Search results
Mar 22, 2022 · This paper focuses on the recognition of cattle using its primary feature, i.e., muzzle point for identification in real time, and also states the current techniques used for identification like Bluetooth, WiFi, RFID, and traditional methods used for identification of cattle with the challenges faced.
Oct 1, 2017 · The muzzle point image pattern is a primary animal biometric characteristic for the recognition of individual cattle. It is similar to the identification of minutiae points in human fingerprints.
- Santosh Kumar, Sanjay Kumar Singh, Amit Kumar Singh
- 26
- 2017
- 01 October 2017
Jul 26, 2023 · Here I am going to provide you Computer Science Notes PDF so that you can increase your basic knowledge of Computer Science and you can prepare for your exam easily.
These lecture notes cover the key ideas involved in designing algorithms. We shall see how they depend on the design of suitable data structures, and how some structures and algorithms
- N = {x ∈ N : x > 0}.
- 2.3 Why is the induction principle true?
- Proof Technique: Direct proof.
- The Well-Ordering Principle.
- −n b =
- 7.1 Ordered pairs
- Proposition 7.1.1. (A ∪ B) × C = (A × C) ∪ (B × C)
- 7.4 Creating relations
- R|S =
- × B such that
- x ∈ A.
- Compositions and Inverse Functions. Given two functions f : A → B and
- Mathematical Logic
- 8.2 Quantifiers
- 8.3 Negations
- 8.4 Logical connectives
- ¬(P → Q) ⇔ P ∧ ¬Q.
- Q) ∧ ¬(P ⇔ ¬P ∨ ¬Q
- (P → Q) ⇔ (¬Q → ¬P ).
- 8.5 Tautologies and logical inference
- (P ∧ (P → Q)) → Q:
- (P → Q) ∧ (¬P → ¬Q)
- 9.1 Fundamental principles
- (n)k
- − n n .
- k l − k .
- 12.1 Statements of the principle
- 13.2 Examples and properties
- 14.1 Introduction
- 14.4 Kinds of graphs
- 15.2 Graph coloring
- 17.1 Drawing graphs in the plane
- topological graph.
- 17.4 Concluding remarks
This is a matter of taste. In general, use the form that will be easiest for the reader of your work to understand. Often it is the least “cluttered” one. Ok, now onto the integers:
Some of you might be surprised by the title question. Isn’t it obvious? I mean, you know, the dominoes are aligned, you knock one down, they all fall. End of story. Right? Not quite. “Common sense” often misleads us. You probably noticed this in daily life, and you’re going to notice it a whole lot if you get into mathematics. Think of optical illu...
Here is a common template for direct proofs: Provide a chain of clear statements, each logically following from our shared knowledge base and the previous ones. The final statement in the chain should be the claim we need to prove. (Optional.) Conclude the proof. For example, “This completes the proof.”
In proving the division algorithm, we considered a certain set S ⊆ N and argued that since it is nonempty, it must have a smallest element. Why is this true? As with induction, we accept this proposition as an axiom. In general, the “well-ordering principle” states that any nonempty set of natural numbers must have a smallest element. As you will p...
+ b) rem n − b) rem n ·n a = (ab) rem n Exponentiation is defined through repeated multiplication.
The definition of a set explicitly disregards the order of the set elements, all that matters is who’s in, not who’s in first. However, sometimes the order is important. This leads to the notion of an ordered pair of two elements x and y, denoted (x, y). The crucial property is: (x, y) = (u, v) if and only if x = u and y = v. This notion can be ext...
Proof. Recall that for two sets X and Y , X = Y if and only if X ⊆ Y and Y ⊆ X. Consider any element (u, v) ∈ (A ∪ B) × C. By definition, u ∈ A ∪ B and v ∈ C. Thus, u ∈ A or u ∈ B. If u ∈ A then (u, v) ∈ A×C and if u ∈ B then (u, v) ∈ B ×C. Thus (u, v) is in A × C or in B × C, and (u, v) ∈ (A × C) ∪ (B × C). This proves that (A ∪ B) × C ⊆ (A × C) ∪...
There are a few ways to define new relations from existing ones, and we describe two important such ways below. Restrictions of relations. Here is one notion that is sometimes useful: Given a relation R on a set A, and a subset S ⊆ A, we can use R to define a relation on S called the restriction of R to S. Denoted by R|S, it is defined as
(a, b) ∈ R : a, b ∈ S . Compositions of relations. For three sets A, B, C, consider a relation R between and B, and a relation S between B and C. The composition of R and S is a relation T between A and C, defined as follows: aT c if and only if there exists some ∈ B, such that aRb and bSc. The composition of R and S is commonly denoted by
If x ∈ A, there exists y ∈ B such that (x, y) ∈ f. If (x, y) ∈ f and (x, z) ∈ f then y = z. function is sometimes called a map or mapping. The set A in the above definition is the domain and B is the codomain of f. function f : A → B is effectively a special kind of relation between A and B, which relates every x ∈ A to exactly one element of B. Th...
As if this wasn’t enough: A function f : A → B is a bijection (or bijective), or a one-to-one correspondence if it is both one-to-one and onto. Alternatively, f : A → B is a bijection if each element of B is of the form f(x) for exactly one x ∈ A.
g : B → C we can define a new function g ◦ f : A → C by (g ◦ f)(x) = g(f(x)) for all
Perhaps the most distinguishing characteristic of mathematics is its reliance on logic. Explicit training in mathematical logic is essential to a mature understanding of mathematics. Familiarity with the concepts of logic is also a prerequisite to studying a number of central areas of computer science, including databases, compilers, and complexity...
Given a predicate P (x) that is defined for all elements in a set A, we can reason about whether P (x) is true for all x ∈ A, or if it’s at least true for some x ∈ A. We can state propositions to this effect using the universal quantifier ∀ and the existential quantifier ∃. ∀x ∈ A : P (x) is true if and only if P (x) is true for all x ∈ A. This pro...
Given a proposition P , the negation of P is the proposition “P is false”. It is true if is false, and false if P is true. The negation of P is denoted by ¬P , read as “not .” If we know the meaning of P , such as when P stands for “It will rain tomorrow,” the proposition ¬P can be stated more naturally than “not P ,” as in “It will not rain tomorr...
The symbol ¬ is an example of a connective. Other connectives combine two propo-sitions (or predicates) into one. The most common are ∧, ∨, ⊕, → and ↔. P ∧ Q is read as “P and Q”; P ∨ Q as “P or Q”; P ⊕ Q as “P xor Q”; P → Q as “P implies Q” or “if P then Q”; and P ↔ Q as “P if and only if Q”. The truth-value of these compound propositions (sometim...
This means that in a negated implication, the negation can be “pushed inside”, somewhat like with quantifiers. In fact, similar equivalences exist for other negated compound statements, as can be verified using truth tables (do it!): Q) ∨ ¬(P ⇔ ¬P ∧ ¬Q
These are the famous DeMorgan’s laws. What they mean is that we can eliminate negated compounds (sounds like a military operation, doesn’t it?) just as we can eliminate negated quantifiers. Here is another important logical equivalence: The implication P → Q is equiva-lent to the contrapositive implication ¬Q → ¬P :
This is demonstrated by the following truth table: Indeed, an implication of the form “If P then Q” is sometimes proved by assuming that Q does not hold and showing that under this assumption P does not hold. This is called a proof by contrapositive. (Despite the similarity, it is different from a proof by contradiction.)
sentence that is true regardless of the values of its terms is called a tautology, while a statement that is always false is a contradiction. Another terminology says that tautologies are valid statements and contradictions are unsatisfiable statements. All other statements are said to be satisfiable, meaning they can be either true or false. Easy ...
We’ve already seen a number of inference rules above, like (P → Q) ⇔ (¬Q → ¬P ), without calling them that. Here are three others, all corresponding to tautologies that you are invited to verify using truth tables: (¬P → F) ⇔ (P ↔ Q) ⇔ (P ↔ Q) ⇔ P (P → Q) ∧ (Q → P )
These three rules are of particular importance. The first formally establishes the validity of proofs by contradiction, and the second and third provide two means for proving “if and only if” statements. We’ve been using these all along, but now we know why they are justified.
The subject of enumerative combinatorics is counting. Generally, there is some set A and we wish to calculate the size |A| of A. Here are some sample problems: How many ways are there to seat n couples at a round table, such that each couple sits together? How many ways are there to express a positive integer n as a sum of positive integers? There ...
k! X = n! . k!(n − k)! This quantity X is denoted by n k , read “n choose k”. This is such an important quantity that we emphasize it again: The number of k-element subsets of an n-element set is n , defined as k
This also has a nice combinatorial interpretation: Choosing a k-element subset B from an n-element set uniquely identifies the complement A \ B of B in A, which is an (n−k)-subset of A. This defines a bijection between k-element and (n−k)-element subsets of A, which implies the identity. Another relation between binomial coefficients is called Pasc...
We only give a combinatorial argument for this one. We are counting the number of ways to choose an l-element subset of an (m + n)-element set A. Fix an m-element subset B ⊆ A. Any l-element subset S of A has k elements from B and l −k elements from A \ B, for some 0 ≤ k ≤ l. For a particular value of k, the number of k-element subsets of B that ca...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
There are many more amazing results associated with planar graphs. Two of the most striking are F ́ary’s theorem and Koebe’s theorem. F ́ary’s theorem states that every planar graph can be drawn in the plane without edge crossings, such that all the arcs are straight line segments. Koebe’s theorem says that every planar graph is in fact isomorphic ...
- 417KB
- 89
Lecture 1: What is HCI / Interaction Design? With the exception of some embedded software and operating system code, the success of a software product is determined by the humans who use the product. These notes present theoretical and practical approaches to making successful and usable software.
People also ask
What is a muzzle point image pattern?
How to collect muzzle pattern directly from the fields?
What is a muzzle point recognition algorithm?
Why are muzzle points used for identification?
Oct 1, 2017 · In this research, we propose the deep learning based approach for identification of individual cattle based on their primary muzzle point (nose pattern) image pattern characteristics to...
