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Transplantation of organs, tissues, etc. --- Transplantation. --- Periodical. --- stem cell therapy --- tissue engineering --- immunosuppression --- endocrine --- preclinical and clinical trials --- surgery --- Transplantations --- Transplantation Immunology --- Transplantation Conditioning --- Medical transplantation --- Organ transplantation --- Organ transplants --- Organs (Anatomy) --- Surgical transplantation --- Tissue transplantation --- Tissues --- Transplant surgery --- Transplantation surgery --- Transplants, Organ --- Surgery --- Preservation of organs, tissues, etc. --- Procurement of organs, tissues, etc. --- Transplantation

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Electromagnetism plays a crucial role in basic and applied physics research. The discovery of electromagnetism as the unifying theory for electricity and magnetism represents a cornerstone in modern physics. Symmetry was crucial to the concept of unification: electromagnetism was soon formulated as a gauge theory in which local phase symmetry explained its mathematical formulation. This early connection between symmetry and electromagnetism shows that a symmetry-based approach to many electromagnetic phenomena is recurrent, even today. Moreover, many recent technological advances are based on the control of electromagnetic radiation in nearly all its spectra and scales, the manipulation of matter–radiation interactions with unprecedented levels of sophistication, or new generations of electromagnetic materials. This is a fertile field for applications and for basic understanding in which symmetry, as in the past, bridges apparently unrelated phenomena―from condensed matter to high-energy physics. In this book, we present modern contributions in which symmetry proves its value as a key tool. From dual-symmetry electrodynamics to applications to sustainable smart buildings, or magnetocardiography, we can find a plentiful crop, full of exciting examples of modern approaches to electromagnetism. In all cases, symmetry sheds light on the theoretical and applied works presented in this book.

electromagnetic knots --- helicity --- spin-orbital momentum --- magnetocardiography --- quadratic penalty --- variational mode decomposition --- correlation coefficient --- interval thresholding method --- periodic structures --- dispersion diagram --- high-order coupling --- glide symmetry --- smart building --- harmonics --- geometric algebra --- Poynting Multivector --- electric-magnetic duality symmetry --- quantum anomalies --- optical helicity --- electromagnetic polarization --- particle creation --- Maxwell theory --- constraint equations --- evolutionary equations --- Barium hexaferrite --- titanium --- hysteresis --- X-ray diffraction --- permanent magnet applications --- n/a --- hopfion --- Bateman construction --- null fields --- magnetic levitation --- electrodynamic structure --- ground high speed system --- finite element analysis --- non-local action --- electrodynamics --- electromagnetic duality symmetry --- Aharonov-Bohm effect --- Harvesting --- low-power applications --- vibration --- micro-generator --- optimal solution --- magnetic circuit --- periodical structure --- effective power density --- symmetry

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According to Carl Friedrich Gauss (1777–1855), mathematics is the queen of the sciences—and number theory is the queen of mathematics. Numbers (integers, algebraic integers, transcendental numbers, p-adic numbers) and symmetries are investigated in the nine refereed papers of this MDPI issue. This book shows how symmetry pervades number theory. In particular, it highlights connections between symmetry and number theory, quantum computing and elementary particles (thanks to 3-manifolds), and other branches of mathematics (such as probability spaces) and revisits standard subjects (such as the Sieve procedure, primality tests, and Pascal’s triangle). The book should be of interest to all mathematicians, and physicists.

quantum computation --- IC-POVMs --- knot theory --- three-manifolds --- branch coverings --- Dehn surgeries --- zeta function --- Pólya-Hilbert conjecture --- Riemann interferometer --- prime numbers --- Prime Number Theorem (P.N.T.) --- modified Sieve procedure --- binary periodical sequences --- prime number function --- prime characteristic function --- limited intervals --- logarithmic integral estimations --- twin prime numbers --- free probability --- p-adic number fields ℚp --- Banach ∗-probability spaces --- C*-algebras --- semicircular elements --- the semicircular law --- asymptotic semicircular laws --- Kaprekar constants --- Kaprekar transformation --- fixed points for recursive functions --- Baker’s theorem --- Gel’fond–Schneider theorem --- algebraic number --- transcendental number --- standard model of elementary particles --- 4-manifold topology --- particles as 3-Braids --- branched coverings --- knots and links --- charge as Hirzebruch defect --- umbral moonshine --- number of generations --- the pe-Pascal’s triangle --- Lucas’ result on the Pascal’s triangle --- congruences of binomial expansions --- primality test --- Miller–Rabin primality test --- strong pseudoprimes --- primality witnesses