633 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Mining Butterflies in Streaming Graphs
This thesis introduces two main-memory systems sGrapp and sGradd for performing the fundamental analytic tasks of biclique counting and concept drift detection over a streaming graph. A data-driven heuristic is used to architect the systems. To this end, initially, the growth patterns of bipartite streaming graphs are mined and the emergence principles of streaming motifs are discovered. Next, the discovered principles are (a) explained by a graph generator called sGrow; and (b) utilized to establish the requirements for efficient, effective, explainable, and interpretable management and processing of streams. sGrow is used to benchmark stream analytics, particularly in the case of concept drift detection.
sGrow displays robust realization of streaming growth patterns independent of initial conditions, scale and temporal characteristics, and model configurations. Extensive evaluations confirm the simultaneous effectiveness and efficiency of sGrapp and sGradd. sGrapp achieves mean absolute percentage error up to 0.05/0.14 for the cumulative butterfly count in streaming graphs with uniform/non-uniform temporal distribution and a processing throughput of 1.5 million data records per second. The throughput and estimation error of sGrapp are 160x higher and 0.02x lower than baselines. sGradd demonstrates an improving performance over time, achieves zero false detection rates when there is not any drift and when drift is already detected, and detects sequential drifts in zero to a few seconds after their occurrence regardless of drift intervals
Semitopology: a new topological model of heterogeneous consensus
A distributed system is permissionless when participants can join and leave
the network without permission from a central authority. Many modern
distributed systems are naturally permissionless, in the sense that a central
permissioning authority would defeat their design purpose: this includes
blockchains, filesharing protocols, some voting systems, and more. By their
permissionless nature, such systems are heterogeneous: participants may only
have a partial view of the system, and they may also have different goals and
beliefs. Thus, the traditional notion of consensus -- i.e. system-wide
agreement -- may not be adequate, and we may need to generalise it.
This is a challenge: how should we understand what heterogeneous consensus
is; what mathematical framework might this require; and how can we use this to
build understanding and mathematical models of robust, effective, and secure
permissionless systems in practice?
We analyse heterogeneous consensus using semitopology as a framework. This is
like topology, but without the restriction that intersections of opens be open.
Semitopologies have a rich theory which is related to topology, but with its
own distinct character and mathematics. We introduce novel well-behavedness
conditions, including an anti-Hausdorff property and a new notion of `topen
set', and we show how these structures relate to consensus. We give a
restriction of semitopologies to witness semitopologies, which are an
algorithmically tractable subclass corresponding to Horn clause theories,
having particularly good mathematical properties. We introduce and study
several other basic notions that are specific and novel to semitopologies, and
study how known quantities in topology, such as dense subsets and closures,
display interesting and useful new behaviour in this new semitopological
context
Pointwise convergence for the Schr\"odinger equation [After Xiumin Du and Ruixiang Zhang]
This expository essay accompanied the author's presentation at the
S\'eminaire Bourbaki on 01 April 2023. It describes the breakthrough work of
Du--Zhang on the Carleson problem for the Schr\"odinger equation, together with
background material in multilinear harmonic analysis.Comment: 72 pages, 6 figures, comments welcome
Sum-Of-Squares Lower Bounds for the Minimum Circuit Size Problem
We prove lower bounds for the Minimum Circuit Size Problem (MCSP) in the Sum-of-Squares (SoS) proof system. Our main result is that for every Boolean function f: {0,1}? ? {0,1}, SoS requires degree ?(s^{1-?}) to prove that f does not have circuits of size s (for any s > poly(n)). As a corollary we obtain that there are no low degree SoS proofs of the statement NP ? P/poly.
We also show that for any 0 < ? < 1 there are Boolean functions with circuit complexity larger than 2^{n^?} but SoS requires size 2^{2^?(n^?)} to prove this. In addition we prove analogous results on the minimum monotone circuit size for monotone Boolean slice functions.
Our approach is quite general. Namely, we show that if a proof system Q has strong enough constraint satisfaction problem lower bounds that only depend on good expansion of the constraint-variable incidence graph and, furthermore, Q is expressive enough that variables can be substituted by local Boolean functions, then the MCSP problem is hard for Q
From Houses of Worship to Worship in Houses: The Social Construction of Sacred Places in Early 21st Century China
While the concept of worship in houses can be traced back to the Christian house church places in Dura Europos between 233 and 256 AD during the Roman Empire, after the foundation of the People's Republic of China in 1949, this kind of church spaces began to appear all across the country. Characterized by the absence of a formal iconic church building or interior, existing types of secular architectural spaces (apartments, offices, basements, etc.) were rented by the Christian community and converted into sacred spaces.
Space is susceptible to manipulations caused by human actions. Now what happens if space is manipulated to house not merely a different function but transcendence? As French Marxist philosopher and sociologist Henri Lefebvre's argument in The Production of Space (1991), space is not only a social product but also a complex social construction, based on values and the social production of meanings, which affects spatial practices and perceptions. An existing space, he says, may outlive its original purpose and the raison d'Ă©tre which initially determined its forms, functions, and structures; it may thus, in a sense, become vacant and susceptible to being diverted, re-appropriated, and utilized for a different purpose than its original intent.
With my analysis of the worship places of urban house churches in early 21st-century China from the perspective of urban context and architectural space (foregrounded by the development of informal church space in the historical context of Chinese society and politics), this research shows how religious metaphors function as the productive mediators in the process of knowledge transfer between architectural and other professional discourses by bringing back social imagination to the politically neutral spaces of every day; de facto reconstructing the social through transduction of the metaphor of informal spaces
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
Bounded-depth Frege complexity of Tseitin formulas for all graphs
We prove that there is a constant K such that Tseitin formulas for a connected graph G requires proofs of size 2tw(G)javax.xml.bind.JAXBElement@531a834b in depth-d Frege systems for [Formula presented], where tw(G) is the treewidth of G. This extends HĂĄstad's recent lower bound from grid graphs to any graph. Furthermore, we prove tightness of our bound up to a multiplicative constant in the top exponent. Namely, we show that if a Tseitin formula for a graph G has size s, then for all large enough d, it has a depth-d Frege proof of size 2tw(G)javax.xml.bind.JAXBElement@25a4b51fpoly(s). Through this result we settle the question posed by M. Alekhnovich and A. Razborov of showing that the class of Tseitin formulas is quasi-automatizable for resolution
The Complexity of Some Geometric Proof Systems
In this Thesis we investigate proof systems based on Integer Linear Programming. These methods inspect the solution space of an unsatisfiable propositional formula and prove that this space contains no integral points.
We begin by proving some size and depth lower bounds for a recent proof system, Stabbing Planes, and along the way introduce some novel methods for doing so.
We then turn to the complexity of propositional contradictions generated uniformly from first order sentences, in Stabbing Planes and Sum-Of-Squares.
We finish by investigating the complexity-theoretic impact of the choice of method of generating these propositional contradictions in Sherali-Adams
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