On the size of binary decision diagrams representing Boolean functions

AbstractWe consider the size of the representation of Boolean functions by several classes of binary decision diagrams (BDDs) (also called branching programs), namely the classes of arbitrary BDDs of real time BDD (RBDD) (i.e. BDDs where each computation path is limited to the number of variables), of free BDDs (FBDDs) (also called read-once-only branching programs), of ordered BDDs (OBDDS) i.e. FBDDs where variables are tested in the same order along all paths), and binary decision trees (BDTs).Using well-known techniques, we first establish asymptotically sharp bounds as a function of n on the minimum size of arbitrary BDDs representing almost all Boolean functions of n variables and provide asymptotic lower and upper bounds, differing only by a factor of two, on the minimum size OBDDs representing almost all Boolean functions of n variables.We then, using a method to obtain exponential lower bounds on complexity of computation of Boolean functions by RBDD, FBDD and OBDD that originated in (Breitbart, 1968), present the highest such bounds to date and also present improved bounds on the relative economy of description of particular Boolean functions by the above classes of BDDs. For each nontrivial pair of BDD classes considered, we exhibit infinite families of Boolean functions representable much more concisely by BDDs in one class than by BDDs in the other

The Third Age of Phage

The third age of phage has begun with the recognition that phages may be key to the great planetary biogeochemical cycles and represent the greatest potential genetic resource in the biospher

Determining the Solution Space of Vertex-Cover by Interactions and Backbones

To solve the combinatorial optimization problems especially the minimal Vertex-cover problem with high efficiency, is a significant task in theoretical computer science and many other subjects. Aiming at detecting the solution space of Vertex-cover, a new structure named interaction between nodes is defined and discovered for random graph, which results in the emergence of the frustration and long-range correlation phenomenon. Based on the backbones and interactions with a node adding process, we propose an Interaction and Backbone Evolution Algorithm to achieve the reduced solution graph, which has a direct correspondence to the solution space of Vertex-cover. By this algorithm, the whole solution space can be obtained strictly when there is no leaf-removal core on the graph and the odd cycles of unfrozen nodes bring great obstacles to its efficiency. Besides, this algorithm possesses favorable exactness and has good performance on random instances even with high average degrees. The interaction with the algorithm provides a new viewpoint to solve Vertex-cover, which will have a wide range of applications to different types of graphs, better usage of which can lower the computational complexity for solving Vertex-cover

Spatial and Temporal Dynamics of Prokaryotic and Viral Community Assemblages in a Lotic System (Manatee Springs, Florida)

How from high-magnitude springs fed by the Floridan aquifer system contributes hundreds of liters of water per second to rivers, creating unique lotic systems. Despite their importance as freshwater sources and their contributions to the state's major rivers, little is known about the composition and spatiotemporal variability of prokaryotic and viral communities of these spring systems or their influence on downstream river sites. At four time points throughout a year, we determined the abundance and diversity of prokaryotic and viral communities at three sites within the first-magnitude Manatee Springs system (the spring head where water emerges from the aquifer, a mixed region where the spring run ends, and a downstream site in the Suwannee River). The abundance of prokaryotes and virus-like particles increased 100-fold from the spring head to the river and few members from the head communities persisted in the river at low abundance, suggesting the springs play a minor role in seeding downstream communities. Prokaryotic and viral communities within Manatee Springs clustered by site, with seasonal variability likely driven by flow. As water flowed through the system, microbial community composition was affected by changes in physiochemical parameters and community coalescence. Evidence of species sorting and mass effects could be seen in the assemblages. Greater temporal fluctuations were observed in prokaryotic and viral community composition with increasing distance from the spring outflow, reflecting the relative stability of the groundwater environment, and comparisons to springs from prior work reaffirmed that distinct first-magnitude springs support unique communities.IMPORTANCE Prokaryotic and viral communities are central to food webs and biogeochemical processes in aquatic environments, where they help maintain ecosystem health. The Floridan aquifer system (FAS), which is the primary drinking water source for millions of people in the southeastern United States, contributes large amounts of freshwater to major river systems in Florida through its springs. However, there is a paucity of information regarding the spatiotemporal dynamics of microbial communities in these essential flowing freshwater systems. This work explored the prokaryotic and viral communities in a first-magnitude spring system fed by the FAS that discharges millions of liters of water per day into the Suwannee River. This study examined microbial community composition through space and time as well as the environmental parameters and metacommunity assembly mechanisms that shape these communities, providing a foundational understanding for monitoring future changes

Death ideation in cancer patients: contributing factors

Advances in cancer research and therapy have improved prognosis and the quality of life of many patients. However, previous epidemiological studies in oncologic patients have shown an increased risk of suicide. Suicidal thoughts, relatively well known in those terminally ill, may be just as important for cancer patients who are survivors or are living with the disease. Nonetheless, there is a relative paucity of data about suicidality in this setting. The authors conducted a prospective observational study to identify death thoughts and to explore the factors associated with suicidal ideation in cancer patients. A sample of 130 patients referred for psychiatric consultation was obtained following informed consent and authorization from the local ethics committee. A semistructured interview assessed sociodemographic data, psychosocial support, and information regarding the cancer process and its treatment. Psychometric instruments were used to evaluate psychopathology, namely the Hospital Anxiety and Depression Scale, the Beck Hopelessness Scale, and the Beck Scale for Suicide Ideation. Psychiatric diagnoses were obtained through the application of the Mini International Neuropsychiatric Interview. Death ideation was identified in 34.6% of patients, yet only 10% had active suicidal thoughts. Risk of suicide was associated with female gender, a psychiatric diagnosis (major depressive disorder, panic disorder, or dysthymia), difficult interpersonal relationships, associated pain, high hopelessness, and depressive and anxiety symptoms. Although suicidal thoughts are frequent in cancer patients at different stages of disease, most are transitory. Risk factors for suicidal ideation have been identified, such as depression, hopelessness, uncontrolled pain, and difficult interpersonal relationships. Further assessment is necessary to identify those at higher risk of attempting suicide, and underlying psychiatric disorders should be vigorously treated

Viral population estimation using pyrosequencing

The diversity of virus populations within single infected hosts presents a major difficulty for the natural immune response as well as for vaccine design and antiviral drug therapy. Recently developed pyrophosphate based sequencing technologies (pyrosequencing) can be used for quantifying this diversity by ultra-deep sequencing of virus samples. We present computational methods for the analysis of such sequence data and apply these techniques to pyrosequencing data obtained from HIV populations within patients harboring drug resistant virus strains. Our main result is the estimation of the population structure of the sample from the pyrosequencing reads. This inference is based on a statistical approach to error correction, followed by a combinatorial algorithm for constructing a minimal set of haplotypes that explain the data. Using this set of explaining haplotypes, we apply a statistical model to infer the frequencies of the haplotypes in the population via an EM algorithm. We demonstrate that pyrosequencing reads allow for effective population reconstruction by extensive simulations and by comparison to 165 sequences obtained directly from clonal sequencing of four independent, diverse HIV populations. Thus, pyrosequencing can be used for cost-effective estimation of the structure of virus populations, promising new insights into viral evolutionary dynamics and disease control strategies.Comment: 23 pages, 13 figure

Metagenomic Analysis of Human Diarrhea: Viral Detection and Discovery

Worldwide, approximately 1.8 million children die from diarrhea annually, and millions more suffer multiple episodes of nonfatal diarrhea. On average, in up to 40% of cases, no etiologic agent can be identified. The advent of metagenomic sequencing has enabled systematic and unbiased characterization of microbial populations; thus, metagenomic approaches have the potential to define the spectrum of viruses, including novel viruses, present in stool during episodes of acute diarrhea. The detection of novel or unexpected viruses would then enable investigations to assess whether these agents play a causal role in human diarrhea. In this study, we characterized the eukaryotic viral communities present in diarrhea specimens from 12 children by employing a strategy of “micro-mass sequencing” that entails minimal starting sample quantity (<100 mg stool), minimal sample purification, and limited sequencing (384 reads per sample). Using this methodology we detected known enteric viruses as well as multiple sequences from putatively novel viruses with only limited sequence similarity to viruses in GenBank