Matrix hypercontractivity streaming algorithms and LDCs the large alphabet case

In this work, we prove a hypercontractive inequality for matrix-valuedfunctions defined over large alphabets . We present a lower bound for LDCs over largealphabets and present upper and lower bounds for the communication complexity of the Hidden Hypermatching problem . We also show that any streaming algorithm achieving a $(r-\varepsilon)-approximation requires $Omega(n^{1-1/t)$ classical or $Oma(n=2) when $r=2$ is $O(\log{n)$ .…

Matrix hypercontractivity streaming algorithms and LDCs the large alphabet case

In this work, we prove a hypercontractive inequality for matrix-valuedfunctions defined over large alphabets . We present a lower bound for LDCs over largealphabets and present upper and lower bounds for the communication complexity of the Hidden Hypermatching problem . We also show that any streaming algorithm achieving a $(r-\varepsilon)-approximation requires $Omega(n^{1-1/t)$ classical or $Oma(n=2) when $r=2$ is $O(\log{n)$ .…

Matrix hypercontractivity streaming algorithms and LDCs the large alphabet case

In this work, we prove a hypercontractive inequality for matrix-valuedfunctions defined over large alphabets . We present a lower bound for LDCs over largealphabets and present upper and lower bounds for the communication complexity of the Hidden Hypermatching problem . We also show that any streaming algorithm achieving a $(r-\varepsilon)-approximation requires $Omega(n^{1-1/t)$ classical or $Oma(n=2) when $r=2$ is $O(\log{n)$ .…

UC Modelling and Security Analysis of the Estonian IVXV Internet Voting System

Estonian Internet voting has been used in national-wide elections since 2005 . The system was initially designed in a heuristic manner, with very few security guarantees . To date, no formal security analysis of the system has been given . For the first time, we provide a rigorous security modeling for the Estonian IVXV system as a ceremony, attempting to capture the effect of actual human behavior on election verifiability in the UC framework .…

The local global property for G invariant terms

For some Maltsev conditions it is enough to check if a finitealgebra satisfies $Sigma$ locally on subsets of bounded size . Thislocal-global property is the main known source of tractability results for deciding Maltsevs conditions . In this paper we investigate the local-globalproperty for the existence of a $G-term, i.e.…

The local global property for G invariant terms

For some Maltsev conditions it is enough to check if a finitealgebra satisfies $Sigma$ locally on subsets of bounded size . Thislocal-global property is the main known source of tractability results for deciding Maltsevs conditions . In this paper we investigate the local-globalproperty for the existence of a $G-term, i.e.…

The local global property for G invariant terms

For some Maltsev conditions it is enough to check if a finitealgebra satisfies $Sigma$ locally on subsets of bounded size . Thislocal-global property is the main known source of tractability results for deciding Maltsevs conditions . In this paper we investigate the local-globalproperty for the existence of a $G-term, i.e.…

Dynamic Meta theorems for Distance and Matching

Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory . Reachability can be maintained withfirst-order update formulas, or equivalently in DynFO in general graphs with nnodes . We extend the meta-theorem forreachability to distance and bipartite maximum matching with the same bounds .…

Dynamic Meta theorems for Distance and Matching

Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory . Reachability can be maintained withfirst-order update formulas, or equivalently in DynFO in general graphs with nnodes . We extend the meta-theorem forreachability to distance and bipartite maximum matching with the same bounds .…

Dynamic Meta theorems for Distance and Matching

Reachability, distance, and matching are some of the most fundamental graph problems that have been of particular interest in dynamic complexity theory . Reachability can be maintained withfirst-order update formulas, or equivalently in DynFO in general graphs with nnodes . We extend the meta-theorem forreachability to distance and bipartite maximum matching with the same bounds .…

SFCDecomp Multicriteria Optimized Tool Path Planning in 3D Printing using Space Filling Curve Based Domain Decomposition

The minimum turncost 3d printing problem is NP-hard, even when the region is a simple polygon . We explore efficient optimization of toolpaths based on multiple criteria for large instances of printing problems . For the Buddha, our framework buildstoolpaths over a total of 799,716 nodes across 169 layers, and for the Bunny it buildsstool paths over 812,733 nodes across 360 layers .…

On the Complexity of Computing Markov Perfect Equilibrium in General Sum Stochastic Games

Stochastic Games (SGs) lay the foundation for the study of multi-agentreinforcement learning (MARL) and sequential agent interactions . We derive that computing an approximate Markov Perfect Equilibrium (MPE) in afinite-state discounted Stochastics Game within the exponential precision is\textbf{PPAD}-complete . Thecompleteness result follows the reduction of the fixed-point problem to {\scEnd of the Line}.…

SFCDecomp Multicriteria Optimized Tool Path Planning in 3D Printing using Space Filling Curve Based Domain Decomposition

The minimum turncost 3d printing problem is NP-hard, even when the region is a simple polygon . We explore efficient optimization of toolpaths based on multiple criteria for large instances of printing problems . For the Buddha, our framework buildstoolpaths over a total of 799,716 nodes across 169 layers, and for the Bunny it buildsstool paths over 812,733 nodes across 360 layers .…

On the Complexity of Computing Markov Perfect Equilibrium in General Sum Stochastic Games

Stochastic Games (SGs) lay the foundation for the study of multi-agentreinforcement learning (MARL) and sequential agent interactions . We derive that computing an approximate Markov Perfect Equilibrium (MPE) in afinite-state discounted Stochastics Game within the exponential precision is\textbf{PPAD}-complete . Thecompleteness result follows the reduction of the fixed-point problem to {\scEnd of the Line}.…

On the Complexity of Computing Markov Perfect Equilibrium in General Sum Stochastic Games

Stochastic Games (SGs) lay the foundation for the study of multi-agentreinforcement learning (MARL) and sequential agent interactions . We derive that computing an approximate Markov Perfect Equilibrium (MPE) in afinite-state discounted Stochastics Game within the exponential precision is\textbf{PPAD}-complete . Thecompleteness result follows the reduction of the fixed-point problem to {\scEnd of the Line}.…

New efficient time stepping schemes for the anisotropic phase field dendritic crystal growth model

In this paper, we propose and analyze a first-order and a second-ordertime-stepping schemes for the anisotropic phase-field dendritic crystal growth model . The proposed schemes are based on an auxiliary variable approach for theAllen-Cahn equation . The idea of the former is to introducesuitable auxiliary variables to facilitate construction of high order stableschemes for a large class of gradient flows .…

A Study of Mixed Precision Strategies for GMRES on GPUs

Support for lower precision computation is becoming more common inaccelerator hardware due to lower power usage, reduced data movement and increased computational performance . However, computational science and engineering (CSE) problems require double precision accuracy in several domains . We seek the best methods for incorporating multiple precisions into the GMRES linear solver; these includeiterative refinement and parallelizable preconditioners .…

Smooth Surfaces via Nets of Geodesics

This work presents an algorithm for the computation and visualization of an underlying unknown surface from a given net of geodesics . It is based on atheoretical result by the author regarding minimal Gaussian curvature surfaces with geodesic boundary conditions .…

J Score A Robust Measure of Clustering Accuracy

Clustering analysis discovers hidden structures in a data set by partitioning them into disjoint clusters . Common problems of current clustering accuracy measures include overlooking unmatched clusters, biases towards excessive clusters, unstable baselines, and difficult interpretation . J-score quantifies how well the hypothetical clusters produced by clustering analysis recover the trueclasses.…

UserBERT Contrastive User Model Pre training

User modeling is critical for personalized web applications . Existing usermodeling methods usually train user models from user behaviors with task-specific labeled data . But labeled data in a target task may be insufficient for training accurate user models . Pre-training user models on unlabeled user behavior data has the potential to improve user modeling for many downstream tasks .…

The Singular Angle of Nonlinear Systems

In this paper, we introduce an angle notion, called the singular angle, forstable nonlinear systems from an input-output perspective . The proposed systemsingular angle describes an upper bound for the “rotating effect” from the system input to output . It is, thus, different from the recently appeared nonlinear systemphase which adopts the complexification of real-valued signals using theHilbert transform .…