Regular expressions are an algebraic way to describe regular languages. They can be defined recursively, with basic elements like symbols and the empty string, and operations like union, concatenation, and Kleene closure. Both regular expressions and finite automata can define the same class of regular languages. It is possible to convert between regular expressions and finite automata by constructing automata from expressions and vice versa.
NFA Non Deterministic Finite Automata by Mudasir khushikMudsaraliKhushik
NFA Non Deterministic Finite Automata.
Basics
tuples of NFA
NFA Examples
Transition Table and man more things which you want to understand like Language, Rules, Alphabets, Descriptive Method, Regular Expression, String, and Finite Automata.
Also since {a} is regular, {a}* is a regular language which is the set of strings consisting of a's such as , a, aa, aaa, aaaa etc. Note also that *, which is the set of strings consisting of a's and b's, is a regular language because {a, b} is regular. Regular expressions are used to denote regular languages.
NFA Non Deterministic Finite Automata by Mudasir khushikMudsaraliKhushik
NFA Non Deterministic Finite Automata.
Basics
tuples of NFA
NFA Examples
Transition Table and man more things which you want to understand like Language, Rules, Alphabets, Descriptive Method, Regular Expression, String, and Finite Automata.
Also since {a} is regular, {a}* is a regular language which is the set of strings consisting of a's such as , a, aa, aaa, aaaa etc. Note also that *, which is the set of strings consisting of a's and b's, is a regular language because {a, b} is regular. Regular expressions are used to denote regular languages.
Finite Automata: Deterministic And Non-deterministic Finite Automaton (DFA)Mohammad Ilyas Malik
The term "Automata" is derived from the Greek word "αὐτόματα" which means "self-acting". An automaton (Automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically.
recognizer for a language, Deterministic finite automata, Non-deterministic finite automata, conversion of NFA to DFA, Regular Expression to NFA, Thomsons Construction
Finite Automata: Deterministic And Non-deterministic Finite Automaton (DFA)Mohammad Ilyas Malik
The term "Automata" is derived from the Greek word "αὐτόματα" which means "self-acting". An automaton (Automata in plural) is an abstract self-propelled computing device which follows a predetermined sequence of operations automatically.
recognizer for a language, Deterministic finite automata, Non-deterministic finite automata, conversion of NFA to DFA, Regular Expression to NFA, Thomsons Construction
Earliest Galaxies in the JADES Origins Field: Luminosity Function and Cosmic ...Sérgio Sacani
We characterize the earliest galaxy population in the JADES Origins Field (JOF), the deepest
imaging field observed with JWST. We make use of the ancillary Hubble optical images (5 filters
spanning 0.4−0.9µm) and novel JWST images with 14 filters spanning 0.8−5µm, including 7 mediumband filters, and reaching total exposure times of up to 46 hours per filter. We combine all our data
at > 2.3µm to construct an ultradeep image, reaching as deep as ≈ 31.4 AB mag in the stack and
30.3-31.0 AB mag (5σ, r = 0.1” circular aperture) in individual filters. We measure photometric
redshifts and use robust selection criteria to identify a sample of eight galaxy candidates at redshifts
z = 11.5 − 15. These objects show compact half-light radii of R1/2 ∼ 50 − 200pc, stellar masses of
M⋆ ∼ 107−108M⊙, and star-formation rates of SFR ∼ 0.1−1 M⊙ yr−1
. Our search finds no candidates
at 15 < z < 20, placing upper limits at these redshifts. We develop a forward modeling approach to
infer the properties of the evolving luminosity function without binning in redshift or luminosity that
marginalizes over the photometric redshift uncertainty of our candidate galaxies and incorporates the
impact of non-detections. We find a z = 12 luminosity function in good agreement with prior results,
and that the luminosity function normalization and UV luminosity density decline by a factor of ∼ 2.5
from z = 12 to z = 14. We discuss the possible implications of our results in the context of theoretical
models for evolution of the dark matter halo mass function.
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...Ana Luísa Pinho
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
What is greenhouse gasses and how many gasses are there to affect the Earth.moosaasad1975
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
THE IMPORTANCE OF MARTIAN ATMOSPHERE SAMPLE RETURN.Sérgio Sacani
The return of a sample of near-surface atmosphere from Mars would facilitate answers to several first-order science questions surrounding the formation and evolution of the planet. One of the important aspects of terrestrial planet formation in general is the role that primary atmospheres played in influencing the chemistry and structure of the planets and their antecedents. Studies of the martian atmosphere can be used to investigate the role of a primary atmosphere in its history. Atmosphere samples would also inform our understanding of the near-surface chemistry of the planet, and ultimately the prospects for life. High-precision isotopic analyses of constituent gases are needed to address these questions, requiring that the analyses are made on returned samples rather than in situ.
(May 29th, 2024) Advancements in Intravital Microscopy- Insights for Preclini...Scintica Instrumentation
Intravital microscopy (IVM) is a powerful tool utilized to study cellular behavior over time and space in vivo. Much of our understanding of cell biology has been accomplished using various in vitro and ex vivo methods; however, these studies do not necessarily reflect the natural dynamics of biological processes. Unlike traditional cell culture or fixed tissue imaging, IVM allows for the ultra-fast high-resolution imaging of cellular processes over time and space and were studied in its natural environment. Real-time visualization of biological processes in the context of an intact organism helps maintain physiological relevance and provide insights into the progression of disease, response to treatments or developmental processes.
In this webinar we give an overview of advanced applications of the IVM system in preclinical research. IVIM technology is a provider of all-in-one intravital microscopy systems and solutions optimized for in vivo imaging of live animal models at sub-micron resolution. The system’s unique features and user-friendly software enables researchers to probe fast dynamic biological processes such as immune cell tracking, cell-cell interaction as well as vascularization and tumor metastasis with exceptional detail. This webinar will also give an overview of IVM being utilized in drug development, offering a view into the intricate interaction between drugs/nanoparticles and tissues in vivo and allows for the evaluation of therapeutic intervention in a variety of tissues and organs. This interdisciplinary collaboration continues to drive the advancements of novel therapeutic strategies.
Toxic effects of heavy metals : Lead and Arsenicsanjana502982
Heavy metals are naturally occuring metallic chemical elements that have relatively high density, and are toxic at even low concentrations. All toxic metals are termed as heavy metals irrespective of their atomic mass and density, eg. arsenic, lead, mercury, cadmium, thallium, chromium, etc.
2. 2
RE’s: Introduction
Regular expressions are an algebraic
way to describe languages.
They describe exactly the regular
languages.
If E is a regular expression, then L(E) is
the language it defines.
We’ll describe RE’s and their languages
recursively.
3. 3
RE’s: Definition
Basis 1: If a is any symbol, then a is a
RE, and L(a) = {a}.
Note: {a} is the language containing one
string, and that string is of length 1.
Basis 2: ε is a RE, and L(ε) = {ε}.
Basis 3: ∅ is a RE, and L(∅) = ∅.
4. 4
RE’s: Definition – (2)
Induction 1: If E1 and E2 are regular
expressions, then E1+E2 is a regular
expression, and L(E1+E2) =
L(E1)L(E2).
Induction 2: If E1 and E2 are regular
expressions, then E1E2 is a regular
expression, and L(E1E2) = L(E1)L(E2).
Concatenation : the set of strings wx such that w
Is in L(E1) and x is in L(E2).
5. 5
RE’s: Definition – (3)
Induction 3: If E is a RE, then E* is a
RE, and L(E*) = (L(E))*.
Closure, or “Kleene closure” = set of strings
w1w2…wn, for some n > 0, where each wi is
in L(E).
Note: when n=0, the string is ε.
6. 6
Precedence of Operators
Parentheses may be used wherever
needed to influence the grouping of
operators.
Order of precedence is * (highest),
then concatenation, then + (lowest).
7. 7
Examples: RE’s
L(01) = {01}.
L(01+0) = {01, 0}.
L(0(1+0)) = {01, 00}.
Note order of precedence of operators.
L(0*) = {ε, 0, 00, 000,… }.
L((0+10)*(ε+1)) = all strings of 0’s
and 1’s without two consecutive 1’s.
8. 8
Equivalence of RE’s and
Automata
We need to show that for every RE,
there is an automaton that accepts the
same language.
Pick the most powerful automaton type: the
ε-NFA.
And we need to show that for every
automaton, there is a RE defining its
language.
Pick the most restrictive type: the DFA.
9. 9
Converting a RE to an ε-NFA
Proof is an induction on the number of
operators (+, concatenation, *) in the
RE.
We always construct an automaton of a
special form (next slide).
10. 10
Form of ε-NFA’s Constructed
No arcs from outside,
no arcs leaving
Start state:
Only state
with external
predecessors
“Final” state:
Only state
with external
successors
15. 15
DFA-to-RE
A strange sort of induction.
States of the DFA are assumed to be
1,2,…,n.
We construct RE’s for the labels of
restricted sets of paths.
Basis: single arcs or no arc at all.
Induction: paths that are allowed to
traverse next state in order.
16. 16
k-Paths
A k-path is a path through the graph of
the DFA that goes though no state
numbered higher than k.
Endpoints are not restricted; they can
be any state.
17. 17
Example: k-Paths
1
3
2
0
0
0
1
1 1
0-paths from 2 to 3:
RE for labels = 0.
1-paths from 2 to 3:
RE for labels = 0+11.
2-paths from 2 to 3:
RE for labels =
(10)*0+1(01)*1
3-paths from 2 to 3:
RE for labels = ??
18. 18
k-Path Induction
Let Rij
k be the regular expression for
the set of labels of k-paths from state i
to state j.
Basis: k=0. Rij
0 = sum of labels of arc
from i to j.
∅ if no such arc.
But add ε if i=j.
20. 20
k-Path Inductive Case
A k-path from i to j either:
1. Never goes through state k, or
2. Goes through k one or more times.
Rij
k = Rij
k-1 + Rik
k-1(Rkk
k-1)* Rkj
k-1.
Doesn’t go
through k
Goes from
i to k the
first time Zero or
more times
from k to k
Then, from
k to j
22. 22
Final Step
The RE with the same language as the
DFA is the sum (union) of Rij
n, where:
1. n is the number of states; i.e., paths are
unconstrained.
2. i is the start state.
3. j is one of the final states.
24. 24
Summary
Each of the three types of automata
(DFA, NFA, ε-NFA) we discussed, and
regular expressions as well, define
exactly the same set of languages: the
regular languages.
25. 25
Algebraic Laws for RE’s
Union and concatenation behave sort of
like addition and multiplication.
+ is commutative and associative;
concatenation is associative.
Concatenation distributes over +.
Exception: Concatenation is not
commutative.
26. 26
Identities and Annihilators
∅ is the identity for +.
R + ∅ = R.
ε is the identity for concatenation.
εR = Rε = R.
∅ is the annihilator for concatenation.
∅R = R∅ = ∅.