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Rok 2024
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Teoria grafów wczoraj i dziś
PublikacjaW pracy naszkicowano kamienie milowe teorii grafów poczynając od pierwszego artykułu Eulera na temat mostów w Królewcu z połowy 18. wieku. Następnie opisano słynny problem 4 barw i jego wariacje. Pracę kończy charakterystyka najnowszych wyzwań teorii grafów.
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Semi-definite programming and quantum information
PublikacjaThis paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations,...
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Quantum strategies for rendezvous and domination tasks on graphs with mobile agents
PublikacjaThis paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach
PublikacjaW kolejnym odcinku serii z Alicją i Bogdanem najpierw ilustrujemy problem dominowania w grafach (kratowych): klasyczny i rzymski. Następnie ilustrujemy znany fakt, że zachłanność nie zawsze się opłaca. Pokażemy mianowicie, że algorytmy zachłanne nie gwarantują uzyskania rozwiązania optymalnego, nawet wówczas gdy problem da się rozwiązać w czasie wielomianowym.
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Equitable colorings of some variation of corona products of cubic graphs
PublikacjaThe problem of determining the value of equitable chromatic number for multicoronas of cubic graphs is studied. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use almost optimal number of colors in the remaining cases.
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Deep Learning-Based, Multiclass Approach to Cancer Classification on Liquid Biopsy Data
PublikacjaThe field of cancer diagnostics has been revolutionized by liquid biopsies, which offer a bridge between laboratory research and clinical settings. These tests are less invasive than traditional biopsies and more convenient than routine imaging methods. Liquid biopsies allow studying of tumor-derived markers in bodily fluids, enabling the development of more precise cancer diagnostic tests for screening, disease monitoring, and...
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Approximation algorithms for job scheduling with block-type conflict graphs
PublikacjaThe problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...
Rok 2023
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Security of Cryptocurrencies: A View on the State-of-the-Art Research and Current Developments
Publikacja[Context] The goal of security is to protect digital assets, devices, and services from being disrupted, exploited or stolen by unauthorized users. It is also about having reliable information available at the right time. [Motivation] Since the inception in 2009 of the first cryptocurrency, few studies have been undertaken to analyze and review the state-of-the-art research and current developments with respect to the security...
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Screening of predicted synergistic multi-target therapies in glioblastoma identifies new treatment strategies
PublikacjaAbstract Background IDH-wildtype glioblastoma (GBM) is a highly malignant primary brain tumor with a median survival of 15 months after standard of care, which highlights the need for improved therapy. Personalized combination therapy has shown to be successful in many other tumor types and could be beneficial for GBM patients. Methods We performed the largest drug combination screen to date in GBM, using a high-throughput effort...
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Rekordowe liczby pierwsze
PublikacjaProblem liczb pierwszych ma długą historię sięgającą czasów starożytnych. W śród liczb całkowitych liczby pierwsze grają rolę analogiczną do pierwiastków w chemii.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 5. Alicja kupuje buty.
PublikacjaNiniejszy miniesej pokazuje, w jaki sposób można efektywnie przeszukiwać uporządkowane tablice 2-wymiarowe oraz, w jaki sposób można radzić sobie (niekiedy) z trudnymi problemami obliczeniowymi.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 4. Alicja i Bogdan w samochodzie.
PublikacjaZilustrowano problem przeszukiwania obiektów w nieznanych przestrzeniach na przykładzie jazdy samochodem.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 3. Alicja i Bogdan remontują mieszkanie.
PublikacjaPoniższe zagadki nawiązują z jednej strony do problemu kafelkowania płaszczyzny, który jest nierozstrzygalny, z drugiej do problemu rozkroju wstęgi, który jest NP-trudny. Jednakże przypadki szczególne, które tu rozważamy, nie są tak trudne i mogą być rozwiązane za pomocą algorytmów działających w czasie wielomianowym.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach
PublikacjaPowracamy tutaj do zagadki sprzed 4 lat pod tym samym tytułem, którą uzupełniamy nowymi komentarzami i nowymi zagadkami na ten temat. Pozwala to nam zilustrować szerzej zasady działania algorytmu zachłannego.
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Platelet RNA Sequencing Data Through the Lens of Machine Learning
PublikacjaLiquid biopsies offer minimally invasive diagnosis and monitoring of cancer disease. This biosource is often analyzed using sequencing, which generates highly complex data that can be used using machine learning tools. Nevertheless, validating the clinical applications of such methods is challenging. It requires: (a) using data from many patients; (b) verifying potential bias concerning sample collection; and (c) adding interpretability...
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Long-term mortality after transcatheter aortic valve implantation for aortic stenosis in immunosuppression-treated patients: a propensity-matched multicentre retrospective registry-based analysis
PublikacjaIntroduction Data regarding patients with a previous medical record of immunosuppression treatment who have undergone transcatheter aortic valve implantation (TAVI) are limited and extremely inconclusive. Available studies are mostly short term observations; thus there is a lack of evidence on efficacy and safety of TAVI in this specific group of patients. Aim To compare the in-hospital and long-term outcomes between patients...
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Longitudinal drug synergy assessment using convolutional neural network image-decoding of glioblastoma single-spheroid cultures
PublikacjaAbstract Background In recent years, drug combinations have become increasingly popular to improve therapeutic outcomes in various diseases, including difficult to cure cancers such as the brain cancer glioblastoma. Assessing the interaction between drugs over time is critical for predicting drug combination effectiveness and minimizing the risk of therapy resistance. However, as viability readouts of drug combination experiments...
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Grafo-mania, czyli rzecz o grafach i algorytmach. Gry chromatyczne na grafach.
PublikacjaW minieseju analizujemy grę 2-osobową, polegającą na tym, że Alicja i Bogdan współdziałają by pomalować mapę narysowaną na płaszczyźnie.
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Generalization of Phylogenetic Matching Metrics with Experimental Tests of Practical Advantages
PublikacjaThe ability to quantify a dissimilarity of different phylogenetic trees is required in various types of phylogenetic studies, for example, such metrics are used to assess the quality of phylogeny construction methods and to define optimization criteria in supertree building algorithms. In this article, starting from the already described concept of matching metrics, we define three new metrics for rooted phylogenetic trees. One...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublikacjaOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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Entangled rendezvous: a possible application of Bell non-locality for mobile agents on networks
PublikacjaRendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, are striving to meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern and future applications. Quantum non-locality, like Bell inequality violation, has shown that in many...
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Edge coloring of graphs of signed class 1 and 2
PublikacjaRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Edge and Pair Queries-Random Graphs and Complexity
PublikacjaWe investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters is NP-hard for bounded degree graphs.
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Complexity Issues on of Secondary Domination Number
PublikacjaIn this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...
Rok 2022
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Weighted 2-sections and hypergraph reconstruction
PublikacjaIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
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Significance of Dermoscopy in Association with Clinical Features in Differentiation of Basal Cell Carcinoma and Benign Trichoblastic Tumours
PublikacjaBackground: Although basal cell carcinoma (BCC) can, in the majority of cases, be diagnosed based on clinical and dermoscopic assessment, a potential overlap with benign adnexal skin tumours seems to exist, including trichoblastic tumours (TT). Methods: Retrospective analysis of clinical and dermoscopic features of benign TT and BCC cases was performed to develop a diagnostic algorithm with a potential utility in clinical practice....
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines: Complexity and Algorithms
PublikacjaIn this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality:...
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Scheduling on Uniform and Unrelated Machines with Bipartite Incompatibility Graphs
PublikacjaThe problem of scheduling jobs on parallel machines under an incompatibility relation is considered in this paper. In this model, a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same machine. We consider job scheduling under the incompatibility relation modeled by a bipartite graph, under the makespan optimality criterion, on uniform and unrelated machines. Unrelated machines...
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Quantum security and theory of decoherence
PublikacjaWe sketch a relation between two crucial, yet independent, fields in quantum information research, viz. quantum decoherence and quantum cryptography. We investigate here how the standard cryptographic assumption of shielded laboratory, stating that data generated by a secure quantum device remain private unless explicitly published, is disturbed by the einselection mechanism of quantum Darwinism explaining the measurement process...
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. Alicja i Bogdan w naleśnikarni
PublikacjaNiniejszym esejem inaugurujemy , po kilkuletniej przerwie, nową serię zagadek algorytmicznych.Pierwszy odcinek nosi nazwę Alicja i Bogdan w naleśnikarni.
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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublikacjaDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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Paired domination versus domination and packing number in graphs
PublikacjaGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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On zero-error codes produced by greedy algorithms
PublikacjaWe present two greedy algorithms that determine zero-error codes and lower bounds on the zero-error capacity. These algorithms have many advantages, e.g., they do not store a whole product graph in a computer memory and they use the so-called distributions in all dimensions to get better approximations of the zero-error capacity. We also show an additional application of our algorithms.
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Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution
PublikacjaWe study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast...
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Infinite chromatic games
PublikacjaIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Hybrid no-signaling-quantum correlations
PublikacjaFundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term HNSQ in the...
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Grafo-mania, czyli rzecz o grafach i algorytmach. Szybkie mnożenie macierzy
PublikacjaMiniesej zawiera komentarz na temat zastosowania sztucznej inteligencji do problemu mnożenia macierzy.
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Grafo-mania, czyli rzecz o grafach i algorytmach. Problem 8 hetmanów
PublikacjaW eseju spojrzano na problem 8 hetmanów na szachownicy z punktu widzenia teorii grafów
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Grafo-mania, czyli rzecz o grafach i algorytmach. Liczby Ramseya
PublikacjaZdefiniowano liczby Ramseya i wskazano na trudności obliczeniowe ich wyznaczania już przy niewielkich wartościach takich liczb.
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Grafo-ania, czyli rzecz o grafach i algorytmach. Drzewa Steinera
PublikacjaProblem: na płaszczyźnie leżą 3 punkty. Znajdź czwarty, taki że jego sumaryczna odległość od 3 pozostałych jest minimalna, Pokazujemy jak rozwiązać ten problem i jego uogólnienie.
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Global defensive secure structures
PublikacjaLet S ⊂ V (G) for a given simple non-empty graph G. We define for any nonempty subset X of S the predicate SECG,S(X) = true iff |NG[X]∩S| ≥ |NG[X]\S|. Let H be a non-empty family of graphs such that for each vertex v ∈ V (G) there is a subgraph H of G containing v and isomorphic to a member of H. We introduce the concept of H-alliance extending the concept of global defensive secure structures. By an H-alliance in a graph G we...
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Efficacy of intralesional bleomycin in treatment resistant viral warts
PublikacjaIntroduction Optimal management of treatment-refractory viral warts caused by human papillomavirus is unknown. One of the treatment methods is intralesional bleomycin solution. Objective To determine risk factors for resistant viral warts (not responding to conventional treatments for ≥ 6 months), to determine the effectiveness and safety of intralesional bleomycin in a group of patients with viral warts resistant to conventional...
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Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
PublikacjaSmart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....
Rok 2021
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User experience and user interface (UX/UI) design of Greencoin mobile application.
PublikacjaThe aim of the Greencoin mobile application is to encourage its users to change their behavior and to act pro-ecologically. The pilot version of the application will operate within the city of Gdańsk. To keep the app’s user base as large as possible, the graphical user interface should be attractive to the broadest possible audience, and the application itself should be easy and fun to use. This work is a continuation of studies...
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Transcriptomic landscape of blood platelets in healthy donors
PublikacjaBlood platelet RNA-sequencing is increasingly used among the scientific community. Aberrant platelet transcriptome is common in cancer or cardiovascular disease, but reference data on platelet RNA content in healthy individuals are scarce and merit complex investigation. We sought to explore the dynamics of platelet transcriptome. Datasets from 204 healthy donors were used for the analysis of splice variants, particularly with...
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Transcriptomic landscape of blood platelets in healthy donors
PublikacjaBACKGROUND Blood platelet RNA-sequencing is increasingly used among the scientific community. Aberrant platelet transcriptome is common in cancer or cardiovascular disease, but reference data on platelet RNA content in healthy individuals are scarce and merit complex investigation. METHODS We sought to explore the dynamics of platelet transcriptome. Datasets from 204 healthy donors were used for the analysis of splice variants,...
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Towards Cancer Patients Classification Using Liquid Biopsy
PublikacjaLiquid biopsy is a useful, minimally invasive diagnostic and monitoring tool for cancer disease. Yet, developing accurate methods, given the potentially large number of input features, and usually small datasets size remains very challenging. Recently, a novel feature parameterization based on the RNA-sequenced platelet data which uses the biological knowledge from the Kyoto Encyclopedia of Genes and Genomes, combined with a classifier...
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Total Completion Time Minimization for Scheduling with Incompatibility Cliques
PublikacjaThis paper considers parallel machine scheduling with incompatibilities between jobs. The jobs form a graph equivalent to a collection of disjoint cliques. No two jobs in a clique are allowed to be assigned to the same machine. Scheduling with incompatibilities between jobs represents a well-established line of research in scheduling theory and the case of disjoint cliques has received increasing attention in recent...
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Total chromatic sum for trees
PublikacjaThe total chromatic sum of a graph is the minimum sum of colors (natural numbers) taken over all proper colorings of vertices and edges of a graph. We provide infinite families of trees for which the minimum number of colors to achieve the total chromatic sum is equal to the total chromatic number. We construct infinite families of trees for which these numbers are not equal, disproving the conjecture from 2012.
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T-colorings, divisibility and circular chromatic number
PublikacjaLet T be a T-set, i.e., a finite set of nonnegative integers satisfying 0 ∈ T, and G be a graph. In the paper we study relations between the T-edge spans espT (G) and espd⊙T (G), where d is a positive integer and d ⊙ T = {0 ≤ t ≤ d (max T + 1): d |t ⇒ t/d ∈ T} . We show that espd⊙T (G) = d espT (G) − r, where r, 0 ≤ r ≤ d − 1, is an integer that depends on T and G. Next we focus on the case T = {0} and show that espd⊙{0} (G) =...