Multiple Scales in Small-World Networks

Small-world architectures may be implicated in a range of phenomena from networks of neurons in the cerebral cortex to social networks and propogation of viruses. Small-world networks are interpolations of regular and random networks that retain the advantages of both regular and random networks by being highly clustered like regular networks and having small average path length between nodes, like random networks. While most of the recent attention on small-world networks has focussed on the effect of introducing disorder/randomness into a regular network, we show that that the fundamental mechanism behind the small-world phenomenon is not disorder/ randomness, but the presence of connections of many different length scales. Consequently, in order to explain the small-world phenomenon, we introduce the concept of multiple scale networks and then state the multiple length scale hypothesis. We show that small-world behavior in randomly rewired networks is a consequence of features common to all multiple scale networks. To support the multiple length scale hypothesis, novel network architectures are introduced that need not be a result of random rewiring of a regular network. In each case it is shown that whenever the network exhibits small-world behavior, it also has connections of diverse length scales. We also show that the distribution of the length scales of the new connections is significantly more important than whether the new connections are long range, medium range or short range

The human and mammalian cerebrum scale by computational power and information resistance

The cerebrum of mammals spans a vast range of sizes and yet has a very regular structure. The amount of folding of the cortical surface and the proportion of white matter gradually increase with size, but the underlying mechanisms remain elusive. Here, two laws are derived to fully explain these cerebral scaling relations. The first law holds that the long-range information flow in the cerebrum is determined by the total cortical surface (i.e., the number of neurons) and the increasing information resistance of long-range connections. Despite having just one free parameter, the first law fits the mammalian cerebrum better than any existing function, both across species and within humans. According to the second law, the white matter volume scales, with a few minor corrections, to the cortical surface area. It follows from the first law that large cerebrums have much local processing and little global information flow. Moreover, paradoxically, a further increase in long-range connections would decrease the efficiency of information flow.Comment: 15 pages, 2 figures; 3 supplement

Alzheimer and vascular brain diseases: Focal and diffuse subforms.

Alois Alzheimer is best known for his description of the pre-senile neurodegenerative disease named after him. However, his previous interest in vascular brain diseases, underlying cognitive and behavioral changes, was very strong. Besides describing the Arteriosclerotic atrophy of the brain and the arteriosclerotic subtype of Senile dementia which he viewed as main forms of vascular brain diseases, he also identified and described a series of conditions he considered subforms. These may be divided, as suggested by the authors of the present paper, into 3 groups: gliosis and sclerosis, subcortical atrophies, and apoplectic. The subforms of the three groups present characteristic neuropathological features and clinical, cognitive and behavioral manifestations. These provide the basis, together with part of the main forms, for the contemporary condition known as Vascular Cognitive Impairment

Cortex, countercurrent context, and dimensional integration of lifetime memory

The correlation between relative neocortex size and longevity in mammals encourages a search for a cortical function specifically related to the life-span. A candidate in the domain of permanent and cumulative memory storage is proposed and explored in relation to basic aspects of cortical organization. The pattern of cortico-cortical connectivity between functionally specialized areas and the laminar organization of that connectivity converges on a globally coherent representational space in which contextual embedding of information emerges as an obligatory feature of cortical function. This brings a powerful mode of inductive knowledge within reach of mammalian adaptations, a mode which combines item specificity with classificatory generality. Its neural implementation is proposed to depend on an obligatory interaction between the oppositely directed feedforward and feedback currents of cortical activity, in countercurrent fashion. Direct interaction of the two streams along their cortex-wide local interface supports a scheme of "contextual capture" for information storage responsible for the lifelong cumulative growth of a uniquely cortical form of memory termed "personal history." This approach to cortical function helps elucidate key features of cortical organization as well as cognitive aspects of mammalian life history strategies

Imaging Studies of Aging, Neurodegenerative Disease, and Alcoholism.

Neurodegenerative diseases such as Alzheimers disease, disorders such as alcoholism, and the aging process can lead to impaired cognitive function and dementia. Researchers and clinicians have used noninvasive imaging techniques to determine the structural and physiological alterations in the brain that are associated with these conditions. Analyses of the brains structure have found that shrinkage (atrophy) of the brain tissue is characteristic for all conditions associated with dementia, but that the specific locations of atrophied brain structures vary among different neurodegenerative diseases and alcohol-induced disorders. Similarly, studies analyzing the metabolism in various brain structures have found that, depending on whether dementia was induced by neurodegenerative diseases, alcoholism, or aging, the affected brain structures vary slightly. Based on such studies, researchers and clinicians now can more accurately define different types of dementia and predict their clinical course