Open Access
Society

Springer Nature
ISSN:
01472011, 19364725, 23386932, 25974874, 27155994, 20870493
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SCImago
Q3
WOS
Q2
Impact factor
1.4
SJR
0.245
CiteScore
1.3
Categories
Social Sciences (miscellaneous)
Sociology and Political Science
Areas
Social Sciences
Years of issue
1968, 1971-1999, 2002-2025
journal names
Society
Top-3 citing journals

SSRN Electronic Journal
(290 citations)

Society
(155 citations)

The American Sociologist
(78 citations)
Top-3 organizations

Rutgers, The State University of New Jersey
(145 publications)

Harvard University
(127 publications)

University of California, Berkeley
(117 publications)

University College Dublin
(22 publications)

University of Cambridge
(20 publications)

University of Oxford
(20 publications)
Top-3 countries
Most cited in 5 years
Found
Publications found: 699

Quantum Field Theory
Wetterich C.
Quantum field theory emerges in a very natural and straightforward way from our general probabilistic setting. We have already seen that very simple unique jump chains or probabilistic cellular automata, like the transport automata, describe twodimensional quantum field theories for free massless fermions. Actually, it is the quantum field theory which arises directly at the most basic level. Single-particle quantum mechanics is obtained as a special case or approximation, rather than being the starting point, as in the historical development of quantum field theory. The generic situation for interesting probabilistic systems describes states with many particles, with a continuum limit admitting an infinite number.

Fundamental Probabilities
Wetterich C.
The advent of quantum mechanics has opened a probabilistic view on fundamental physics. It has come, however, with new concepts and rules like wave functions, non-commuting operators, and the rules for associating these quantities with observations. The unusual probabilistic features have opened many debates on their interpretation, as well as on suggestions for extensions of quantum mechanics.

Qubit Automaton
Wetterich C.
In the present section, we concentrate on quantum mechanics for a single qubit. A simple local chain with three classical Ising spins already realizes many characteristic features of quantum mechanics, such as non-commuting operators for observables, the quantum rule for computing expectation values, discrete measurement values corresponding to the spectrum of operators, the uncertainty principle, unitary evolution, and complex structure.

Quantum Mechanics
Wetterich C.
In this chapter, we discuss probabilistic automata that realize all features of quantum mechanics.We start with quantum mechanics for a two-state system or a single qubit. The quantum spin in an arbitrary direction is associated with a corresponding classical Ising spin. For the quantum subsystem, the deterministic evolution for the automaton results in the unitary evolution according to the von Neumann equation for the quantum density matrix. Suitable updating rules can realize an arbitrary Hamiltonian for a single qubit. Quantum mechanics for a single qubit is the extension of the quantum clock system to rotations in three-dimensional space or on the two-dimensional sphere.

Discussion and Conclusions
Wetterich C.
This book proposes a probabilistic formulation of the fundamental laws of nature. On a fundamental level, the description of the universe is entirely based on the concepts of classical statistics: observables that take definite values in the states of the system, probabilities for these states, and expectation values of observables computed from these probabilities. The overall probability distribution covers everything in the world, including all times, all locations, and all possible events.

Fermions
Wetterich C.
In this section we present a first simple classical statistical model that is equivalent to a quantum field theory. It is a generalized Ising model which describes free massless fermions in one time and one space dimension. Even though this two-dimensional model remains extremely simple, all aspects of the formalism of quantum mechanics are already visible. This concerns both the Schr¨odinger or von Neumann equation for a unitary evolution and the appearance of non-commuting operators for observables like position or momentum.

Fundamental Probabilism
Wetterich C.
The starting point of the present work is the assumption that the fundamental description of our world is probabilistic [25,52–54]. The basic objects for this description are probability distributions and observables. Deterministic physics arises as an approximation for particular cases. Our description of probabilities remains within the standard setting of classical statistics. No separate laws for quantum mechanics will be introduced. They follow from the classical statistical setting for particular classes of subsystems.

Probabilistic and Deterministic Evolution
Wetterich C.
Different types of evolution are distinguished by the way the probabilistic information propagates. This is reflected by the question of how boundary properties influence behavior in the bulk.

Entanglement in Classical and Quantum Statistics
Wetterich C.
Entanglement describes situations where two parts of a system are connected and cannot be separated. The properties in one part depend on the properties of the other part. The quantitative description of such situations is given by correlation functions. There is no conceptual difference between entanglement in classical statistics and entanglement in quantum mechanics [185]. In this chapter, we will explicitly construct probabilistic automata that realize the maximally entangled state of a twoqubit quantum system.

Embedding Quantum Mechanics in Classical Statistics
Wetterich C.
It has often been asserted that an embedding of quantum mechanics in classical statistics is not possible. The present work demonstrates by explicit examples that this claim is not justified.

Continuous Classical Variables
Wetterich C.
The use of continuous classical variables brings us closer to the quantum particle, for which we have argued that it involves an infinite number of degrees of freedom. If we allow for an arbitrary orthogonal evolution of the classical wave function, we can find a bit-quantum map which maps this to the evolution of a quantum particle in a potential according to the usual Schrödinger equation.

Subsystems
Wetterich C.
Subsystems are a central ingredient for a probabilistic description of the world. For most practical purposes, one does not want to deal with the overall probability distribution for all events in the universe from the past to the future. One rather concentrates on subsystems.

Probabilistic Time
Wetterich C.
Time is a fundamental concept in physics. It is the first structure among observables that we will discuss. Rather than being postulated as an “a priori concept” with physics formulated in a pregiven time and space, probabilistic time is a powerful concept to order and organize observables. There is no time outside the correlations for the observables of the statistical system.

Correlated Computing
Wetterich C.
As already emphasized, the crucial feature of quantum computing is the large number of correlations between the associated classical bits. These correlations result from the quantum constraint of positivity of the density matrix for the quantum subsystem.

Introduction
Wetterich C.
Since the discovery of quantum mechanics, probabilities have play a central role in fundamental physics. The mathematical formalism of quantum mechanics makes statements about expectation values of observables. The expectation value describes the mean value of an observable for an ensemble of many identical measurements. It is a genuinely probabilistic concept since every possible measurement value of the observable is weighted by the probability of finding it. The quantum laws for the computation of these probabilities are often felt to be mysterious.
Top-100
Citing journals
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SSRN Electronic Journal
290 citations, 1.92%
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Society
155 citations, 1.03%
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7 publications, 0.11%
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|
University of California, Santa Barbara
7 publications, 0.11%
|
|
Wayne State University
7 publications, 0.11%
|
|
University of Calgary
7 publications, 0.11%
|
|
University of Florida
7 publications, 0.11%
|
|
University of Rochester
7 publications, 0.11%
|
|
University of Tennessee at Chattanooga
7 publications, 0.11%
|
|
University of Nottingham
6 publications, 0.09%
|
|
Tufts University
6 publications, 0.09%
|
|
University of Massachusetts Dartmouth
6 publications, 0.09%
|
|
University of Sheffield
6 publications, 0.09%
|
|
Robert Morris University
6 publications, 0.09%
|
|
Show all (70 more) | |
20
40
60
80
100
120
140
160
|
Publishing organizations in 5 years
5
10
15
20
25
|
|
University College Dublin
22 publications, 3.61%
|
|
University of Oxford
20 publications, 3.28%
|
|
University of Cambridge
20 publications, 3.28%
|
|
New York University
15 publications, 2.46%
|
|
University of Warwick
13 publications, 2.13%
|
|
Trinity College Dublin
10 publications, 1.64%
|
|
London School of Economics and Political Science
9 publications, 1.48%
|
|
Wake Forest University
9 publications, 1.48%
|
|
Boston University
8 publications, 1.31%
|
|
University of Michigan
6 publications, 0.98%
|
|
University of Sheffield
6 publications, 0.98%
|
|
Indiana University Bloomington
6 publications, 0.98%
|
|
University of Birmingham
5 publications, 0.82%
|
|
Yale University
5 publications, 0.82%
|
|
Free International University of Social Studies "Guido Carli"
5 publications, 0.82%
|
|
University of York
5 publications, 0.82%
|
|
University College London
4 publications, 0.66%
|
|
Pennsylvania State University
4 publications, 0.66%
|
|
University of Auckland
4 publications, 0.66%
|
|
University of Johannesburg
4 publications, 0.66%
|
|
University of California, Berkeley
4 publications, 0.66%
|
|
Harvard University
4 publications, 0.66%
|
|
University of South Florida
4 publications, 0.66%
|
|
Hebrew University of Jerusalem
3 publications, 0.49%
|
|
University of Bayreuth
3 publications, 0.49%
|
|
Australian National University
3 publications, 0.49%
|
|
University of Technology Sydney
3 publications, 0.49%
|
|
La Trobe University
3 publications, 0.49%
|
|
Flinders University
3 publications, 0.49%
|
|
Hanyang University
3 publications, 0.49%
|
|
University of Texas at Austin
3 publications, 0.49%
|
|
Erasmus University Rotterdam
3 publications, 0.49%
|
|
University of Delaware
3 publications, 0.49%
|
|
University of Tehran
2 publications, 0.33%
|
|
University of Delhi
2 publications, 0.33%
|
|
Nanjing University
2 publications, 0.33%
|
|
University of Helsinki
2 publications, 0.33%
|
|
London School of Hygiene & Tropical Medicine
2 publications, 0.33%
|
|
Kingston University
2 publications, 0.33%
|
|
University of Sydney
2 publications, 0.33%
|
|
George Washington University
2 publications, 0.33%
|
|
George Mason University
2 publications, 0.33%
|
|
University of California, Los Angeles
2 publications, 0.33%
|
|
Newcastle University
2 publications, 0.33%
|
|
Loyola University Maryland
2 publications, 0.33%
|
|
Huaihua University
2 publications, 0.33%
|
|
Max Planck Institute for the Study of Societies
2 publications, 0.33%
|
|
University of Bristol
2 publications, 0.33%
|
|
University of St Andrews
2 publications, 0.33%
|
|
McGill University
2 publications, 0.33%
|
|
Queen's University at Kingston
2 publications, 0.33%
|
|
University of Minnesota
2 publications, 0.33%
|
|
University of Duisburg-Essen
2 publications, 0.33%
|
|
WZB Berlin Social Science Center
2 publications, 0.33%
|
|
HTW Berlin - University of Applied Sciences
2 publications, 0.33%
|
|
Cardiff University
2 publications, 0.33%
|
|
University of Leeds
2 publications, 0.33%
|
|
Technical University of Ostrava
2 publications, 0.33%
|
|
University of Maryland, Baltimore
2 publications, 0.33%
|
|
University of Pennsylvania
2 publications, 0.33%
|
|
University of Reading
2 publications, 0.33%
|
|
University of Exeter
2 publications, 0.33%
|
|
University of Nevada, Las Vegas
2 publications, 0.33%
|
|
Texas Tech University
2 publications, 0.33%
|
|
University of Connecticut
2 publications, 0.33%
|
|
Portland State University
2 publications, 0.33%
|
|
University of Essex
2 publications, 0.33%
|
|
University College Cork (National University of Ireland, Cork)
2 publications, 0.33%
|
|
PJSC Sberbank
1 publication, 0.16%
|
|
Koc University
1 publication, 0.16%
|
|
University of Jeddah
1 publication, 0.16%
|
|
Prince Mohammad Bin Fahd University
1 publication, 0.16%
|
|
Tarbiat Modares University
1 publication, 0.16%
|
|
New York University Abu Dhabi
1 publication, 0.16%
|
|
Marmara University
1 publication, 0.16%
|
|
Abdullah Gul University
1 publication, 0.16%
|
|
Indian Institute of Technology Guwahati
1 publication, 0.16%
|
|
Indian Institute of Technology Gandhinagar
1 publication, 0.16%
|
|
Indian Institute of Technology Jodhpur
1 publication, 0.16%
|
|
University of Hyderabad
1 publication, 0.16%
|
|
University of Kerala
1 publication, 0.16%
|
|
Bursa Uludağ University
1 publication, 0.16%
|
|
Gebze Technical University
1 publication, 0.16%
|
|
Islamic Azad University, Isfahan
1 publication, 0.16%
|
|
Central University of Tamil Nadu
1 publication, 0.16%
|
|
Christ University
1 publication, 0.16%
|
|
Beijing Normal University
1 publication, 0.16%
|
|
University of Tübingen
1 publication, 0.16%
|
|
Tel Aviv University
1 publication, 0.16%
|
|
Ben-Gurion University of the Negev
1 publication, 0.16%
|
|
Bar-Ilan University
1 publication, 0.16%
|
|
Manipal Academy of Higher Education
1 publication, 0.16%
|
|
Hamad Bin Khalifa University
1 publication, 0.16%
|
|
University of Liège
1 publication, 0.16%
|
|
University of Lisbon
1 publication, 0.16%
|
|
Uppsala University
1 publication, 0.16%
|
|
University of Haifa
1 publication, 0.16%
|
|
Stockholm University
1 publication, 0.16%
|
|
Sapienza University of Rome
1 publication, 0.16%
|
|
Aalto University
1 publication, 0.16%
|
|
Show all (70 more) | |
5
10
15
20
25
|
Publishing countries
500
1000
1500
2000
2500
3000
3500
|
|
USA
|
USA, 3181, 48.42%
USA
3181 publications, 48.42%
|
United Kingdom
|
United Kingdom, 248, 3.78%
United Kingdom
248 publications, 3.78%
|
Canada
|
Canada, 108, 1.64%
Canada
108 publications, 1.64%
|
Germany
|
Germany, 55, 0.84%
Germany
55 publications, 0.84%
|
Republic of Korea
|
Republic of Korea, 55, 0.84%
Republic of Korea
55 publications, 0.84%
|
Ireland
|
Ireland, 45, 0.69%
Ireland
45 publications, 0.69%
|
Australia
|
Australia, 41, 0.62%
Australia
41 publications, 0.62%
|
Israel
|
Israel, 40, 0.61%
Israel
40 publications, 0.61%
|
France
|
France, 29, 0.44%
France
29 publications, 0.44%
|
China
|
China, 29, 0.44%
China
29 publications, 0.44%
|
Italy
|
Italy, 28, 0.43%
Italy
28 publications, 0.43%
|
Czech Republic
|
Czech Republic, 19, 0.29%
Czech Republic
19 publications, 0.29%
|
Netherlands
|
Netherlands, 17, 0.26%
Netherlands
17 publications, 0.26%
|
Nigeria
|
Nigeria, 15, 0.23%
Nigeria
15 publications, 0.23%
|
Sweden
|
Sweden, 13, 0.2%
Sweden
13 publications, 0.2%
|
South Africa
|
South Africa, 12, 0.18%
South Africa
12 publications, 0.18%
|
India
|
India, 11, 0.17%
India
11 publications, 0.17%
|
Denmark
|
Denmark, 9, 0.14%
Denmark
9 publications, 0.14%
|
Japan
|
Japan, 9, 0.14%
Japan
9 publications, 0.14%
|
Turkey
|
Turkey, 8, 0.12%
Turkey
8 publications, 0.12%
|
Austria
|
Austria, 6, 0.09%
Austria
6 publications, 0.09%
|
Spain
|
Spain, 6, 0.09%
Spain
6 publications, 0.09%
|
Finland
|
Finland, 6, 0.09%
Finland
6 publications, 0.09%
|
Switzerland
|
Switzerland, 6, 0.09%
Switzerland
6 publications, 0.09%
|
Georgia
|
Georgia, 5, 0.08%
Georgia
5 publications, 0.08%
|
Iran
|
Iran, 5, 0.08%
Iran
5 publications, 0.08%
|
New Zealand
|
New Zealand, 5, 0.08%
New Zealand
5 publications, 0.08%
|
Norway
|
Norway, 5, 0.08%
Norway
5 publications, 0.08%
|
USSR
|
USSR, 5, 0.08%
USSR
5 publications, 0.08%
|
Poland
|
Poland, 4, 0.06%
Poland
4 publications, 0.06%
|
Serbia
|
Serbia, 4, 0.06%
Serbia
4 publications, 0.06%
|
Yugoslavia
|
Yugoslavia, 4, 0.06%
Yugoslavia
4 publications, 0.06%
|
Russia
|
Russia, 3, 0.05%
Russia
3 publications, 0.05%
|
Argentina
|
Argentina, 3, 0.05%
Argentina
3 publications, 0.05%
|
Belgium
|
Belgium, 3, 0.05%
Belgium
3 publications, 0.05%
|
Bulgaria
|
Bulgaria, 3, 0.05%
Bulgaria
3 publications, 0.05%
|
Greece
|
Greece, 3, 0.05%
Greece
3 publications, 0.05%
|
Saudi Arabia
|
Saudi Arabia, 3, 0.05%
Saudi Arabia
3 publications, 0.05%
|
Singapore
|
Singapore, 3, 0.05%
Singapore
3 publications, 0.05%
|
Jamaica
|
Jamaica, 3, 0.05%
Jamaica
3 publications, 0.05%
|
Portugal
|
Portugal, 2, 0.03%
Portugal
2 publications, 0.03%
|
Brazil
|
Brazil, 2, 0.03%
Brazil
2 publications, 0.03%
|
Ghana
|
Ghana, 2, 0.03%
Ghana
2 publications, 0.03%
|
Egypt
|
Egypt, 2, 0.03%
Egypt
2 publications, 0.03%
|
UAE
|
UAE, 2, 0.03%
UAE
2 publications, 0.03%
|
Tanzania
|
Tanzania, 2, 0.03%
Tanzania
2 publications, 0.03%
|
Kazakhstan
|
Kazakhstan, 1, 0.02%
Kazakhstan
1 publication, 0.02%
|
Estonia
|
Estonia, 1, 0.02%
Estonia
1 publication, 0.02%
|
Bangladesh
|
Bangladesh, 1, 0.02%
Bangladesh
1 publication, 0.02%
|
Benin
|
Benin, 1, 0.02%
Benin
1 publication, 0.02%
|
Brunei
|
Brunei, 1, 0.02%
Brunei
1 publication, 0.02%
|
Hungary
|
Hungary, 1, 0.02%
Hungary
1 publication, 0.02%
|
Zimbabwe
|
Zimbabwe, 1, 0.02%
Zimbabwe
1 publication, 0.02%
|
Qatar
|
Qatar, 1, 0.02%
Qatar
1 publication, 0.02%
|
Cuba
|
Cuba, 1, 0.02%
Cuba
1 publication, 0.02%
|
Luxembourg
|
Luxembourg, 1, 0.02%
Luxembourg
1 publication, 0.02%
|
Malaysia
|
Malaysia, 1, 0.02%
Malaysia
1 publication, 0.02%
|
Mexico
|
Mexico, 1, 0.02%
Mexico
1 publication, 0.02%
|
Monaco
|
Monaco, 1, 0.02%
Monaco
1 publication, 0.02%
|
Myanmar
|
Myanmar, 1, 0.02%
Myanmar
1 publication, 0.02%
|
San Marino
|
San Marino, 1, 0.02%
San Marino
1 publication, 0.02%
|
Slovakia
|
Slovakia, 1, 0.02%
Slovakia
1 publication, 0.02%
|
Thailand
|
Thailand, 1, 0.02%
Thailand
1 publication, 0.02%
|
Tunisia
|
Tunisia, 1, 0.02%
Tunisia
1 publication, 0.02%
|
Uganda
|
Uganda, 1, 0.02%
Uganda
1 publication, 0.02%
|
Philippines
|
Philippines, 1, 0.02%
Philippines
1 publication, 0.02%
|
Chile
|
Chile, 1, 0.02%
Chile
1 publication, 0.02%
|
Ethiopia
|
Ethiopia, 1, 0.02%
Ethiopia
1 publication, 0.02%
|
Show all (38 more) | |
500
1000
1500
2000
2500
3000
3500
|
Publishing countries in 5 years
50
100
150
200
250
|
|
USA
|
USA, 207, 33.93%
USA
207 publications, 33.93%
|
United Kingdom
|
United Kingdom, 148, 24.26%
United Kingdom
148 publications, 24.26%
|
Ireland
|
Ireland, 43, 7.05%
Ireland
43 publications, 7.05%
|
Germany
|
Germany, 19, 3.11%
Germany
19 publications, 3.11%
|
Canada
|
Canada, 17, 2.79%
Canada
17 publications, 2.79%
|
Australia
|
Australia, 16, 2.62%
Australia
16 publications, 2.62%
|
Nigeria
|
Nigeria, 14, 2.3%
Nigeria
14 publications, 2.3%
|
India
|
India, 10, 1.64%
India
10 publications, 1.64%
|
China
|
China, 8, 1.31%
China
8 publications, 1.31%
|
Italy
|
Italy, 8, 1.31%
Italy
8 publications, 1.31%
|
Israel
|
Israel, 6, 0.98%
Israel
6 publications, 0.98%
|
Netherlands
|
Netherlands, 6, 0.98%
Netherlands
6 publications, 0.98%
|
Finland
|
Finland, 6, 0.98%
Finland
6 publications, 0.98%
|
Czech Republic
|
Czech Republic, 6, 0.98%
Czech Republic
6 publications, 0.98%
|
South Africa
|
South Africa, 6, 0.98%
South Africa
6 publications, 0.98%
|
France
|
France, 5, 0.82%
France
5 publications, 0.82%
|
Austria
|
Austria, 4, 0.66%
Austria
4 publications, 0.66%
|
Spain
|
Spain, 4, 0.66%
Spain
4 publications, 0.66%
|
New Zealand
|
New Zealand, 4, 0.66%
New Zealand
4 publications, 0.66%
|
Republic of Korea
|
Republic of Korea, 4, 0.66%
Republic of Korea
4 publications, 0.66%
|
Greece
|
Greece, 3, 0.49%
Greece
3 publications, 0.49%
|
Denmark
|
Denmark, 3, 0.49%
Denmark
3 publications, 0.49%
|
Iran
|
Iran, 3, 0.49%
Iran
3 publications, 0.49%
|
Turkey
|
Turkey, 3, 0.49%
Turkey
3 publications, 0.49%
|
Argentina
|
Argentina, 2, 0.33%
Argentina
2 publications, 0.33%
|
Belgium
|
Belgium, 2, 0.33%
Belgium
2 publications, 0.33%
|
Ghana
|
Ghana, 2, 0.33%
Ghana
2 publications, 0.33%
|
Saudi Arabia
|
Saudi Arabia, 2, 0.33%
Saudi Arabia
2 publications, 0.33%
|
Tanzania
|
Tanzania, 2, 0.33%
Tanzania
2 publications, 0.33%
|
Sweden
|
Sweden, 2, 0.33%
Sweden
2 publications, 0.33%
|
Japan
|
Japan, 2, 0.33%
Japan
2 publications, 0.33%
|
Russia
|
Russia, 1, 0.16%
Russia
1 publication, 0.16%
|
Portugal
|
Portugal, 1, 0.16%
Portugal
1 publication, 0.16%
|
Bangladesh
|
Bangladesh, 1, 0.16%
Bangladesh
1 publication, 0.16%
|
Benin
|
Benin, 1, 0.16%
Benin
1 publication, 0.16%
|
Bulgaria
|
Bulgaria, 1, 0.16%
Bulgaria
1 publication, 0.16%
|
Brunei
|
Brunei, 1, 0.16%
Brunei
1 publication, 0.16%
|
Zimbabwe
|
Zimbabwe, 1, 0.16%
Zimbabwe
1 publication, 0.16%
|
Qatar
|
Qatar, 1, 0.16%
Qatar
1 publication, 0.16%
|
Monaco
|
Monaco, 1, 0.16%
Monaco
1 publication, 0.16%
|
Myanmar
|
Myanmar, 1, 0.16%
Myanmar
1 publication, 0.16%
|
Norway
|
Norway, 1, 0.16%
Norway
1 publication, 0.16%
|
UAE
|
UAE, 1, 0.16%
UAE
1 publication, 0.16%
|
Poland
|
Poland, 1, 0.16%
Poland
1 publication, 0.16%
|
Slovakia
|
Slovakia, 1, 0.16%
Slovakia
1 publication, 0.16%
|
Uganda
|
Uganda, 1, 0.16%
Uganda
1 publication, 0.16%
|
Philippines
|
Philippines, 1, 0.16%
Philippines
1 publication, 0.16%
|
Chile
|
Chile, 1, 0.16%
Chile
1 publication, 0.16%
|
Switzerland
|
Switzerland, 1, 0.16%
Switzerland
1 publication, 0.16%
|
Ethiopia
|
Ethiopia, 1, 0.16%
Ethiopia
1 publication, 0.16%
|
Show all (20 more) | |
50
100
150
200
250
|
1 profile journal article
Lenshie Nsemba
🥼 🤝
PhD in Political Science, Lecturer, Full member of the Nigerian Academy of Science

Taraba State University
26 publications,
143 citations
h-index: 7
Research interests
Political Science
1 profile journal article
Bharti Simant Shankar
🤝 🥼
PhD in Political Science, Lecturer
30 publications,
39 citations
h-index: 3