COMBINATORIAL RECONSTRUCTION OF TWO-DIMENSIONAL WORDS IN THE HYPOTHESIS SHIFT 1

The article considers the formulation of the problem of reconstruction of two-dimensional words by a given multiset of subwords, under the hypothesis that this subset is generated by the displacement of a two-dimensional window of fixed size by an unknown two-dimensional word with a shift 1. A variant of the combinatorial solution of this reconstruction problem is proposed, based on a two-fold application of the one-dimensional word reconstruction method using the search for Eulerian paths or cycles in the de Bruyne multiorgraph. The efficiency of the method is discussed under the conditions of a square two-dimensional shift window one having a large linear size.

Study of the Leidenfrost Effect on Heterogeneous Surfaces of Complex Structure

This work is devoted to a research of water droplets that are put in-between two parallel metal strings the distance between which is comparable to linear size of the droplet. Strings are heated by Joule heating to temperatures that exceed critical temperatures of nucleate and film boiling. Different configurations of strings’ side surface have been tested: smooth and with winding made of the same material (intermittent and uninterrupted). Experiments have shown that droplets on these types of surface do not boil away quickly or fall down. Instead they displayed behavior that can be described as floating, either stable or with directed motion, depending on surface structure or relief. Multiple experiments have shown that it is quite similar to Leidenfrost effect demonstrated on a flat overheated surface by liquids.

Quantum algorithms and approximating polynomials for composed functions with shared inputs

We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let f be an m-bit Boolean function and consider an n-bit function F obtained by applying f to conjunctions of possibly overlapping subsets of n variables. If f has quantum query complexity Q(f), we give an algorithm for evaluating F using O~(Q(f)⋅n) quantum queries. This improves on the bound of O(Q(f)⋅n) that follows by treating each conjunction independently, and our bound is tight for worst-case choices of f. Using completely different techniques, we prove a similar tight composition theorem for the approximate degree of f.By recursively applying our composition theorems, we obtain a nearly optimal O~(n1−2−d) upper bound on the quantum query complexity and approximate degree of linear-size depth-d AC0 circuits. As a consequence, such circuits can be PAC learned in subexponential time, even in the challenging agnostic setting. Prior to our work, a subexponential-time algorithm was not known even for linear-size depth-3 AC0 circuits.As an additional consequence, we show that AC0∘⊕ circuits of depth d+1 require size Ω~(n1/(1−2−d))≥ω(n1+2−d) to compute the Inner Product function even on average. The previous best size lower bound was Ω(n1+4−(d+1)) and only held in the worst case (Cheraghchi et al., JCSS 2018).

Duality Pairs and Homomorphisms to Oriented and Unoriented Cycles

In the homomorphism order of digraphs, a duality pair is an ordered pair of digraphs $(G,H)$ such that for any digraph, $D$, $G\to D$ if and only if $D\not \to H$. The directed path on $k+1$ vertices together with the transitive tournament on $k$ vertices is a classic example of a duality pair. In this work, for every undirected cycle $C$ we find an orientation $C_D$ and an oriented path $P_C$, such that $(P_C,C_D)$ is a duality pair. As a consequence we obtain that there is a finite set, $F_C$, such that an undirected graph is homomorphic to $C$, if and only if it admits an $F_C$-free orientation. As a byproduct of the proposed duality pairs, we show that if $T$ is an oriented tree of height at most $3$, one can choose a dual of $T$ of linear size with respect to the size of $T$.

Growth and morphometric characteristics of the scallop Flexopecten glaber (Bivalvia: Pectinidae) reared in cages off the coast of Crimea (Black Sea)

The spat of the scallop Flexopecten glaber were collected in cages with the Pacific oyster Crassostrea gigas cultured on a mussel-and-oyster farm (outer roadstead of Sevastopol Bay). For two years they were reared in plastic cages at a depth of 2-3 m. The cages were periodically withdrawn to measure the size and weight parameters of the molluscs: the length (L, mm), height (H, mm), and width (D, mm) of shells and the total live weight (W, g). The correlations among the parameters under study are presented. The changes in the indices of the frontal (D/L) and sagittal (H/L) curvatures, convexity ((H+D)/L) and conditional volume (H×D×L/1000) of the shells in ontogenesis are shown. Upon reaching a shell length of 30-35 mm, the allometry of the volumetric and weight growth of molluscs changed from positive to negative. The largest values of the shell convexity index were registered in thesame length range. A conclusion about the interval-type growth of F. glaber in linear size and weight is made. It is suggested that the optimal strategy of shell formation in F. glaber in ontogenesis implies the ripening and the first reproduction of the molluscs occurring at the highest volumetric characteristics of the shell. The relationships for the linear size and weight growth ofF. glaber in the first two years of life are obtained. It is concluded that the scallop F. glaber should be considered as a possible element for the diversification of the existing aquaculture of molluscs (mussels and oysters) off the coast of Crimea.

Thermal Changes in the Mass, Size and Density of Steel Fiber Concrete after Calefaction

This report outlines the results of an experimental study conducted on the effects high temperatures have on changes in linear sizes, mass, and density of steel fiber concrete containing fiber with varying durability, types, diameter, and percentages by volume. After being exposed to heat, the steel fiber concrete reduces in linear size, as well as decreasing in mass and density. Changes are seen as a result of rising temperatures between 20-1100 °С The impact on the change in mass, size and density of the quantity and type of fiber is not unambiguous, it does not fully correspond to the theoretical concepts considered in the work and require additional research.

Finite-Size Effects with Boundary Conditions on Bose-Einstein Condensation

We investigate the statistical distribution for ideal Bose gases with constant particle density in the 3D box of volume V=L3. By changing linear size L and imposing different boundary conditions on the system, we present a numerical analysis on the characteristic temperature and condensate fraction and find that a smaller linear size is efficient to increase the characteristic temperature and condensate fraction. Moreover, there is a singularity under the antiperiodic boundary condition.