Enumerating five families of pattern-avoiding inversion sequences; and introducing the powered Catalan numbers

The first problem addressed by this article is the enumeration of some families of pattern-avoiding inversion sequences. We solve some enumerative conjectures left open by the foundational work on the topics by Corteel et al., some of these being also solved independently by Lin, and Kim and Lin. The strength of our approach is its robustness: we enumerate four families $F_1 \subset F_2 \subset F_3 \subset F_4$ of pattern-avoiding inversion sequences ordered by inclusion using the same approach. More precisely, we provide a generating tree (with associated succession rule) for each family $F_i$ which generalizes the one for the family $F_{i-1}$. The second topic of the paper is the enumeration of a fifth family $F_5$ of pattern-avoiding inversion sequences (containing $F_4$). This enumeration is also solved \emph{via} a succession rule, which however does not generalize the one for $F_4$. The associated enumeration sequence, which we call the \emph{powered Catalan numbers}, is quite intriguing, and further investigated. We provide two different succession rules for it, denoted $\Omega_{pCat}$ and $\Omega_{steady}$, and show that they define two types of families enumerated by powered Catalan numbers. Among such families, we introduce the \emph{steady paths}, which are naturally associated with $\Omega_{steady}$. They allow us to bridge the gap between the two types of families enumerated by powered Catalan numbers: indeed, we provide a size-preserving bijection between steady paths and valley-marked Dyck paths (which are naturally associated with $\Omega_{pCat}$). Along the way, we provide several nice connections to families of permutations defined by the avoidance of vincular patterns, and some enumerative conjectures.Comment: V2 includes modifications suggested by referees (in particular, a much shorter Section 3, to account for arXiv:1706.07213

Event-related brain potentials in the study of inhibition: cognitive control, source localization and age-related modulations

In the previous 15 years, a variety of experimental paradigms and methods have been employed to study inhibition. In the current review, we analyze studies that have used the high temporal resolution of the event-related potential (ERP) technique to identify the temporal course of inhibition to understand the various processes that contribute to inhibition. ERP studies with a focus on normal aging are specifically analyzed because they contribute to a deeper understanding of inhibition. Three time windows are proposed to organize the ERP data collected using inhibition paradigms: the 200 ms period following stimulus onset; the period between 200 and 400 ms after stimulus onset; and the period between 400 and 800 ms after stimulus onset. In the first 200 ms, ERP inhibition research has primarily focused on N1 and P1 as the ERP components associated with inhibition. The inhibitory processing in the second time window has been associated with the N2 and P3 ERP components. Finally, in the third time window, inhibition has primarily been associated with the N400 and N450 ERP components. Source localization studies are analyzed to examine the association between the inhibition processes that are indexed by the ERP components and their functional brain areas. Inhibition can be organized in a complex functional structure that is not constrained to a specific time point but, rather, extends its activity through different time windows. This review characterizes inhibition as a set of processes rather than a unitary process

Innerspec: Technical Report

In this report we describe “InnerSpec”, an approach for symmetric object detection that is based both on the com- putation of a symmetry measure for each pixel and on gra- dient information analysis. The symmetry value is obtained as the energy balance of the even-odd decomposition of an oriented square patch with respect to its central axis. Such an operation is akin to the computation of a row-wise con- volution in the midpoint. The candidate symmetry axes are then identified through the localization of peaks along the direction perpendicular to each considered angle. These axes are finally evaluated by computing the image gradient in their neighborhood, in particular checking whether the gradient information displays specular characteristics

Rare and Complex Epilepsies from Childhood to Adulthood: Requirements for Separate Management or Scope for a Lifespan Holistic Approach?

Purpose: In this descriptive review, we describe current models of transition in rare and complex epilepsy syndromes and propose alternative approaches for more holistic management based on disease biology. // Recent Findings: Previously published guidance and recommendations on transition strategies in individuals with epilepsy have not been systematically and uniformly applied. There is significant heterogeneity in models of transition/transfer of care across countries and even within the same country. // Summary: We provide examples of the most severe epilepsy and related syndromes and emphasise the limited data on their outcome in adulthood. Rare and complex epilepsy syndromes have unique presentations and require high levels of expertise and multidisciplinary approach. Lifespan clinics, with no transition, but instead continuity of care from childhood to adulthood with highly specialised input from healthcare providers, may represent an alternative effective approach. Effectiveness should be measured by evaluation of quality of life for both patients and their families/caregivers

A New Video authentication Template Based on Bubble random Sampling

The rapid growth of digital video distribution has highlighted new important issues in digital rights management, as well as in other important applications such as video authentication. Digital watermarking offers a promising solution against piracy and it is therefore a very active area of research. However, robustness to video manipulations, either malicious or not, is a demanding task because there are many different types of possible attacks that can be envisioned. Among these, geometric and temporal distortions play the major roles. The countermeasures against these specific attacks are still an open challenge. In this paper we propose the use of a video authentication template based on bubble random sampling. The authentication template is introduced in order to ensure temporal synchronization and to prevent content tampering. The simulation results are encouraging and this approach is therefore worth further development efforts

Promotion of proliferation and metastasis of hepatocellular carcinoma by LncRNA00673 based on the targeted-regulation of notch signaling pathway

we read with great interest the paper by Dr. Chen et al1, recently published in European Review for Medical and Pharmacological Sciences and titled ‘‘Promotion of proliferation and metastasis of hepatocellular carcinoma by LncRNA00673 based on the targeted-regulation of notch signaling pathway’’. Authors concluded that lncRNA00673 is highly expressed and may be a potential target for the treatment of Hepatocellular Carcinoma (HCC). Moreover, according to authors, it can promote the proliferation and metastasis of HCC by the regulation of Notch signaling pathway. We congratulate the authors for their interesting work

A Symphony of Regulations Centered on p63 to Control Development of Ectoderm-Derived Structures

The p53-related transcription factor p63 is critically important for basic cellular functions during development of the ectoderm and derived structure and tissues, including skin, limb, palate, and hair. On the one side, p63 is required to sustain the proliferation of keratinocyte progenitors, while on the other side it is required for cell stratification, commitment to differentiate, cell adhesion, and epithelial-mesenchymal signaling. Molecules that are components or regulators of the p63 pathway(s) are rapidly being identified, and it comes with no surprise that alterations in the p63 pathway lead to congenital conditions in which the skin and other ectoderm-derived structures are affected. In this paper, we summarize the current knowledge of the molecular and cellular regulations centered on p63, derived from the comprehension of p63-linked human diseases and the corresponding animal models, as well as from cellular models and high-throughput molecular approaches. We point out common themes and features, that allow to speculate on the possible role of p63 downstream events and their potential exploitation in future attempts to correct the congenital defect in preclinical studies

Novel Cellular and Molecular Interactions During Limb Development, Revealed from Studies on the Split Hand Foot Congenital Malformation

The embryonic development of the limbs is widely used as a paradigm for the comprehension of the cellular processes and molecular mechanisms underlying organogenesis and pattern formation. The chick, mouse and (recently), zebrafish embryos are excellent models, for the ease of experimental manipulation and the availability of several mutant strains with limb malformation defects

A proposal for Video Signature Tool and Video Fingerprinting

In this document we present and evaluate a video signature system, proposed by Signals and Communications Laboratory – Department of Electronic for Automation, University of Brescia (Italy)