Systolic freedom of loop space

Given a pair of integers m and n such that 1 < m < n, we show that every n-dimensional manifold admits metrics of arbitrarily small total volume, and possessing the following property: every m-dimensional submanifold of less than unit m-volume is necessarily torsion in homology. This result is different from the case of a pair of complementary dimensions, for which a direct geometric construction works and gives the analogous theorem in complete generality. In the present paper, we use Sullivan's telescope model for the rationalisation of a space to observe systolic freedom.Comment: This is an updated version of the published pape

Challenges of Internet of Things and Big Data Integration

The Internet of Things anticipates the conjunction of physical gadgets to the In-ternet and their access to wireless sensor data which makes it expedient to restrain the physical world. Big Data convergence has put multifarious new opportunities ahead of business ventures to get into a new market or enhance their operations in the current market. considering the existing techniques and technologies, it is probably safe to say that the best solution is to use big data tools to provide an analytical solution to the Internet of Things. Based on the current technology deployment and adoption trends, it is envisioned that the Internet of Things is the technology of the future, while to-day's real-world devices can provide real and valuable analytics, and people in the real world use many IoT devices. Despite all the advertisements that companies offer in connection with the Internet of Things, you as a liable consumer, have the right to be suspicious about IoT advertise-ments. The primary question is: What is the promise of the Internet of things con-cerning reality and what are the prospects for the future.Comment: Proceedings of the International Conference on International Conference on Emerging Technologies in Computing 2018 (iCETiC '18), 23rd -24th August, 2018, at London Metropolitan University, London, UK, Published by Springer-Verla

Around the tangent cone theorem

A cornerstone of the theory of cohomology jump loci is the Tangent Cone theorem, which relates the behavior around the origin of the characteristic and resonance varieties of a space. We revisit this theorem, in both the algebraic setting provided by cdga models, and in the topological setting provided by fundamental groups and cohomology rings. The general theory is illustrated with several classes of examples from geometry and topology: smooth quasi-projective varieties, complex hyperplane arrangements and their Milnor fibers, configuration spaces, and elliptic arrangements.Comment: 39 pages; to appear in the proceedings of the Configurations Spaces Conference (Cortona 2014), Springer INdAM serie

Decision Problems in Information Theory

Constraints on entropies are considered to be the laws of information theory. Even though the pursuit of their discovery has been a central theme of research in information theory, the algorithmic aspects of constraints on entropies remain largely unexplored. Here, we initiate an investigation of decision problems about constraints on entropies by placing several different such problems into levels of the arithmetical hierarchy. We establish the following results on checking the validity over all almost-entropic functions: first, validity of a Boolean information constraint arising from a monotone Boolean formula is co-recursively enumerable; second, validity of "tight" conditional information constraints is in ???. Furthermore, under some restrictions, validity of conditional information constraints "with slack" is in ???, and validity of information inequality constraints involving max is Turing equivalent to validity of information inequality constraints (with no max involved). We also prove that the classical implication problem for conditional independence statements is co-recursively enumerable

Design of a decision support system for improving air quality assessment

Establishing a system that allows the transition from environmental and traffic monitoring to environmental management at the personal level has become a necessity. Such a system will improve the life quality, reduce health costs and increase the support of vulnerable groups (i.e., the elderly, children). ESTABLISH project aims to advance an innovative platform which allows converting environmental (sensor) data into actionable information for users to provide a healthier and safer environment thereby improving the quality of life. Smart adaptive services providing real-time feedback tailored to specific user and application needs will be developed by combining networked sensors and other data sources with adaptive models. This paper will present the on-going research within the ESTABLISH project related to the development of a decision support component which assesses the air quality. Based on real-time monitoring and quantification methods, and certain types of notifications for risk groups and general populations, the proposed system links pollutant concentrations to individual health risks. The proposed decision support for air quality assessment is structured on two components. The first component is represented by the comparison with the limit values provided by the legislation, and the second is the forecast of near-real-time air pollution episodes (based on trigger values). Thus, for each pollutant considered (PM2.5, PM10, SO2, NO2, O3, and CO) the frequency of pollutants concentrations measurement, the averaging periods according to the legislation, the averaging period and the limit values used for the notification component were established

Quantum communication networks with optical vortices

Quantum communications bring a paradigm change in internet security by using quantum resources to establish secure keys between parties. Present-day quantum communications networks are mainly point-to-point and use trusted nodes and key management systems to relay the keys. Future quantum networks, including the quantum internet, will have complex topologies in which groups of users are connected and communicate with each-other. Here we investigate several architectures for quantum communication networks. We show that photonic orbital angular momentum (OAM) can be used to route quantum information between different nodes. Starting from a simple, point-to-point network, we will gradually develop more complex architectures: point-to-multipoint, fully-connected and entanglement-distribution networks. As a particularly important result, we show that an $n$-node, fully-connected network can be constructed with a single OAM sorter and $n-1$ OAM values. Our results pave the way to construct complex quantum communication networks with minimal resources.Comment: 10 pages, 9 figure

Chamber basis of the Orlik-Solomon algebra and Aomoto complex

We introduce a basis of the Orlik-Solomon algebra labeled by chambers, so called chamber basis. We consider structure constants of the Orlik-Solomon algebra with respect to the chamber basis and prove that these structure constants recover D. Cohen's minimal complex from the Aomoto complex.Comment: 16 page