Many problems from complexity theory can be phrased in terms of tensors. I will begin by reviewing basic properties of tensors and discussing several measures of the complexity of a tensor. I'll then focus on the complexity of matrix multiplication. Since March 2012 there have been significant...
In thiswork,we prove tighter upper bounds for various complexity measures in terms of sensitivity. More precisely, we show that deg(f)~(1-o(1)) = O(2~(s(f))) and C(f) 鈮 2~(s(f)-1)s(f); these in turn imply various corollaries regarding the relation between sensitvity and...
In thinking in terms of consecutive time, however, evolution does not march from the past into the future. Instead, the species is precognitively aware of those changes it wants to make, and from the “future” it alters the “present” state of the chromosomes and genes to bring about in...
This would free the statement of profit or loss and other comprehensive income from the need to formally to classify gains and losses between SOPL and OCI. This would reduce complexity and gains and losses could only ever be recognised once. However, there would still remain ...
On the flip side,closeness centralityfocuses on how efficiently a node can interact with all other nodes in the network. It measures the average length of the shortest paths between a given node and all other nodes. Nodes with high closeness centrality are central in terms of their ability to...
When choosing or building a data protection mechanism, you should weigh its vulnerabilities against potential threats. This assessment may be easier if you think of your solution in terms of the basic data protection techniques already discussed. For example, if you store database connection informati...
Economic and Social Rights under the EU Charter of Fundamental Rights: A Legal Perspective This collection of essays by leading scholars in this field considers the significance of the inclusion of economic and social rights within the EU Charter, in terms of protection of individual and collective...
Directed by Johannes Roberts (The Other Side of the Door), this ladies-in-peril shark thriller might lack the bite of last year’s The Shallows, but it delivers enough of the requisite suspense moments to ensure that it succeeds on its own B-movie terms.Mandy Moore (TV’s This Is Us)...
The real damage came from the unexpected and sudden freezing of the entire securitisation industry. Almost instantaneously, confidence vanished and the complexity which made possible the “multiplication of bread” during the boom, turned into a source of counterparty risk, both real and imaginary. Ev...
of both collecting contractual cash flows and selling some of the investment in debt. Since the contractual terms of the debt instruments would give rise on specified dates to cash flows that are solely payments of principal and interest and the busin...