Let I be an ideal generated by quadrics in a standard graded polynomial ring S over field. A question of Avramov, Conca, and Iyengar asks whether the Betti numbers R = / can bounded above binomial coefficients on minimal number generators if is Koszul. This has been answered affirmatively for Koszul algebras defined three almost complete intersections with any generators. We give strong affirma...

Abstract One of the goals science is to understand relation between a whole and its parts, as exemplified by problem certifying entanglement system from knowledge reduced states. Here, we focus on different but related question: can collection marginal information reveal new information? We answer this affirmatively show that (non-) entangled states may exhibit (meta)transitivity entanglement, ...

Abstract In card-based cryptography, designing AND protocols in committed format is a major research topic. The state-of-the-art protocol proposed by Koch, Walzer, and Härtel ASIACRYPT 2015 uses only four cards, which the minimum permissible number. minimality of their relies on somewhat complicated shuffles having non-uniform probabilities possible outcomes. Restricting allowed to uniform clos...

This paper considers the following game on a hypercube, first suggested by Lagarias and Saks. Suppose 2 pebbles are distributed onto vertices of an n-cube (with 2 vertices). A pebbling step is to remove two pebbles from some vertex and then place one pebble at an adjacent vertex. The question of interest is to determine if it is possible to get one pebble to a specified vertex by repeatedly usi...

Insufficient sleep may lead to adverse cardio-metabolic effects by influencing body weight, blood pressure, and glucose tolerance. We aimed to assess the relation between sleep duration and indices of obesity including body mass index (BMI) and waist circumference in a sample population in central Iran. We selected a sub-sample of 1770 individuals from Isfahan Healthy Heart Program. The data re...

Polio vaccinators and law enforcement officials protecting them, have been killed in the line of duty since 2012 in Pakistan. This study was conducted to determine the opinions of university students in Islamabad and Rawalpindi, regarding the importance of polio vaccination, and the role of international donor agencies. Nine hundred forty-six students participated in this study; 833 (88.1%) stu...

Is there a gene or, rather, a set of genes which code for mind? To refine this question further,can all our cognitive processes and states be accounted for mainly or even entirely in genetic terms? Clearly, environmental factors are important, since a person may have a gene for X which is never triggered because the right environmental conditions are not present. The question of whether there i...

We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under consideration. In particular, for the symmetric four-state substitution model which is also known as Jukes-Cantor model, we answer affirmatively a conjecture of...

Given in the plane a set S of m point sites simple polygon P n vertices, we consider problem computing geodesic farthest-point Voronoi diagram for P. It is known that has an $$\Omega (n+m\log m)$$ time lower bound. Previously, randomized algorithm was proposed [Barba, SoCG 2019] solves $$O(n+m\log expected time. The previous best deterministic algorithms solve $$O(n\log \log n+ m\log [Oh, Barba...