN and wN : k[TN ] → O N be the canonical valuation which sends a Laurent polyno-mial p(t) = ∑ℓi=1 citαi to the support function wN (p) = min {αi \| ci 6...	{ "page_id": null, "source": 7361, "title": "from dpo" }
rank valuations, and tropical geometry .SIAM J. Appl. Algebra Geometry, 3(2) (2019), 292–336. K. Kaveh and C. Manon, Toric bundles, valuations, and tropical geometry over the semifield of piecewise linear functions . arXiv:1907.00543[math.AG]. K. Kaveh and C. Manon and T. Murata, On degenerations of projective variet...	{ "page_id": null, "source": 7361, "title": "from dpo" }
upon by a unipotent group Ga with finitely many orbits. The maximal torus T of GL( V ) scaling the given basis of V admits a one-parameter subgroup whose fixed points are tuples of coordinate subspaces indexed by {I∗ = ( I1, . . . , I n) \| Ii ⊂ { 1, . . . , n + 1 }, \|Ii\| = i, I i \ { i + 1 } ⊂ Ii+1 }, and such that the...	{ "page_id": null, "source": 7361, "title": "from dpo" }
subrepresentations U of a representation P ⊕ I of a Dynkin quiver Q, where P is a projective representation, I is an injective representation, 2888 Oberwolfach Report 46/2019 and the class [ U ] of U in the Grothendieck group of Q equals [ P ]. Namely, the variety Fl a(V ) arises when Q is a linearly oriented type An q...	{ "page_id": null, "source": 7361, "title": "from dpo" }
a locally complete intersection variety which is equidimensional, and it is a flat degeneration of both Fl( V ) and of Fl a(V ). Its irreducible components are naturally parametrized by non-crossing arc dia-grams: an arc diagram is a subset A of {(i, j ) \| 1 ≤ i < j ≤ n}; it is called non-crossing if there is no pair (...	{ "page_id": null, "source": 7361, "title": "from dpo" }

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