Complexity classifications for different equivalence and audit problems for Boolean circuits

We study Boolean circuits as a representation of Boolean functions and consider different equivalence, audit, and enumeration problems. For a number of restricted sets of gate types (bases) we obtain efficient algorithms, while for all other gate types we show these problems are at least NP-hard.Comment: 25 pages, 1 figur

Maintaining Triangle Queries under Updates

We consider the problem of incrementally maintaining the triangle queries with arbitrary free variables under single-tuple updates to the input relations. We introduce an approach called IVM$^\epsilon$ that exhibits a trade-off between the update time, the space, and the delay for the enumeration of the query result, such that the update time ranges from the square root to linear in the database size while the delay ranges from constant to linear time. IVM$^\epsilon$ achieves Pareto worst-case optimality in the update-delay space conditioned on the Online Matrix-Vector Multiplication conjecture. It is strongly Pareto optimal for the triangle queries with zero or three free variables and weakly Pareto optimal for the triangle queries with one or two free variables.Comment: 47 pages, 18 figure

Personal genome editing algorithms to identify increased variant-induced off-target potential

Clustered regularly interspaced short palindromic repeats (CRISPR) technologies allow for facile genomic modification in a site-specific manner. A key step in this process is the in-silico design of single guide RNAs (sgRNAs) to efficiently and specifically target a site of interest. To this end, it is necessary to enumerate all potential off-target sites within a given genome that could be inadvertently altered by nuclease-mediated cleavage. Off-target sites are quasi-complementary regions of the genome in which the specified sgRNA can bind, even without a perfect complementary nucleotides sequence. This problem is known as off-target sites enumeration and became common after discovery of CRISPR technology. To solve this problem, many in-silico solutions were proposed in the last years but, currently available software for this task are limited by computational efficiency, variant support, genetic annotation, assessment of the functional impact of potential off-target effects at population and individual level, and a user-friendly graphical interface designed to be usable by non-informatician without any programming knowledge. This thesis addresses all these topics by proposing two software to directly answer the off-target enumeration problem and perform all the related analysis. In details, the thesis proposes CRISPRitz, a tool designed and developed to compute fast and exhaustive searches on reference and alternative genome to enumerate all the possible off-target for a user-defined set of sgRNAs with specific thresholds of mismatches (non-complementary bps in RNA-DNA binding) and bulges (bubbles that alters the physical structure of RNA and DNA limiting the binding activity). The thesis also proposes CRISPRme, a tool developed starting from CRISPRitz, which answers the requests of professionals and technicians to implement a comprehensive and easy to use interface to perform off-target enumeration, analysis and assessment, with graphical reports, a graphical interface and the capability of performing real-time query on the resulting data to extract desired targets, with a focus on individual and personalized genome analysis

Information Storage and Retrieval for Probe Storage using Optical Diffraction Patterns

A novel method for fast information retrieval from a probe storage device is considered. It is shown that information can be stored and retrieved using the optical diffraction patterns obtained by the illumination of a large array of cantilevers by a monochromatic light source. In thermo-mechanical probe storage, the information is stored as a sequence of indentations on the polymer medium. To retrieve the information, the array of probes is actuated by applying a bending force to the cantilevers. Probes positioned over indentations experience deflection by the depth of the indentation, probes over the flat media remain un-deflected. Thus the array of actuated probes can be viewed as an irregular optical grating, which creates a data-dependent diffraction pattern when illuminated by laser light. We develop a low complexity modulation scheme, which allows the extraction of information stored in the pattern of indentations on the media from Fourier coefficients of the intensity of the diffraction pattern. We then derive a low-complexity maximum likelihood sequence detection algorithm for retrieving the user information from the Fourier coefficients. The derivation of both the modulation and the detection schemes is based on the Fraunhofer formula for data-dependent diffraction patterns. We show that for as long as the Fresnel number F<0.1, the optimal channel detector derived from Fraunhofer diffraction theory does not suffer any significant performance degradation.Comment: 14 pages, 11 figures. Version 2: minor misprints corrected, experimental section expande