Ambiguity and Communication

The ambiguity of a nondeterministic finite automaton (NFA) N for input size n is the maximal number of accepting computations of N for an input of size n. For all k, r 2 N we construct languages Lr,k which can be recognized by NFA's with size k poly(r) and ambiguity O(nk), but Lr,k has only NFA's with exponential size, if ambiguity o(nk) is required. In particular, a hierarchy for polynomial ambiguity is obtained, solving a long standing open problem (Ravikumar and Ibarra, 1989, Leung, 1998)

Types and functions of international economic relations and international business

Проведено аналіз сучасних видів і методів здійснення міжнародної економічної діяльності, що дозволить уточнити та поглибити сутність міжнародного підприємництва і скласти класифікацію функцій його здійснення. Розглянуто останні дослідження провідних науковців щодо визначення поняття міжнародного підприємництва, запропоновано визначення міжнародного підприємництва, як сукупність певних угод, за допомогою яких переміщують товари, послуги та ресурси через державні кордони на міжнародному рівні. Встановлено, що кожне міжнародне підприємство, яке приймає участь у міжнародній підприємницький діяльності, відноситься до певної правової форми і діє відповідно до норм цивільного і торгового права своєї держави.The analysis of modern types and methods of international economic activity is carried out. This allowed to clarify and deepen the essence of international entrepreneurship, made it possible to classify the functions of implementing international entrepreneurship. The last researches of leading scientists on definition of the concept of international business are considered. The definition of international ent repreneurship as a set of definite agreements with which to move goods, services and resources across national borders at the international level is proposed. It has been established that every international enterprise that participates in international business activities is part of a certain legal form and acts in accordance with the norms of civil and commercial law of its state

The Parameterized Approximability of TSP with Deadlines

Modern algorithm theory includes numerous techniques to attack hard problems, such as approximation algorithms on the one hand and parameterized complexity on the other hand. However, it is still uncommon to use these two techniques simultaneously, which is unfortunate, as there are natural problems that cannot be solved using either technique alone, but rather well if we combine them. The problem to be studied here is not only natural, but also practical: Consider TSP, generalized as follows. We impose deadlines on some of the vertices, effectively constraining them to be visited prior to a given point of time. The resulting problem DlTSP (a special case of the well-known TSP with time windows) inherits its hardness from classical TSP, which is both well known from practice and renowned to be one of the hardest problems with respect to approximability: Within polynomial time, not even a polynomial approximation ratio (let alone a constant one) can be achieved (unless P = NP). We will show that DlTSP is even harder than classical TSP in the following sense. Classical TSP, despite its hardness, admits good approximation algorithms if restricted to metric (or near-metric) inputs. Not so DlTSP (and hence, neither TSP with time windows): We will prove that even for metric inputs, no constant approximation ratio can ever be achieved (unless P = NP). This is where parameterization becomes crucial: By combining methods from the field of approximation algorithms with ideas from the theory of parameterized complexity, we apply the concept of parameterized approximation. Thereby, we obtain a 2.5-approximation algorithm for DlTSP with a running time of k! · poly(|G|), where k denotes the number of deadlines. Furthermore, we prove that there is no fpt-algorithm with an approximation guarantee of 2-ε for any ε > 0, unless P = NP. Finally, we show that, unlike TSP, DlTSP becomes much harder when relaxing the triangle inequality. More precisely, for an arbitrary small violation of the triangle inequality, DlTSP does not admit an fpt-algorithm with approximation guarantee ((1-ε)/2)|V| for any ε > 0, unless P = N

Online graph coloring against a randomized adversary

Electronic version of an article published as Online graph coloring against a randomized adversary. "International journal of foundations of computer science", 1 Juny 2018, vol. 29, núm. 4, p. 551-569. DOI:10.1142/S0129054118410058 © 2018 copyright World Scientific Publishing Company. https://www.worldscientific.com/doi/abs/10.1142/S0129054118410058We consider an online model where an adversary constructs a set of 2s instances S instead of one single instance. The algorithm knows S and the adversary will choose one instance from S at random to present to the algorithm. We further focus on adversaries that construct sets of k-chromatic instances. In this setting, we provide upper and lower bounds on the competitive ratio for the online graph coloring problem as a function of the parameters in this model. Both bounds are linear in s and matching upper and lower bound are given for a specific set of algorithms that we call “minimalistic online algorithms”.Peer ReviewedPostprint (author's final draft

On the Approximability and Hardness of Minimum Topic Connected Overlay and Its Special Instances

In the context of designing a scalable overlay network to support decentralized topic-based pub/sub communication, the Minimum Topic-Connected Overlay problem (Min-TCO in short) has been investigated: Given a set of t topics and a collection of n users together with the lists of topics they are interested in, the aim is to connect these users to a network by a minimum number of edges such that every graph induced by users interested in a common topic is connected. It is known that Min-TCO is NP-hard and approximable within O(log t) in polynomial time. In this paper, we further investigate the problem and some of its special instances. We give various hardness results for instances where the number of topics in which an user is interested in is bounded by a constant, and also for the instances where the number of users interested in a common topic is constant. For the latter case, we present a first constant approximation algorithm. We also present some polynomial-time algorithms for very restricted instances of Min-TCO.Comment: 20 page

On the Approximability of TSP on Local Modifications of Optimally Solved Instances

Given an instance of TSP together with an optimal solution, we consider the scenario in which this instance is modified locally, where a local modification consists in the alteration of the weight of a single edge. More generally, for a problem U, let LM-U (local-modification-U) denote the same problem as U, but in LM-U, we are also given an optimal solution to an instance from which the input instance can be derived by a local modification. The question is how to exploit this additional knowledge, i.e., how to devise better algorithms for LM-U than for U. Note that this need not be possible in all cases: The general problem of LM-TSP is as hard as TSP itself, i.e., unless P=NP, there is no polynomial-time p(n)-approximation algorithm for LM-TSP for any polynomial p. Moreover, LM-TSP where inputs must satisfy the β-triangle inequality (LM-Δβ-TSP) remains NP-hard for all β>½. However, for LM-Δ-TSP (i.e., metric LM-TSP), we will present an efficient 1.4-approximation algorithm. In other words, the additional information enables us to do better than if we simply used Christofides' algorithm for the modified input. Similarly, for all 1<β<3.34899, we achieve a better approximation ratio for LM-Δ-TSP than for Δβ-TSP. For ½≤β<1, we show how to obtain an approximation ratio arbitrarily close to 1, for sufficiently large input graphs

Lapses in Responsiveness: Characteristics and Detection from the EEG

Performance lapses in occupations where public safety is paramount can have disastrous consequences, resulting in accidents with multiple fatalities. Drowsy individuals performing an active task, like driving, often cycle rapidly between periods of wake and sleep, as exhibited by cyclical variation in both EEG power spectra and task performance measures. The aim of this project was to identify reliable physiological cues indicative of lapses, related to behavioural microsleep episodes, from the EEG, which could in turn be used to develop a real-time lapse detection (or better still, prediction) system. Additionally, the project also sought to achieve an increased understanding of the characteristics of lapses in responsiveness in normal subjects. A study was conducted to determine EEG and/or EOG cues (if any) that expert raters use to detect lapses that occur during a psychomotor vigilance task (PVT), with the subsequent goal of using these cues to design an automated system. A previously-collected dataset comprising physiological and performance data of 10 air traffic controllers (ATCs) was used. Analysis showed that the experts were unable to detect the vast majority of lapses based on EEG and EOG cues. This suggested that, unlike automated sleep staging, an automated lapse detection system needed to identify features not generally visible in the EEG. Limitations in the ATC dataset led to a study where more comprehensive physiological and performance data were collected from normal subjects. Fifteen non-sleep-deprived male volunteers aged 18-36 years were recruited. All performed a 1-D continuous pursuit visuomotor tracking task for 1 hour during each of two sessions that occurred between 1 and 7 weeks apart. A video camera was used to record head and facial expressions of the subject. EEG was recorded from electrodes at 16 scalp locations according to the 10-20 system at 256 Hz. Vertical and horizontal EOG was also recorded. All experimental sessions were held between 12:30 and 17:00 hours. Subjects were asked to refrain from consuming stimulants or depressants, for 4 h prior to each session. Rate and duration were estimated for lapses identified by a tracking flat spot and/or video sleep. Fourteen of the 15 subjects had one or more lapses, with an overall rate of 39.3 ± 12.9 lapses per hour (mean ± SE) and a lapse duration of 3.4 ± 0.5 s. The study also showed that lapsing and tracking error increased during the first 30 or so min of a 1-h session, then decreased during the remaining time, despite the absence of external temporal cues. EEG spectral power was found to be higher during lapses in the delta, theta, and alpha bands, and lower in the beta, gamma, and higher bands, but correlations between changes in EEG power and lapses were low. Thus, complete lapses in responsiveness are a frequent phenomenon in normal subjects - even when not sleep-deprived - undertaking an extended, monotonous, continuous visuomotor task. This is the first study to investigate and report on the characteristics of complete lapses of responsiveness during a continuous tracking task in non-sleep-deprived subjects. The extent to which non-sleep-deprived subjects experience complete lapses in responsiveness during normal working hours was unexpected. Such findings will be of major concern to individuals and companies in various transport sectors. Models based on EEG power spectral features, such as power in the traditional bands and ratios between bands, were developed to detect the change of brain state during behavioural microsleeps. Several other techniques including spectral coherence and asymmetry, fractal dimension, approximate entropy, and Lempel-Ziv (LZ) complexity were also used to form detection models. Following the removal of eye blink artifacts from the EEG, the signal was transformed into z-scores relative to the baseline of the signal. An epoch length of 2 s and an overlap of 1 s (50%) between successive epochs were used for all signal processing algorithms. Principal component analysis was used to reduce redundancy in the features extracted from the 16 EEG derivations. Linear discriminant analysis was used to form individual classification models capable of detecting lapses using data from each subject. The overall detection model was formed by combining the outputs of the individual models using stacked generalization with constrained least-squares fitting used to determine the optimal meta-learner weights of the stacked system. The performance of the lapse detector was measured both in terms of its ability to detect lapse state (in 1-s epochs) and lapse events. Best performance in lapse state detection was achieved using the detector based on spectral power (SP) features (mean correlation of φ = 0.39 ± 0.06). Lapse event detection performance using SP features was moderate at best (sensitivity = 73.5%, selectivity = 25.5%). LZ complexity feature-based detector showed the highest performance (φ = 0.28 ± 0.06) out of the 3 non-linear feature-based detectors. The SP+LZ feature-based model had no improvement in performance over the detector based on SP alone, suggesting that LZ features contributed no additional information. Alpha power contributed the most to the overall SP-based detection model. Analysis showed that the lapse detection model was detecting phasic, rather than tonic, changes in the level of drowsiness. The performance of these EEG-based lapse detection systems is modest. Further research is needed to develop more sensitive methods to extract cues from the EEG leading to devices capable of detecting and/or predicting lapses

Communications in cellular automata

The goal of this paper is to show why the framework of communication complexity seems suitable for the study of cellular automata. Researchers have tackled different algorithmic problems ranging from the complexity of predicting to the decidability of different dynamical properties of cellular automata. But the difference here is that we look for communication protocols arising in the dynamics itself. Our work is guided by the following idea: if we are able to give a protocol describing a cellular automaton, then we can understand its behavior