Search

Quantum computations are very important branch of modern cryptology. According to the number of working physical qubits available in general-purpose quantum computers and in quantum annealers, there is no coincidence, that nowadays quantum annealers allow to solve larger problems. In this paper we focus on solving discrete logarithm problem (DLP) over binary fields using quantum annealing. It is worth to note, that however solving DLP over prime fields using quantum annealing has been considered before, no author, until now, has considered DLP over binary fields using quantum annealing. Therefore, in this paper, we aim to bridge this gap. We present a polynomial transformation of the discrete logarithm problem over binary fields to the Quadratic Unconstrained Binary Optimization (QUBO) problem, using approximately $3n^2$ logical variables for the binary field $\mathbb{F}_{2^n}$. In our estimations, we assume the existence of an optimal normal base of II type in the given fields. Such a QUBO instance can then be solved using quantum annealing., Comment: This is the author's version of a post-conference paper from the CECC 2024 conference. The paper has been submitted for consideration to the International Journal of Electronics and Telecommunications

This paper demonstrates that applying spin reversal transformations (SRT), commonly known as a sufficient method for privacy enhancing in problems solved using quantum annealing, does not guarantee privacy for all possible problems. We show how to recover the original problem from the Ising problem obtained using SRT when the resulting problem in Ising form represents the algebraic attack on the $E_0$ stream cipher. A small example is used to illustrate how to retrieve the original problem from the one transformed by SRT. Moreover, it is shown that our method is efficient even for full-scale problems.

We study B+- -- > K+-K+K- decays using the QCD factorization model with final state interactions between K+ and K- mesons taken into account. The parameters of the model are fitted to the data of the BABAR and LHCb collaborations. We describe the K Kbar effective mass distributions and examine the CP-violating asymmetry effects in the full range of the Dalitz plot., Comment: 22 pages, 8 figures

The $B^0 \to K^0_S K^+ K^- $ decay amplitude is derived within a quasi-two-body QCD factorization framework in terms of kaon form factors and $B^0$ to two-kaon-transition functions. The final state kaon-kaon interactions in the $S$, $P$, and $D$ waves are taken into account. The unitarity constraints are satisfied for the two kaons in scalar states. It is shown that with few terms of the full decay amplitude one may reach a fair agreement with the total branching fraction and Dalitz-plot projections published in 2010 by the Belle Collaboration and in 2012 by the $\textit{BABAR}$ Collaboration. With 13 free parameters, our model fits the corresponding 422 data with a $\chi^2$ of 583.6 which leads to a $\chi^2$ per degree of freedom equal to 1.43. The dominant branching fraction arises from the $f_0(K^+K^-) K^0_S$ mode with 83.0$\%$ of the total branching. The next important mode is dominated by $\phi K^0_S$ plus small $\omega K^0_S$ and $\rho^0 K^0_S$ modes with 18.3$\%$ of the total. Then follows the $a_0^\pm K^\mp$ mode with 6.2$\%$. Adding the other smaller modes, the total percentage sum is 107.7$\%$ which indicates a small interference contribution. In most regions of the Dalitz plot, our model gives rather small $CP$ asymmetry, but in some parts its values can be large and positive or negative. Its predicted total value is equal to -0.11$\%$. The calculated time dependent $\textit{CP}$-asymmetry parameters agree, within errors, with those obtained by the $\textit{BABAR}$ analysis. Our model amplitude can be the basis for a parametrization in experimental Dalitz plot analyses of LHCb and Belle II Collaborations., Comment: 32 pages, 9 figures, submitted to Phys. Rev. D

In this paper, we work with simple and finite graphs. We study a generalization of the \emph{Cage Problem}, which has been widely studied since cages were introduced by Tutte \cite{T47} in 1947 and after Erd\" os and Sachs \cite{ES63} proved their existence in 1963. An \emph{$(r,g)$-graph} is an $r$-regular graph in which the shortest cycle has length equal to $g$; that is, it is an $r$-regular graph with girth $g$. An \emph{$(r,g)$-cage} is an $(r,g)$-graph with the smallest possible number of vertices among all $(r,g)$-graphs; the order of an $(r,g)$-cage is denoted by $n(r,g)$. The Cage Problem consists of finding $(r,g)$-cages; it is well-known that $(r,g)$-cages have been determined only for very limited sets of parameter pairs $(r, g)$. There exists a simple lower bound for $n(r,g)$, given by Moore and denoted by $n_0(r,g)$. The cages that attain this bound are called \emph{Moore cages}., Comment: 18 pages

The paper discusses an approach to decipher large collections of handwritten index cards of historical dictionaries. Our study provides a working solution that reads the cards, and links their lemmas to a searchable list of dictionary entries, for a large historical dictionary entitled the Dictionary of the 17th- and 18th-century Polish, which comprizes 2.8 million index cards. We apply a tailored handwritten text recognition (HTR) solution that involves (1) an optimized detection model; (2) a recognition model to decipher the handwritten content, designed as a spatial transformer network (STN) followed by convolutional neural network (RCNN) with a connectionist temporal classification layer (CTC), trained using a synthetic set of 500,000 generated Polish words of different length; (3) a post-processing step using constrained Word Beam Search (WBC): the predictions were matched against a list of dictionary entries known in advance. Our model achieved the accuracy of 0.881 on the word level, which outperforms the base RCNN model. Within this study we produced a set of 20,000 manually annotated index cards that can be used for future benchmarks and transfer learning HTR applications.

Recommender system research has oftentimes focused on approaches that operate on large-scale datasets containing millions of user interactions. However, many small businesses struggle to apply state-of-the-art models due to their very limited availability of data. We propose a graph-based recommender model which utilizes heterogeneous interactions between users and content of different types and is able to operate well on small-scale datasets. A genetic algorithm is used to find optimal weights that represent the strength of the relationship between users and content. Experiments on two real-world datasets (which we make available to the research community) show promising results (up to 7% improvement), in comparison with other state-of-the-art methods for low-data environments. These improvements are statistically significant and consistent across different data samples.

This paper presents a new use case for continuous crowdsourcing, where multiple players collectively control a single character in a video game. Similar approaches have already been proposed, but they suffer from certain limitations: (1) they simply consider static time frames to group real-time inputs from multiple players; (2) then they aggregate inputs with simple majority vote, i.e., each player is uniformly weighted. We present a continuous crowdsourcing multiplayer game equipped with our Crowdsourcing Controller. The Crowdsourcing Controller addresses the above-mentioned limitations: (1) our Dynamic Input Frame approach groups incoming players' input in real-time by dynamically adjusting the frame length; (2) our Continuous Reliability System estimates players' skills by assigning them a reliability score, which is later used in a weighted majority vote to aggregate the final output command. We evaluated our Crowdsourcing Controller offline with simulated players and online with real players. Offline and online experiments show that both components of our Crowdsourcing Controller lead to higher game scores, i.e., longer playing time. Moreover, the Crowdsourcing Controller is able to correctly estimate and update players' reliability scores.

We review the theory of semiattractors associated with non-contractive Iterated Function Systems (IFSs) and demonstrate its applications on a concrete example. In particular, we present criteria for the existence of semiattractors due to Lasota and Myjak. We also discuss the Kieninger criterion which allows us to characterise when a semiattractor is strongly-fibred. Finally, we consider a specific example of a non-contractive IFS introduced by Barnsley and Vince. We find an invariant measure for this system which allows us to describe its semiattractor. The difficulty in analysing this IFS stems from the fact that it is neither eventually contractive nor contractive on average.

We define two non-metrizable compact spaces and show that they are attractors of iterated function systems. Both of them, the split square and the split carpet, are constructed using the product of split intervals., Comment: 7 pages, 2 figures

Iterated function systems (IFSs) and their attractors have been central to the theory of fractal geometry almost from its inception. And contractivity of the functions in the IFS has been central to the theory of iterated functions systems. If the functions in the IFS are contractions, then the IFS is guaranteed to have a unique attractor. Recently, however, there has been an interest in what occurs to the attractor at the boundary between contractvity and expansion of the IFS. That is the subject of this paper. For a family $F_t$ of IFSs depending on a real parameter $t>0$, the existence and properties of two types of transition attractors, called the lower transition attractor $A_{\bullet}$ and the upper transition attractor $A^{\bullet}$, are investigated. A main theorem states that, for a wide class of IFS families, there is a threshold $t_0$ such that the IFS $F_t$ has a unique attractor $A_t$ for $tt_0$. At the threshold $t_0$, there is an $F_{t_0}$-invariant set $A^{\bullet}$ such that $A^{\bullet} = \lim_{t\rightarrow t_0} A_t$.

The temperature dependence of stellar electron-capture (EC) rates is investigated, with a focus on nuclei around $N=50$, just above $Z=28$, which play an important role during the collapse phase of core-collapse supernovae (CCSN). Two new microscopic calculations of stellar EC rates are obtained from a relativistic and a non-relativistic finite-temperature quasiparticle random-phase approximation approaches, for a conventional grid of temperatures and densities. In both approaches, EC rates due to Gamow-Teller transitions are included. In the relativistic calculation contributions from first-forbidden transitions are also included, and add strongly to the EC rates. The new EC rates are compared with large-scale shell model calculations for the specific case of $^{86}$Kr, providing insight into the finite-temperature effects on the EC rates. At relevant thermodynamic conditions for core-collapse, the discrepancies between the different calculations of this work are within about one order of magnitude. Numerical simulations of CCSN are performed with the spherically-symmetric GR1D simulation code to quantify the impact of such differences on the dynamics of the collapse. These simulations also include EC rates based on two parametrized approximations. A comparison of the neutrino luminosities and enclosed mass at core bounce shows that differences between simulations with different sets of EC rates are relatively small ($\approx 5\%$), suggesting that the EC rates used as inputs for these simulations have become well constrained.