A quantifier describes a mathematical operator that determines the validity of statements. Quantifiers, also called quantifiers, are assigned to the so-called predicate logic. Predicate logic is an extension of propositional logic. Informally, quantifiers are also called written abbreviations of spoken statements.
The most common types of quantifiers are all-quantors and existential quantifiers. Other types of quantifiers, such as number quantifiers or unique existential quantifiers, can be traced back to all-quantifiers or existential quantifiers.
An all quantifier can be interpreted as a conjunction, i.e. as a concatenation of logical AND links. It determines the validity of a statement form, for example A(?). ? represents a variable. The notation ∀? says "for all/every ? is valid". The all quantifier can be seen as an upside-down letter "A". The expression ∀? : ?² ≤ 0 means, for example: "for all ? it is true that ?² ≤ 0", where "for all" represents the all-quantor, ? the variable and ?² ≤ 0 the propositional form.
In contrast to an all-quantifier, an existential quantifier can be regarded as a disjunction, i.e. as a concatenation of logical OR operations. The expression ∃? describes "there exists at least one ?", for which the postposed statement form applies. ∃? : ?² ≤ 0 means in comparison to before: "there is at least one number ? to which the propositional form ?² ≤ 0 applies", i.e. the propositional form is true. The symbol ∃ can be seen as a horizontally mirrored letter "E".
For both all-quantifiers and existential quantifiers, the reference quantity to which the respective quantifier refers must be unambiguously defined. If it is not clear from the context, the reference quantity for all-quantors must be specified by the expression ∀? ∊ M : A(?), for existential quantifiers the expression ∃? ∊ M : A(?) can be defined. The element sign ∊ indicates that the object ∀? or ∃? is an element of a set M.
What are quantifiers in regular expressions (regex)?
Regular expressions, or regex for short, describe character strings which are used in programming languages or in the search-and-replace function and which are assigned to the Description of these chains by certain syntactic rules serve. Regex can be interpreted as a general notation for describing textual patterns and are used in textual analysis, structural as well as Data analytics.
Quantifiers in regular expressions specify the truth condition for a match in the search. The Quantors are divided into a greedy version and a non-greedy or inert version.. While a greedy version tries to find an element as often as possible, a lazy version tries to find an element as rarely as possible. The following table shows the notation of the standard quantifiers in their greedy and lazy versions.
with zero or more occurrences.
with one or more occurrences.
with zero or one occurrence.
Conformity with exactly n Occurrence.
Compliance with at least n Occurrence.
Consistency with n to m Occurrence.
In addition to the described standard expressions in Regex, there are other special forms such as lookahead and lookbehind. These are used to search for expressions that return only a (relevant) part of the searched expression and are intended for further processing.
LookaheadIf, for example, every "a" in a text is searched for which is followed by the letter "b" and only "a" is to be returned, this can be achieved by Lookahead. The syntax "a(?=b)" searches for the term "ab" always returns only "a" as a result.
LookbehindThe opposite is true for lookbehind. The name lookbehind is explained by the fact that preceding characters are also included in the search. The syntax for "(? <=a)b" also searches for the term "ab", but always returns only "b" as a result.
A quantum computer is a processor that functions according to the laws of quantum mechanics. Unlike a conventional computer, a quantum computer does not work on the basis of electrical states, but on the basis of quantum mechanical states. Important in quantum mechanics is the superposition principle and quantum entanglement. There are already theoretical studies that show that certain computer science problems can be solved much more efficiently by exploiting quantum mechanical effects than is comparatively the case with a classical computer. For example, the search in really extremely large databases can function particularly efficiently and the factorisation of large numbers can also be carried out more quickly. This makes it possible to reduce the calculation time of many mathematical and physical problems quite significantly. So far, however, the quantum computer is a predominantly theoretical concept and there have been various proposals for its realisation. However, quantum computers have already been tested on a small scale in the laboratory. At first, these had only a few qubits. The biggest success to date is 65 qubits for the processor, which was set as a record in August 2020. Not only the number of qubits is decisive for success, a low error rate for computing and reading is also important, as is the time for which qubits can be maintained without errors.
Where can quantum computers be used?
In principle, quantum computers can perform all the calculations of conventional computers, but there are particular strengths where classical supercomputers have particular difficulties due to their complexity. For example, quantum computers succeed above all in optimisation tasks in finance and logistics and in simulations of new chemical substances for advanced biotechnology and the development of medicines and in the development of new types of accumulators. Quantum computers can also be used helpfully in cryptography. Such a quantum computer is also advantageous in energy optimisation.
A hybrid computer consisting of a quantum computer and a conventional computer can also be used in a VW navigation system. Such a quantum computer is already said to exist with 2048 qubits.
What are the difficulties with quantum computers?
Quantum computers require complex cooling to function properly and are therefore not available for the consumer market for the foreseeable future. However, research will already be able to benefit from such computer systems in the medium term. There are numerous simulations that can be made with the help of quantum computers.
How expensive is quantum computing?
The special flagship of Germany's technology location is the first quantum computer. This one costs 11,621 € monthly rent. The computer has a total of 27 qubits and is stable enough for industrial operation. IBM is planning a quantum computer with more than 1,000 qubits by 2023.
Quantitative Analysis (abbreviated "QA") is a scientific technique that involves mathematical and statistical measurement, modelling and research to explain certain behaviours. In Quantitative Analysis, analysts usually use numerical values to express a reality. Quantitative analysis is used for various things, such as evaluating performance, predicting real events and valuing financial instruments. For example, it can be used to predict future changes in a country's gross domestic product (GDP).
In financial research, QA aims to evaluate a profitable investment opportunity and estimate any change in micro- and macroeconomic value. In this way, investors and managers can use this information in decision-making.
What does quantitative analysis involve?
QA provides analysts with important tools to examine and analyse all events in the past, present and near future. Anything that involves numbers can be quantified. Therefore, QA can be used in various fields such as financial analysis, analytical chemistry, organised sports and social sciences. Analysts who rely mainly on QA are called quants or quant jockeys. Even governments rely on this type of analysis to make economic policy decisions. They do this by monitoring and evaluating statistical data such as employment figures and GDP. In the financial industry, analysts use QA to analyse different investment opportunities and so it helps investors make their final decision. For example, QA can be used to analyse when is the right time to buy or sell securities.
Qualitative analysis involves the study of simple statistical data and complex calculations, e.g. the calculation of option valuations. For real events, this analysis involves quantifying trends in patterns and strategies with the aim of identifying the correlation between different variables. There are several forms of quantitative analysis, but the most common are the following:
Contribution margin accounting
This method has already been adopted by many people, including hedge fund managers. It is advanced, which is due to the development and advances in computer technology. However big the difference between quantitative and qualitative analysis, most analysts use both methods. Quantitative analysis is heavily based on mathematics and is widely used as a stand-alone approach. However, in certain circumstances it is used in conjunction with Qualitative Analysis. Quantitative Analysis is used to identify potential investments and then Qualitative Analysis helps to find the perfect investment. QA also plays a major role in risk management. This form of analysis has its proponents in the real world, in companies and governments.