Isoperimetric Inequalities for Real-Valued Functions with Applications to Monotonicity Testing

We generalize the celebrated isoperimetric inequality of Khot, Minzer, and Safra (SICOMP 2018) for Boolean functions to the case of real-valued functions f:{0,1}^d ? ?. Our main tool in the proof of the generalized inequality is a new Boolean decomposition that represents every real-valued function f over an arbitrary partially ordered domain as a collection of Boolean functions over the same domain, roughly capturing the distance of f to monotonicity and the structure of violations of f to monotonicity. We apply our generalized isoperimetric inequality to improve algorithms for testing monotonicity and approximating the distance to monotonicity for real-valued functions. Our tester for monotonicity has query complexity O?(min(r ?d,d)), where r is the size of the image of the input function. (The best previously known tester makes O(d) queries, as shown by Chakrabarty and Seshadhri (STOC 2013).) Our tester is nonadaptive and has 1-sided error. We prove a matching lower bound for nonadaptive, 1-sided error testers for monotonicity. We also show that the distance to monotonicity of real-valued functions that are ?-far from monotone can be approximated nonadaptively within a factor of O(?{d log d}) with query complexity polynomial in 1/? and the dimension d. This query complexity is known to be nearly optimal for nonadaptive algorithms even for the special case of Boolean functions. (The best previously known distance approximation algorithm for real-valued functions, by Fattal and Ron (TALG 2010) achieves O(d log r)-approximation.

Sublinear-Time Computation in the Presence of Online Erasures

We initiate the study of sublinear-time algorithms that access their input via an online adversarial erasure oracle. After answering each query to the input object, such an oracle can erase $t$ input values. Our goal is to understand the complexity of basic computational tasks in extremely adversarial situations, where the algorithm's access to data is blocked during the execution of the algorithm in response to its actions. Specifically, we focus on property testing in the model with online erasures. We show that two fundamental properties of functions, linearity and quadraticity, can be tested for constant $t$ with asymptotically the same complexity as in the standard property testing model. For linearity testing, we prove tight bounds in terms of $t$, showing that the query complexity is $\Theta(\log t)$. In contrast to linearity and quadraticity, some other properties, including sortedness and the Lipschitz property of sequences, cannot be tested at all, even for $t=1$. Our investigation leads to a deeper understanding of the structure of violations of linearity and other widely studied properties. We also consider implications of our results for algorithms that are resilient to online adversarial corruptions instead of erasures

Periodontal Considerations in Adult Orthodontic Patients

The relationship between periodontology and orthodontics consists of a highly complex, bidirectional and close interaction that is nowadays characterized by controversial scientific opinions and clinical approaches. The relevant increasing number of adult orthodontic patients which in most cases present already-compromised periodontal tissues has markedly highlighted the potential of orthodontic treatment in enhancing or deteriorating periodontal health and also the outmost relevance of peculiar periodontal planning prior and during orthodontic treatment. Since the progress in adult orthodontics trend is rapid, there is also an increasing need for evidence-based protocols that might guide clinicians through a comprehensive, interdisciplinary and successful treatment. This chapter has been compiled with the aim of providing orthodontists, periodontists and general practitioners with sound evidence-based protocols and valid clinical approaches that have proven to be successful for numerous patients over long follow-ups. It is structured following the steps for a correct therapy management, starting from comprehensive examination and diagnosis to before and during orthodontic treatment considerations, and finally analysing the present state of new adult orthodontic technologies

Clinical efficacy of minimally invasive surgical (MIS) and non-surgical (MINST) treatments of periodontal intra-bony defect. A systematic review and network meta-analysis of RCT's

Objective: The aim of this systematic review was to explore the efficacy of different minimal invasive surgical (MIS) and non-surgical (MINST) approaches for the treatment of intra-bony defect in terms of clinical attachment level (CAL) gain and periodontal pocket depth (PPD) reduction. / Methods: A detailed review protocol was designed according to PRISMA guideline. Online search was conducted on PubMed, Cochrane library and Embase. Only randomized clinical trials (RCTs) testing MIS or MINST procedure, with or without the application of a regenerative tool for the treatment of intra-bony defect, were included. Cochrane checklist for risk of bias assessment was used. Network meta-Analysis (NMAs) was used to rank the treatment efficacy. / Results: Nine RCTs accounting for 244 patients and a total of 244 defects were included. Only two studies were at low risk of bias. CAL gain for included treatment ranged from 2.58 ± 1.13 mm to 4.7 ± 2.5 mm while PPD reduction ranged from 3.19 ± 0.71 mm to 5.3 ± 1.5 mm. On the basis of the ranking curve, MINST showed the lowest probability to be the best treatment option for CAL gain. Pairwise comparisons and treatment rankings suggest superiority for regenerative approaches (CAL difference 0.78 mm, (0.14–1.41); P < 0.05) and surgical treatment elevating only the buccal or palatal flap (CAL difference: 0.95 mm, (0.33–1.57); P < 0.05). / Conclusions: Minimally invasive surgical (MIS) and non-surgical (MINST) periodontal therapy show promising results in the treatment of residual pocket with intra-bony defect. / Clinical relevance: MIS procedures represent a reliable treatment for isolated intra-bony defect

Bone Regeneration Induced by Bone Porcine Block with Bone Marrow Stromal Stem Cells in a Minipig Model of Mandibular “Critical Size” Defect

Introduction. Adding stem cells to biodegradable scaffolds to enhance bone regeneration is a valuable option. Different kinds of stem cells with osteoblastic activity were tested, such as bone marrow stromal stem cells (BMSSCs). Aim. To assess a correct protocol for osteogenic stem cell differentiation, so BMSSCs were seeded on a bone porcine block (BPB). Materials and Methods. Bone marrow from six minipigs was extracted from tibiae and humeri and treated to isolate BMSSCs. After seeding on BPB, critical-size defects were created on each mandible of the minipigs and implanted with BPB and BPB/BMSSCs. After three months, histomorphometric analysis was performed. Results. Histomorphometric analysis provided percentages of the three groups. Tissues present in control defects were 23 ± 2% lamellar bone, 28 ± 1% woven bone, and 56 ± 4% marrow spaces; in BPB defects were 20 ± 5% BPB, 32 ± 2% lamellar bone, 24 ± 1% woven bone, and 28 ± 2% marrow spaces; in BPB/BMSSCs defects were 17 ± 4% BPB/BMSSCs, 42 ± 2% lamellar bone, 12 ± 1% woven bone, and 22 ± 3% marrow spaces. Conclusion. BPB used as a scaffold to induce bone regeneration may benefit from the addition of BDPSCs in the tissue-engineered constructs

Genetic variability and history of a native Finnish horse breed

Background: The Finnhorse was established as a breed more than 110 years ago by combining local Finnish landraces. Since its foundation, the breed has experienced both strong directional selection, especially for size and colour, and severe population bottlenecks that are connected with its initial foundation and subsequent changes in agricultural and forestry practices. Here, we used sequences of the mitochondrial control region and genomic single nucleotide polymorphisms (SNPs) to estimate the genetic diversity and differentiation of the four Finnhorse breeding sections: trotters, pony-sized horses, draught horses and riding horses. Furthermore, we estimated inbreeding and effective population sizes over time to infer the history of this breed. Results: We found a high level of mitochondrial genetic variation and identified 16 of the 18 haplogroups described in present-day horses. Interestingly, one of these detected haplogroups was previously reported only in the Przewalski’s horse. Female effective population sizes were in the thousands, but declines were evident at the times when the breed and its breeding sections were founded. By contrast, nuclear variation and effective population sizes were small (approximately 50). Nevertheless, inbreeding in Finnhorses was lower than in many other horse breeds. Based on nuclear SNP data, genetic differentiation among the four breeding sections was strongest between the draught horses and the three other sections (FST=0.007–0.018), whereas based on mitochondrial DNA data, it was strongest between the trotters and the pony-sized and riding horses (ΦST= 0.054–0.068). Conclusions: The existence of a Przewalski’s horse haplogroup in the Finnhorse provides new insights into the domestication of the horse, and this finding supports previous suggestions of a close relationship between the Finnhorse and eastern primitive breeds. The high level of mitochondrial DNA variation in the Finnhorse supports its domestication from a large number of mares but also reflects that its founding depended on many local landraces. Although inbreeding in Finnhorses was lower than in many other horse breeds, the small nuclear effective popula- tion sizes of each of its breeding sections can be considered as a warning sign, which warrants changes in breeding practices.Peer reviewe