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Over the past three decades we have steadily increased our knowledge on the genetic basis of many severe disorders. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, mainly due to the relatively tedious and expensive process of genotyping. Since the genetic variations that underlie the disorders are relatively rare in the population, they can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective genotyping protocol to detect carriers for severe genetic disorders. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies. The mathematical framework presented here has some important distinctions from the ’traditional’ compressed sensing and group testing frameworks in order to address biological and technical constraints of our setting.

In the study of random access machines (RAMs) it has been shown that the availability of an extra input integer, having no special properties other than being sufficiently large, is enough to reduce the computational complexity of some problems. However, this has only been shown so far for specific problems. We provide a characterization of the power of such extra inputs for general problems.To do so, we first correct a classical result by Simon and Szegedy (1992) as well as one by Simon (1981). In the former we show mistakes in the proof and correct these by an entirely new construction, with no great change to the results. In the latter, the original proof direction stands with only minor modifications, but the new results are far stronger than those of Simon (1981).In both cases, the new constructions provide the theoretical tools required to characterize the power of arbitrary large numbers.1 Arithmetic complexity is the computational complexity of a problem under the RAM[+, , ×, ÷] model, which is defined later on in this section.

Path planning is an NP-complete problem with numerous practical applications, and is especially important for the navigation and control of autonomous robots. However, due to its computational complex nature, an optimal solution is often very difficult to be found using traditional methods.In this research, a swarm intelligence approach inspired by the biological behavior of glowworms is studied and applied to the robot path optimization problem. Computer simulation results show this firefly algorithm can successfully find the optimal path in a dynamic environment, and outperforms the ant colony algorithm (ACO) for a larger grid workspace in terms of both path length and computational cost.

Background Network motifs are connectivity structures that occur with significantly higher frequency than chance, and are thought to play important roles in complex biological networks, for example in gene regulation, interactomes, and metabolomes. Network motifs may also become pivotal in the rational design and engineering of complex biological systems underpinning the field of synthetic biology. Distinguishing true motifs from arbitrary substructures, however, remains a challenge. Results Here we demonstrate both theoretically and empirically that implicit assumptions present in mainstream methods for motif identification do not necessarily hold, with the ramification that motif studies using these mainstream methods are less able to effectively differentiate between spurious results and events of true statistical significance than is often presented. We show that these difficulties cannot be overcome without revising the methods of statistical analysis used to identify motifs. Conclusions Present-day methods for the discovery of network motifs, and, indeed, even the methods for defining what they are, are critically reliant on a set of incorrect assumptions, casting a doubt on the scientific validity of motif-driven discoveries. The implications of these findings are therefore far-reaching across diverse areas of biology.

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