Given the current knowledge of complex representations of finite quasi-simple groups, obtaining good upper bounds for their characters values still remains a difficult problem, a satisfactory solution of which would have significant implications in a number of applications. We will report on recent results that produce such character bounds, and discuss some such applications, in and outside of group theory.

The vagus nerve (CN X) originates in the medulla, which was archaically called the bulb (also where the commonly used term “bulbar” comes from), and also called the myelencephalon. The term vagus has Latin roots, meaning “wanderer/ing,” and may have acquired its name due to its winding path through the body and subsequent innervation of many organs. It exits the skull through the jugular foramen (like a tunnel) with two other nerves – glossopharyngeal nerve (CN IX) and spinal accessary nerve (CN XI). Though the vagus nerve has many functions, one of its main functions is to provide parasympathetic innervation to the heart and gut, and thus help to rest and digest.

The internal acoustic meatus is a foramen located in the posterior cranial fossa through which the facial nerve, vestibulocochlear nerve, and labyrinthine artery pass. Near the entry and exit of this canal is a common location for tumors called acoustic neuromas/vestibular schwannomas, which produce dysfunction of the facial nerve and vestibulocochlear nerves, for example, imbalance and hearing loss.

The basal ganglia refers to a group of deep subcortical gray matter structures that are connected to widespread areas of the cerebral cortex and play a role in selecting actions. The neuroembryologic origins of these structures are diverse, as they include telencephalic, diencephalic, and mesencephalic structures. The telencephalic nuclei represent what many refer to as “basal ganglia,” which include the caudate nucleus, putamen, and globus pallidus.

Some immediate applications of the theory of elliptic functions and modular forms to problems of physical interest are presented, including the construction of the Green functions and functional determinants for the two-dimensional quantum field theories of the bc fields, the scalar field, and the spinor fields on the torus. In particular, it will be shown how the singular terms in the operator product expansion of holomorphic fields for the bc system essentially determine arbitrary correlation functions on the torus in terms of elliptic functions. Along the way, a brief but reasonably systematic introduction will be presented of two-dimensional conformal field theory methods.

The primary motor cortex (M1) is located in the precentral gyrus in the frontal lobe. It is separated from the primary sensory cortex (S1) by the central sulcus. It is a six-layered agranular cortex. It consists of Brodmann areas 4 and 6. Area 4 is mainly located in the anterior bank of the central sulcus, whereas area 6 is located on the crown of the precentral gyrus.

Now in Boston, Weinberg describes how his earlier work on current algebra led to effective field theory. With the Vietnam War going on, JASON work focuses on the war effort. In 1967, Weinberg takes up a lectureship at MIT and published his most-cited paper, “A Model of Leptons,” which heralded electroweak theory. He attends the Solvay conference in Brussels in 1967, but misses being in the group photo. Back in Boston, Weinberg discusses making friends through his election to the American Academy of Arts and Sciences. He becomes involved in an independent study of the US’ anti-ballistic missile program, concluding that this would hasten the arms race between the US and the Soviet Union.

Chapter 5 considers the surveillance of potential terrorists and their arrest, including the force that may be employed to do so. Once in custody, criminal suspects should be interviewed without the threat or use of physical coercion in order to gather evidence to decide whether or not it is right to engage a prosecution for terrorism (or other criminal offences). In certain circumstances, control orders or similar judicial decisions may limit the actions at large of an individual suspect with a view to protecting the public. Most controversial of all, preventive detention by the State may sometimes be made where an individual has been convicted of no crime and is not being held on remand with a view to future prosecution. The chapter addresses these issues in turn considering the treatment of terrorist suspects in accordance with fundamental human rights.

The semicircular canals are specialized endolymph-filled structures in the inner ear that help regulate the position sense of the head and overall balance. Like the cochlea, the semicircular canals are bony labyrinths housed in the petrous portion of the temporal bone. Each inner ear has three semicircular canals on each side. Named the lateral, superior, and posterior canals, each is oriented at an approximately 90-degree angle from the other two, and each contoured to make approximately two-thirds of a full circle.

The goal of this book is to exhibit the profound and myriad interrelations between the mathematics of modular forms and the physics of string theory. Our presentation is intended to be informal but mathematically precise, logically complete, and reasonably self-contained. The exposition is kept as simple as possible so as to be accessible to adventurous undergraduates, motivated graduate students, and dedicated professionals interested in the interface between theoretical physics and pure mathematics. Assuming little more than a knowledge of complex function theory, we introduce elliptic functions and elliptic curves as a lead-in to modular forms and their various deep generalizations. Following an economical introduction to string theory, its perturbative expansion, toroidal compactification, and supergravity limit are used to illustrate the power of modular invariance in physics. Dualities and their realization via modular forms in Yang–Mills theories with extended supersymmetry are studied both via the Seiberg–Witten solution and via their superconformal phase. Appendices are included to review foundational topics, and 75 exercises with detailed solutions give the reader ample opportunity for practice.

The superior mesenteric plexus/ganglion is positioned retroperitoneal atop the abdominal aorta at the level of the superior mesenteric artery. Its major function is innervating the organs of the midgut, namely the jejunum, ileum, and ascending colon.

The dorsal column medial lemniscus pathway is responsible for transmission of vibration and position sense. As one of the key ascending sensory pathways, it brings sensory information up the spinal cord from the periphery.

OK! OK! I know this one was tough. The conus medullaris is the cone located at the base of the spinal cord. Strobile is the Latin word for cone, and it is located around the meeting of the kyphotic (thoracic spine) curve and the lordotic (lumbar spine) curve. It ends around L1–L2.

The S1 nerve root is the first nerve root of the sacral spinal cord segment. It is the second most commonly implicated nerve root in radiculopathies caused by a herniated disc.

Back in Berkeley, Weinberg reconsiders how we understand some of the theories of physics, that is, why they actually are true. He begins teaching a general relativity course starting from physical principles, rather than the usual geometric approach. These course notes later became the basis for his book Gravitation and Cosmology. Around this time, Louise was pregnant, so Weinberg avoided opportunities to travel to spend more time at home. He begins working on functional analysis, but discovers the Russian Faddeev has already done foundational work in this area. Weinberg then reexamines what he knows about quantum field theory, and jettisons the Heisenberg–Pauli canonical formalism, taking particles as his starting point. This led him to a clearer understaning of antimatter. He embarks on a series of papers about massless particles. in 1964, he is promoted to full professor. Louise applied to Harvard Law School, prompting a move to Cambridge, Mass.