Updated index.rst

index.rst

@@ -355,7 +355,7 @@ isolate the meanings of common pictogram B in three ways by 1) Set intersection
 	24. A random integer partition can be generated by a Pseudorandom generator. This extends the Partition-HashTable isomorphism to PRG-Partition-Hashtable transitive equivalence: PRG produces random partitions of integer, random partitions map to random buckets in tabulation hashing.
 	25. Computational Geometric Parallel RAM Factorization applies datastructures (e.g Parallel construction of segment trees/wavelet trees/interval trees/k-d trees) and algorithms (Planar Point Location, ray shooting queries) from Computational Geometry and Number Theory. Factorization in number theory is a multiplicative partition problem - Factorisatio Numerorum - as opposed to additive partitions. Quantum Computational version of Computational Geometric factorization has also been described in the context of quantum to classical decoherence. Computational Geometric Parallel RAM Factorization allocates O((logN)^k) arithmetic progression line segments (or a PSLG formed by a pixel array polygon) of a rasterized hyperbolic arc, to O(N/(logN)^k) PRAM-multicore processors which could be binary or interpolation searched in O((logN)^(k+1)) or O((logN)^k*loglogN) parallel RAM time. Parallel Rasterization of hyperbolic curve which creates line segments of pixels from hyperbola in parallel could be performed by advanced GPU architectures - e.g NVIDIA CUDA - illustrations - https://research.nvidia.com/sites/default/files/pubs/2011-08_High-Performance-Software-Rasterization/laine2011hpg_paper.pdf.
 	26. Program Analysis is a converse of complement diophantine problem and is an approximation of Rice Theorem which ordains any non-trivial property of recursively enumerable sets is Undecidable
-	27. Software Analytics based on static and dynamic analyses (SATURN CFG/Valgrind CallGraphs/FlameGraphs/Points-to Graphs/FTrace) and applying Centrality/Graph Mining/Latent Semantic Indexing/Graph Edit Distance/Graph Isomorphism on them is a Program Analysis problem. Various Program Analyzers in userspace and kernelspace have been implemented in AstroInfer,USBmd and VIRGO linux kernel repositories which use Degree centrality,PageRank,Cyclomatic Complexity measures,Graph Isomorphism,Degree Sequence EMD Similarity among others. Some userspace usecases for Read-Copy-Update, Software Transactional Memory - Lockfree - synchronization have also been implemented for wrapping VIRGO32 and VIRGO64 kernelspace RPC cloud system calls. VIRGO32 and VIRGO64 linux kernels feature a kernelspace Bakery algorithm kernel driver implementation for Cloud synchronization. GRAFIT course materials have some spillover analytics implementations and catechisms for classroom pedagogy - notable of them being Earliest Deadline First Worst Case Execution Time (EDF WCET Survival Index Timeout) OS Scheduler which depends on static code analyzers - IPET,CFG,SyntaxTree,LongestPath - or Master Theorem for WCET approximation.
+	27. Software Analytics based on static and dynamic analyses (SATURN CFG/Valgrind CallGraphs/FlameGraphs/Points-to Graphs/FTrace) and applying Centrality/Graph Mining/Latent Semantic Indexing/Graph Edit Distance/Graph Isomorphism on them is a Program Analysis problem. Various Program Analyzers in userspace and kernelspace have been implemented in AstroInfer,USBmd and VIRGO linux kernel repositories which use Degree centrality,PageRank,Cyclomatic Complexity measures,Graph Isomorphism,Degree Sequence EMD Similarity among others. Some userspace usecases for Read-Copy-Update, Software Transactional Memory - Lockfree - synchronization have also been implemented for wrapping VIRGO32 and VIRGO64 kernelspace RPC cloud system calls. VIRGO32 and VIRGO64 linux kernels feature a kernelspace Bakery algorithm kernel driver implementation for Cloud synchronization. GRAFIT course materials have some spillover analytics implementations and catechisms for classroom pedagogy - notable of them being Earliest Deadline First Worst Case Execution Time (EDF WCET Survival Index Timeout) OS Scheduler which depends on static code analyzers - IPET,CFG,SyntaxTree,LongestPath - or Master Theorem-Busy Beaver Turing Machine encoding for WCET approximation.
         28. Automated Debugging (e.g delta debugging, streaming common program state subgraphs) and Debug Analytics(finding minimum size program state automaton for isolating and resolving buggy code changes - finding and resolving bugs are two different problems because resolution of bug might necessitate major refactoring and rewrites) is a Software Analytics problem. Epidemics are modelled by Chaotic Strange attractors and Game theory (adversarial game between pestilence and infected) and Cybercrimes are epidemics infecting electronics. Software Analytics for Cybercrime forensics therefore have game theoretic reasoning (adversarial game between criminals and affected)
 	29. Set Partitions (Complementary Sets, LSH Partitions, Separate Chaining Hash tables, Histograms, Electronic Voting Machines etc.,) have a reduction to Space Filling/Packing by Exact Square Tile Cover of Rectangle from a fundamental result in number theory - Lagrange Four Square Theorem. This kind of square tile cover of a rectangle can be written as a non-linear quadratic programming optimization which solves integer factorization indirectly. Lagrangian Square Tiles are arranged in rectangle found by computational geometric factorization which is also an instance of NP-Hard exact Coin Problem/Money Changing Problem/Integer Linear Programming and polynomial time approximation problem by least squares (e.g LSMR). NeuronRain implements both Exact (CVXOPT GLPK Integer Linear Programming) and Approximate (LSMR least squares) reductions from set partitions to square tile cover by computational geometric factorization.
         30. Computational Geometric Factorization by Parallel Planar Point Location rectifies a hyperbolic continuous curve to set of straightline segments as part of factorization which are searched. Each rectified segment is an arithmetic progression defineable by an arithmetic progression diophantine or generating functions and set of these diophantines represent the exact cover (set of subsets) of points on rectified hyperbolic curve. Arithmetic progressions arise in Ramsey theory while arbitrarily coloring integer sequences. This rectification of a hyperbola by axis-parallel line segments is a union of arithmetic progressions.
@@ -445,7 +445,7 @@ On the other hand, pedestrian networks are as important as transportation networ
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 	61.NeuronRain theorizes and implements multiple Logical clocks for (unidirectional and bidirectional) Timeout and Graphic Event Models-Causal Event Models:
 		61.1 EventNet GEM Tensor - a Graphical Event Model of events and actors per event for capturing Causality relationship between events on Cloud (e.g Money Trail - Monetary Transactions, Causality between frames of video in Large Scale Visuals). EventNet logical clocks do not rule out cycles and retrocausality and can be decomposed as linear function of Tensor component basis implying time could be multidimensional similar to any topological space.
-		61.2 Survival Index Based Timeout for OS Schedulers - Unidirectional (Downward clockticks) Dynamic Hashing based Process Timeout mechanism for OS Scheduler - derived from an earlier proprietary Survival Index Transaction Timeout Manager (Sun Microsystems-Oracle: patent pending) implemented in iPlanet Application Server (iAS) now opensourced as Eclipse GlassFish and Oracle GlassFish - https://projects.eclipse.org/proposals/eclipse-glassfish, https://www.oracle.com/middleware/technologies/glassfish-server.html
+		61.2 Survival Index Based Timeout for OS Schedulers - implemented in userspace based on SCHED_DEADLINE scheduling policy-chrt command and read in kernelspace through VIRGO kernel_analytics driver and exported kernelwide - Unidirectional (Downward clockticks) Dynamic Hashing based Process Timeout mechanism for OS Scheduler - algorithm derived from an earlier proprietary Survival Index Transaction Timeout Manager (Sun Microsystems-Oracle: patent pending) implemented in iPlanet Application Server (iAS) now opensourced as Eclipse GlassFish and Oracle GlassFish - https://projects.eclipse.org/proposals/eclipse-glassfish, https://www.oracle.com/middleware/technologies/glassfish-server.html
 		61.3 Expirable C++ Objects - Reference Counting of objects (mostly images and Neuro currencies) which is a bidirectional logical clock of increment and decrement (Upward and Downward clockticks) - Object is reaped by Garbage collector when refcount reaches 0. Collatz conjecture defined as: {x(n+1) = x(n)/2 if x(n) is even and 3x(n) + 1 if x(n) is odd and {x(n)} sequence always ends in 1} is a bidirectional clock and might be useful to simulate lifetime reference count (trajectory of ups and downs) of an object. EMD sequence for Towers of Hanoi intermediate computations mentioned earlier (47) is a Collatz-like sequence of exponential number of elements terminating always in 0 and could be another instance of bidirectional refcount clock.
 		61.4 KingCobra Atomic Transactional Refcounting within linux kernel for cloud RPC - reference count of an object is globally persisted within move semantics - For an object move over VIRGO64 cloud kernelspace RPC, sender decrements global refcount of object and receiver increments its global refcount within an atomic transactional block - requires XA transactional Linux kernel supporting 2-phase commit. An example Userspace Distributed Reference Counting framework - Ray Actor Model - https://docs.ray.io/en/master/ray-core/memory-management.html - maintains a global ledger of objects, ip-addresses and processes holding references to those objects.
 	62. Factorization and Multiplication (Mutual Nick's Class reducibility of Division,Multiplication and Iterated integer addition - [Beame-Cook-Hoover] Theorem - Wallace Tree Circuits and FFTs - https://courses.cs.washington.edu/courses/cse532/08sp/lect08.pdf) are mutual inverses - Efficient circuits for linear complexity integer multiplications have been devised making room for the possibility of efficient factorization e.g Russian Peasant or Egyptian multiplication example multiplication of 101 * 115 = 11615 is a tableau of 2 columns that could be written as product of factor and sum of exponents of 2 (Right columns in Rows of odd Left columns are added) - Tableau is of size O(log(factor)):