Turing Machine (TM) is a mathematical model which consists of an infinite length tape divided into cells on which input is given. It consists of a head which reads the input tape. A state register stores the state of the Turing machine. After reading an input symbol, it is replaced with another symbol, its internal state is changed, and it moves from one cell to the right or left. If the TM reaches the final state, the input string is accepted, otherwise rejected.
Consistency in formatting and styling is crucial in a Table of Contents. Using consistent font styles, indentation, and numbering conventions enhances readability and makes it easier for readers to distinguish between different levels of headings and subheadings. Clear visual cues, such as bold or italicized text, can be employed to differentiate entries and aid navigation.
In addition to textual representation, a ToC can incorporate visual elements such as page numbers, hyperlinks, or bookmarks. Page numbers are particularly valuable in print documents, allowing readers to locate specific sections directly. Hyperlinks or bookmarks are beneficial in digital formats, enabling readers to click on entries in the ToC and instantly navigate to the corresponding section.
An often overlooked aspect of Table of Contents design is its role in improving document accessibility. For individuals with visual impairments or reading difficulties, a ToC serves as a valuable tool for accessing information. By providing a structured overview of the content, it enables users of assistive technologies to navigate and comprehend the document more effectively. Ensuring that the ToC is properly tagged and formatted in digital documents is essential for accessibility compliance.
Moreover, a Table of Contents can be enhanced with additional features to augment its functionality. For instance, some documents include supplementary lists, such as a List of Figures or List of Tables, which provide readers with a separate overview of visual or tabular content within the document. Cross-referencing between the ToC and these lists allows readers to easily locate specific figures or tables referenced in the text.
In conclusion, a Table of Contents is a vital component of lengthy documents, serving as a roadmap for readers and aiding in efficient information retrieval. By providing an organized overview of the document's structure, a well-designed ToC enhances document accessibility, readability, and comprehension. Adhering to best practices and incorporating visual cues, formatting consistency, and supplementary lists further optimizes the usefulness of a Table of Contents. Whether in print or digital form, a thoughtfully constructed ToC significantly improves the user experience and facilitates seamless navigation through complex documents
A simple implementation of Turing Machine in C++ programming language.
for the Theory of Languages and Automata course.
Computer Engineering at Khaje Nasir Toosi University of Technology (KNTU).
the source code is available on my github profile:
https://github.com/sina-rostami/Turing-Machine-Implementation
Consistency in formatting and styling is crucial in a Table of Contents. Using consistent font styles, indentation, and numbering conventions enhances readability and makes it easier for readers to distinguish between different levels of headings and subheadings. Clear visual cues, such as bold or italicized text, can be employed to differentiate entries and aid navigation.
In addition to textual representation, a ToC can incorporate visual elements such as page numbers, hyperlinks, or bookmarks. Page numbers are particularly valuable in print documents, allowing readers to locate specific sections directly. Hyperlinks or bookmarks are beneficial in digital formats, enabling readers to click on entries in the ToC and instantly navigate to the corresponding section.
An often overlooked aspect of Table of Contents design is its role in improving document accessibility. For individuals with visual impairments or reading difficulties, a ToC serves as a valuable tool for accessing information. By providing a structured overview of the content, it enables users of assistive technologies to navigate and comprehend the document more effectively. Ensuring that the ToC is properly tagged and formatted in digital documents is essential for accessibility compliance.
Moreover, a Table of Contents can be enhanced with additional features to augment its functionality. For instance, some documents include supplementary lists, such as a List of Figures or List of Tables, which provide readers with a separate overview of visual or tabular content within the document. Cross-referencing between the ToC and these lists allows readers to easily locate specific figures or tables referenced in the text.
In conclusion, a Table of Contents is a vital component of lengthy documents, serving as a roadmap for readers and aiding in efficient information retrieval. By providing an organized overview of the document's structure, a well-designed ToC enhances document accessibility, readability, and comprehension. Adhering to best practices and incorporating visual cues, formatting consistency, and supplementary lists further optimizes the usefulness of a Table of Contents. Whether in print or digital form, a thoughtfully constructed ToC significantly improves the user experience and facilitates seamless navigation through complex documents
A simple implementation of Turing Machine in C++ programming language.
for the Theory of Languages and Automata course.
Computer Engineering at Khaje Nasir Toosi University of Technology (KNTU).
the source code is available on my github profile:
https://github.com/sina-rostami/Turing-Machine-Implementation
Richard's entangled aventures in wonderlandRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
Thanks...!
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Richard's aventures in two entangled wonderlandsRichard Gill
Since the loophole-free Bell experiments of 2020 and the Nobel prizes in physics of 2022, critics of Bell's work have retreated to the fortress of super-determinism. Now, super-determinism is a derogatory word - it just means "determinism". Palmer, Hance and Hossenfelder argue that quantum mechanics and determinism are not incompatible, using a sophisticated mathematical construction based on a subtle thinning of allowed states and measurements in quantum mechanics, such that what is left appears to make Bell's argument fail, without altering the empirical predictions of quantum mechanics. I think however that it is a smoke screen, and the slogan "lost in math" comes to my mind. I will discuss some other recent disproofs of Bell's theorem using the language of causality based on causal graphs. Causal thinking is also central to law and justice. I will mention surprising connections to my work on serial killer nurse cases, in particular the Dutch case of Lucia de Berk and the current UK case of Lucy Letby.
Introduction:
RNA interference (RNAi) or Post-Transcriptional Gene Silencing (PTGS) is an important biological process for modulating eukaryotic gene expression.
It is highly conserved process of posttranscriptional gene silencing by which double stranded RNA (dsRNA) causes sequence-specific degradation of mRNA sequences.
dsRNA-induced gene silencing (RNAi) is reported in a wide range of eukaryotes ranging from worms, insects, mammals and plants.
This process mediates resistance to both endogenous parasitic and exogenous pathogenic nucleic acids, and regulates the expression of protein-coding genes.
What are small ncRNAs?
micro RNA (miRNA)
short interfering RNA (siRNA)
Properties of small non-coding RNA:
Involved in silencing mRNA transcripts.
Called “small” because they are usually only about 21-24 nucleotides long.
Synthesized by first cutting up longer precursor sequences (like the 61nt one that Lee discovered).
Silence an mRNA by base pairing with some sequence on the mRNA.
Discovery of siRNA?
The first small RNA:
In 1993 Rosalind Lee (Victor Ambros lab) was studying a non- coding gene in C. elegans, lin-4, that was involved in silencing of another gene, lin-14, at the appropriate time in the
development of the worm C. elegans.
Two small transcripts of lin-4 (22nt and 61nt) were found to be complementary to a sequence in the 3' UTR of lin-14.
Because lin-4 encoded no protein, she deduced that it must be these transcripts that are causing the silencing by RNA-RNA interactions.
Types of RNAi ( non coding RNA)
MiRNA
Length (23-25 nt)
Trans acting
Binds with target MRNA in mismatch
Translation inhibition
Si RNA
Length 21 nt.
Cis acting
Bind with target Mrna in perfect complementary sequence
Piwi-RNA
Length ; 25 to 36 nt.
Expressed in Germ Cells
Regulates trnasposomes activity
MECHANISM OF RNAI:
First the double-stranded RNA teams up with a protein complex named Dicer, which cuts the long RNA into short pieces.
Then another protein complex called RISC (RNA-induced silencing complex) discards one of the two RNA strands.
The RISC-docked, single-stranded RNA then pairs with the homologous mRNA and destroys it.
THE RISC COMPLEX:
RISC is large(>500kD) RNA multi- protein Binding complex which triggers MRNA degradation in response to MRNA
Unwinding of double stranded Si RNA by ATP independent Helicase
Active component of RISC is Ago proteins( ENDONUCLEASE) which cleave target MRNA.
DICER: endonuclease (RNase Family III)
Argonaute: Central Component of the RNA-Induced Silencing Complex (RISC)
One strand of the dsRNA produced by Dicer is retained in the RISC complex in association with Argonaute
ARGONAUTE PROTEIN :
1.PAZ(PIWI/Argonaute/ Zwille)- Recognition of target MRNA
2.PIWI (p-element induced wimpy Testis)- breaks Phosphodiester bond of mRNA.)RNAse H activity.
MiRNA:
The Double-stranded RNAs are naturally produced in eukaryotic cells during development, and they have a key role in regulating gene expression .
This presentation explores a brief idea about the structural and functional attributes of nucleotides, the structure and function of genetic materials along with the impact of UV rays and pH upon them.
1. A TuringMachine is an acceptingdevice whichacceptsthe languages(recursivelyenumerable set)
generatedbytype 0 grammars.It was inventedin1936 by AlanTuring.
Definition
A TuringMachine (TM) is a mathematical model whichconsistsof aninfinite lengthtape dividedinto
cellsonwhichinputisgiven.Itconsistsof a headwhichreadsthe inputtape.A state registerstores
the state of the Turing machine.Afterreadinganinputsymbol,itisreplacedwithanothersymbol,
itsinternal state ischanged,andit movesfromone cell tothe right or left.If the TM reachesthe
final state,the inputstringisaccepted,otherwise rejected.
A TM can be formallydescribedasa7-tuple (Q,X,∑, δ, q0, B, F) where −
Q is a finite setof states
X isthe tape alphabet
∑ is the inputalphabet
δ isa transitionfunction;δ:Q × X → Q × X × {Left_shift,Right_shift}.
q0 is the initial state
B is the blanksymbol
F isthe setof final states
Comparisonwiththe previousautomaton
The followingtable shows acomparisonof how a Turingmachine differsfromFiniteAutomatonand
PushdownAutomaton.
2. Machine Stack Data Structure Deterministic?
Finite Automaton N.A Yes
PushdownAutomaton Last In FirstOut(LIFO) No
TuringMachine Infinite tape Yes
Example of Turingmachine
Turingmachine M = (Q,X, ∑, δ, q0, B, F) with
Q = {q0, q1, q2, qf}
X = {a,b}
∑ = {1}
q0 = {q0}
B = blanksymbol
F = {qf }
δ isgivenby−
Tape alphabetsymbol PresentState ‘q0’ PresentState ‘q1’ PresentState ‘q2’
a 1Rq1 1Lq0 1Lqf
b 1Lq2 1Rq1 1Rqf
Here the transition1Rq1 impliesthatthe write symbol is1,the tape movesright,and the nextstate
isq1. Similarly,the transition1Lq2 impliesthatthe write symbol is1,the tape movesleft,andthe
nextstate isq2.
Time and Space Complexityof aTuringMachine
For a Turing machine,the time complexityreferstothe measure of the numberof timesthe tape
moveswhenthe machine isinitializedforsome inputsymbolsandthe space complexityisthe
numberof cellsof the tape written.
Time complexityall reasonable functions−
4. Turingmachine wasinventedin1936 byAlanTuring.It is an acceptingdevice whichaccepts
Recursive Enumerable Language generatedbytype 0grammar.
There are variousfeaturesof the Turingmachine:
It has an external memorywhichremembersarbitrarylongsequence of input.
It has unlimitedmemorycapability.
The model hasa facilitybywhichthe inputatleftor righton the tape can be readeasily.
The machine can produce a certainoutputbasedon itsinput.Sometimesitmaybe requiredthatthe
same inputhas to be usedto generate the output.Sointhismachine,the distinctionbetweeninput
and outputhas beenremoved.Thusacommon setof alphabetscanbe usedforthe Turing machine.
Formal definitionof Turingmachine
A Turingmachine can be definedasacollectionof 7 components:
Q: the finite setof states
∑: the finite setof inputsymbols
T: the tape symbol
q0: the initial state
F: a set of final states
B: a blanksymbol usedasa endmarkerfor input
δ: a transitionormappingfunction.
The mappingfunctionshowsthe mappingfromstatesof finite automataandinputsymbol onthe
tape to the nextstates,external symbolsandthe directionformovingthe tape head.Thisisknown
as a triple or a program forturingmachine.
(q0, a) → (q1, A,R)
That meansinq0 state,if we readsymbol 'a' thenit will goto state q1, replaceda byX and move
aheadright(Rstandsfor right).
5. Example:
ConstructTM for the language L ={0n1n} where n>=1.
Solution:
We have alreadysolvedthisproblembyPDA.InPDA,we have a stack to rememberthe previous
symbol.The mainadvantage of the Turingmachine iswe have a tape headwhichcan be moved
forwardor backward,and the inputtape can be scanned.
The simple logicwhichwe will applyisreadouteach '0' mark itby A and thenmove aheadalong
withthe inputtape and findout1 convertitto B. Now,repeatthisprocessforall a's andb's.
Nowwe will see howthisturingmachine workfor0011.
The simulationfor0011 can be shownas below:
or 0011 can be shownas below:
TuringMachine
Now,we will see howthisturingmachine will worksfor0011. Initially,state isq0and headpointsto
0 as:
TuringMachine
The move will be δ(q0,0) = δ(q1,A,R) whichmeansitwill goto state q1, replaced0 by A andhead
will move tothe rightas:
6. TuringMachine
The move will be δ(q1,0) = δ(q1,0, R) whichmeansitwill notchange any symbol,remaininthe
same state and move to the rightas:
TuringMachine
The move will be δ(q1,1) = δ(q2,B, L) whichmeansitwill goto state q2, replaced1 by B and head
will move toleftas:
TuringMachine
Nowmove will be δ(q2,0) = δ(q2,0, L) whichmeansitwill notchange anysymbol,remaininthe
same state and move to leftas:
TuringMachine
The move will be δ(q2,A) = δ(q0,A,R), itmeanswill goto state q0, replacedA by A andheadwill
move to the rightas:
TuringMachine
The move will be δ(q0,0) = δ(q1,A,R) whichmeansitwill goto state q1, replaced0 by A,and head
will move torightas:
TuringMachine
The move will be δ(q1,B) = δ(q1,B, R) whichmeansitwill notchange any symbol,remaininthe
same state and move to rightas:
TuringMachine
The move will be δ(q1,1) = δ(q2,B, L) whichmeansitwill goto state q2, replaced1 by B and head
will move toleftas:
7. TuringMachine
The move δ(q2,B) = (q2,B, L) whichmeansit will notchange anysymbol,remaininthe same state
and move toleftas:
TuringMachine
Nowimmediatelybefore BisA that meansall the 0?s are marketby A. Sowe will move rightto
ensure thatno 1 ispresent.The move will be δ(q2,A) =(q0, A,R) whichmeansitwill goto state q0,
will notchange anysymbol,andmove to rightas:
TuringMachine
The move δ(q0,B) = (q3,B, R) whichmeansitwill goto state q3, will notchange any symbol,and
move to rightas:
TuringMachine
The move δ(q3,B) = (q3,B, R) whichmeansitwill notchange any symbol,remaininthe same state
and move toright as:
TuringMachine
The move δ(q3,Δ) = (q4, Δ, R) whichmeansitwill goto state q4 whichis the HALT state and HALT
state is alwaysanaccept state for any TM.
TuringMachine
The same TM can be representedbyTransitionDiagram:
